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{"sheet":"GUIDE_SOLUTIONS","index":0,"n_rows":92,"n_cols":3,"rows_kept":92,"cut":false,"hidden":false,"merged":[]}
[null,"                                                            GUIDE TO REAL OPTION VALUE SOLUTIONS"]
[]
["#1 Session","CHAPTER 2","INTRODUCTION TO BASICS"]
[null,"EXERCISE 2.1","Put Binomial, No Income"]
[null,"EXERCISE 2.2","Call Binomial, No Income"]
[null,"EXERCISE 2.3",{"$f":"C5","v":"Call Binomial, No Income"}]
[null,"PROBLEM 2.4","Black-Scholes Deferral Option"]
[null,"PROBLEM 2.5",{"$f":"C7","v":"Black-Scholes Deferral Option"}]
[null,"PROBLEM 2.6","Margrabe Exchange"]
["#2 Session","CHAPTER 3","STRATEGIES"]
[null,"EXERCISE 3.1","Write Call Strategy: \"Texas Marketing Hedge\""]
[null,"EXERCISE 3.2","Buy Protective Put Strategy"]
[null,"EXERCISE 3.3","Write Extreme Call Strategy: \"Wildcat Texas Hedge\""]
[null,"PROBLEM 3.4","Buy Protective Call Option for Asset User"]
[null,"PROBLEM 3.5","Buy Put funded by Write Call for Leveraged Assets"]
[null,"PROBLEM 3.6","Maria's Unusual Salary Insurance Arrangement"]
["#3 Session","CHAPTER 4","AMERICAL PERPETUAL"]
[null,"EXERCISE 4.1","Real American Perpetual Call Option"]
[null,"EXERCISE 4.2",{"$f":"C18","v":"Real American Perpetual Call Option"}]
[null,"EXERCISE 4.3",{"$f":"C19","v":"Real American Perpetual Call Option"}]
[null,"PROBLEM 4.4","Perpetual American Option PDE"]
[null,"PROBLEM 4.5","Hedging Writing a Real Option"]
[null,"PROBLEM 4.6","Hedging a Long Position in a Real Option"]
["#  Session","CHAPTER 5","AMERICAN EXCHANGE"]
[null,"EXERCISE 5.1","Perpetual American Exchange Real Option"]
[null,"EXERCISE 5.2","Volatile Perpetual American Exchange Real Option"]
[null,"EXERCISE 5.3","Perpetual American QUANTO Exchange Real Option"]
[null,"PROBLEM 5.4",{"$f":"C25","v":"Perpetual American Exchange Real Option"}]
[null,"PROBLEM 5.5",{"$f":"C28","v":"Perpetual American Exchange Real Option"}]
[null,"PROBLEM 5.6",{"$f":"C26","v":"Volatile Perpetual American Exchange Real Option"}]
["#  Session","CHAPTER 6","AMERICAN FINITE"]
[null,"EXERCISE 6.1","European Real Option"]
[null,"EXERCISE 6.2","European and Finite American Real Option"]
[null,"EXERCISE 6.3","American Finite Call Approximation (BAW)"]
[null,"PROBLEM 6.4","CEA American Put Option Approximation"]
[null,"PROBLEM 6.5",{"$f":"C35","v":"CEA American Put Option Approximation"}]
[null,"PROBLEM 6.6","CEAM American Put Option Approximation"]
["#6  Session","CHAPTER 7","SEQUENTIAL"]
[null,"EXERCISE 7.1","Geske European Compound Call Option"]
[null,"EXERCISE 7.2","European Compound Exchange Option"]
[null,"EXERCISE 7.3",{"$f":"C39","v":"Geske European Compound Call Option"}]
[null,"PROBLEM 7.4","American Finite Sequential Exchange Option"]
[null,"PROBLEM 7.5","Three Stage Sequential Perpetual American Call Option"]
[null,"PROBLEM 7.6","Three Stage Sequential Perpetual American Exchange Option"]
["#4 Session","CHAPTER 8","SCALE"]
[null,"EXERCISE 8.1","Marshallian & Simple Option Enter Triggers"]
[null,"EXERCISE 8.2","Marshallian & Simple Option Enter Options"]
[null,"EXERCISE 8.3",{"$f":"C46","v":"Marshallian & Simple Option Enter Triggers"}]
[null,"PROBLEM 8.4","Entry-Exit Stochastic Model"]
[null,"PROBLEM 8.5",{"$f":"C49","v":"Entry-Exit Stochastic Model"}]
[null,"PROBLEM 8.6","Invest, Revert, Contract & Abandonment Model"]
["#9 Session","CHAPTER 9","COMPETITION"]
[null,"EXERCISE 9.1","Duopoly Competition with First Mover Advantage: Simple"]
[null,"PROBLEM 9.2","Rivalry Under P & Q Uncertainty: Simple"]
[null,"PROBLEM 9.3","Rivalry Under R & K Uncertainty: Simple"]
[null,"PROBLEM 9.4","Duopoly Competition with First Mover Advantage"]
[null,"PROBLEM 9.5","Rivalry Under P & Q Uncertainty"]
[null,"PROBLEM 9.6","Rivalry Under R & K Uncertainty"]
["#8 Session","CHAPTER 10","REAL DEBT STRATEGY"]
[null,"EXERCISE 10.1","Equity, Debt Values with Endogenous Bankruptcy"]
[null,"EXERCISE 10.2",{"$f":"C60","v":"Equity, Debt Values with Endogenous Bankruptcy"}]
[null,"EXERCISE 10.3",{"$f":"C60","v":"Equity, Debt Values with Endogenous Bankruptcy"}]
[null,"PROBLEM 10.4","Mortgage Value with Taxes"]
[null,"PROBLEM 10.5","Lender Value"]
[null,"PROBLEM 10.6","Fair Arrangements"]
["# Session","CHAPTER 11","RENEWAL OPTIONS"]
[null,"EXERCISE 11.1","NPV Single Renewal"]
[null,"EXERCISE 11.2","Renewal Stochastic Price"]
[null,"EXERCISE 11.3","Renewal Stochastic Price"]
[null,"PROBLEM 11.4","Renewal Stochastic Price & Cost"]
[null,"PROBLEM 11.5","Renewal Stochastic Price"]
[null,"PROBLEM 11.6","Renewal Stochastic Price & Cost"]
["#5 Session","CHAPTER 12","SWITCHING OPTIONS"]
[null,"EXERCISE 12.1","Single Output Switch"]
[null,"EXERCISE 12.1A","Single Output Switch"]
[null,"EXERCISE 12.2","Single In/Out Switch"]
[null,"EXERCISE 12.3","Single Input Switch"]
[null,"PROBLEM 12.4","Multiple Output Switching"]
[null,"PROBLEM 12.4A","Multiple Output Switching"]
[null,"PROBLEM 12.5","Multiple In/Out Switching"]
[null,"PROBLEM 12.6","Multiple Input Switching"]
["# Session","CHAPTER 13","REVENUE OPTIONS"]
[null,"EXERCISE 13.1","Single Output Switching"]
[null,"EXERCISE 13.2","Optimal Discount Fare Booking"]
[null,"EXERCISE 13.3","Overbooking"]
[null,"PROBLEM 13.4","Multiple Output Switching"]
[null,"PROBLEM 13.5","Optimal Discount Fare Booking"]
[null,"PROBLEM 13.6","Overbooking"]
["#7 Session","CHAPTER 14","INCENTIVE OPTIONS"]
[null,"EXERCISE 14.1"," Proportional Subsidy"]
[null,"PROBLEM 14.4"," Proportional Subsidy"]
["REAL OPTION VALUE EXCEL 3 16 SOLUTIONS"]

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["PUT BINOMIAL MODEL"]
["EXERCISE 2.1"]
["s",0.3]
["INTEREST RATE",0.05]
["TIME",1]
["EXERCISE=K",42]
["u",{"$f":"EXP(B3*SQRT(B5))","v":1.3498588075760032},null,"B7=","EXP(B3*SQRT(B5))"]
["d",{"$f":"1/B7","v":0.74081822068171788},null,"B8=","1/B7"]
["a",{"$f":"EXP(B4*B5)","v":1.0512710963760241},null,"B9=","EXP(B4*B5)"]
["p",{"$f":"(B9-B8)/(B7-B8)","v":0.50974086518177042},null,"B10=","(B9-B8)/(B7-B8)"]
["SQUARE FEET",100000,null,null," "]
[" "," ",null,null," "]
["PERIOD 0","PERIOD 1",null,null," "]
[]
[" "]
["RENT/SQ FT"]
[null,{"$f":"$B$7*$A$18","v":56.694069918192135},null,"B17=","$B$7*$A$18"]
[42]
[null,{"$f":"$B$8*$A$18","v":31.114365268632152},null,"B19=","$B$8*$A$18"]
[]
["PUT OPTION VALUE/SQ FT"]
[null,{"$f":"IF((B17<$B$6),(B17-$B$6),0)","v":0},null,"B22=","IF((B17<$B$6),(B17-$B$6),0)"]
[{"$f":"EXP(-B4*B5)*(B22*$B$10+(1-$B$10)*B24)","v":5.076503942460513},null,null,"A23=","EXP(-B4*B5)*(B22*$B$10+(1-$B$10)*B24)"]
[null,{"$f":"IF((B19<$B$6),-(B19-$B$6),0)","v":10.885634731367848},null,"B24=","IF((B19<$B$6),-(B19-$B$6),0)"]
[]
["TOTAL PUT OPTION VALUE"]
[{"$f":"B11*A23","v":507650.39424605132},null,null,"A27=","B11*A23"]

{"sheet":"Exercise 2.2","index":2,"n_rows":34,"n_cols":4,"rows_kept":34,"cut":false,"hidden":false,"merged":[]}
["One-Step Binomial Call "]
["Exercise 2.2"]
["VOLATILITY",0.3]
["RATE",0.05]
["TIME",1]
["up",{"$f":"EXP(B3*SQRT(B5))","v":1.3498588075760032}]
["down",{"$f":"1/B6","v":0.74081822068171788}]
["probability",{"$f":"(EXP(B4*B5)-B7)/(B6-B7)","v":0.50974086518177042}]
[]
[{"$f":"A6","v":"up"},"EXP(B3*SQRT(B5))"]
[{"$f":"A7","v":"down"},"1/B6"]
[{"$f":"A8","v":"probability"},"(EXP(B4*B5)-B7)/(B6-B7)"]
[]
[]
["Time",0,1]
[null," "]
["Expected",null,{"$f":"B18*B6","v":94490.116530320229},"u"]
["Earnings",70000]
[null,null,{"$f":"B18*B7","v":51857.275447720254},"d"]
[]
[null,null,{"$f":"B22","v":75000},"u"]
["Cost",75000]
[null,null,{"$f":"B22","v":75000},"d"]
[]
[null,null,{"$f":"MAX((C17-C21),0)","v":19490.116530320229},"u"]
["Call Value",{"$f":"EXP(-B4*B5)*(C25*B8+(1-B8)*C27)","v":9450.3776398941245}]
[null,null,{"$f":"MAX((C19-C23),0)","v":0},"d"]
["C25=",null,"MAX((C17-C21),0)"]
["C27=",null,"MAX((C19-C23),0)"]
["B26=","                                                EXP(-B4*B5)*(C25*B8+(1-B8)*C27)"]
[]
[]
[" ",null," "]
[" "]

{"sheet":"Exercise 2.3","index":3,"n_rows":32,"n_cols":4,"rows_kept":32,"cut":false,"hidden":false,"merged":[]}
["One-Step Binomial Call "]
["Exercise 2.3"]
["VOLATILITY",0.4]
["RATE",0.1]
["TIME",1]
["up",{"$f":"EXP(B3*SQRT(B5))","v":1.4918246976412703}]
["down",{"$f":"1/B6","v":0.67032004603563933}]
["probability",{"$f":"(EXP(B4*B5)-B7)/(B6-B7)","v":0.52933464368107019}]
[]
[{"$f":"A6","v":"up"},"EXP(B3*SQRT(B5))"]
[{"$f":"A7","v":"down"},"1/B6"]
[{"$f":"A8","v":"probability"},"(EXP(B4*B5)-B7)/(B6-B7)"]
[]
[]
["Time",0,1]
[null," "]
[" ",null,{"$f":"B18*B6","v":62.656637300933355},"u"]
["Rent",42]
[null,null,{"$f":"B18*B7","v":28.15344193349685},"d"]
[]
[null,null,{"$f":"B22","v":45},"u"]
["Exercise Price",45]
[null,null,{"$f":"B22","v":45},"d"]
[]
[null,null,{"$f":"MAX((C17-C21),0)","v":17.656637300933355},"u"]
["Call Value",{"$f":"EXP(-B4*B5)*(C25*B8+(1-B8)*C27)","v":8.4568546470345218}]
[null,null,{"$f":"MAX((C19-C23),0)","v":0},"d"]
["C25=",null,"MAX((C17-C21),0)"]
["C27=",null,"MAX((C19-C23),0)"]
["B26=","                                                EXP(-B4*B5)*(C25*B8+(1-B8)*C27)"]
["SF",100000]
["Total Call Option Value ",{"$f":"B26*B31","v":845685.46470345219}]

{"sheet":"Problem 2.4","index":4,"n_rows":20,"n_cols":3,"rows_kept":20,"cut":false,"hidden":false,"merged":[]}
["DEFERRAL OPTION"]
["Problem 2.4"]
[]
[" "," "]
["ASSET VALUE",500]
["INVESTMENT COST",450]
["RISKLESS RATE",0.04]
["DIVIDEND",0.04]
["TIME / YEARS",5]
["VOLATILITY",0.2]
["CALL PRICE",{"$f":"B5*B15*EXP(-B8*B9)-B6*B16*EXP(-B7*B9)","v":91.145664723121683},"B5*B15*EXP(-B8*B9)-B6*B16*EXP(-B7*B9)"]
[]
["d1",{"$f":"(LN(B5/B6)+(B7-B8+B10^2/2)*B9)/(B10*SQRT(B9))","v":0.45920007290530968},"(LN(B5/B6)+(B7-B8+B10^2/2)*B9)/(B10*SQRT(B9))"]
["d2",{"$f":"B13-B10*SQRT(B9)","v":1.1986477405351692E-2},"B13-B10*SQRT(B9)"]
["N(d1)",{"$f":"NORMSDIST(B13)","v":0.67695475088695689},"NORMSDIST(B13)"]
["N(d2)",{"$f":"NORMSDIST(B14)","v":0.50478179812514556},"NORMSDIST(B14)"]
[]
["SF",100000]
["TOTAL REAL CALL OPTION VALUE",{"$f":"B11*B18","v":9114566.4723121691}]
["INTRINSIC REAL CALL VALUE",{"$f":"(B5-B6)*B18","v":5000000}]

{"sheet":"Problem 2.5","index":5,"n_rows":19,"n_cols":3,"rows_kept":19,"cut":false,"hidden":false,"merged":[]}
["DEFERRAL OPTION"]
[" "]
["Problem 2.5"]
[" "," "]
["ASSET VALUE",1200]
["INVESTMENT COST",1338]
["RISKLESS RATE",0.05]
["DIVIDEND",0]
["TIME / YEARS",2]
["VOLATILITY",0.5]
["CALL PRICE",{"$f":"B5*B15*EXP(-B8*B9)-B6*B16*EXP(-B7*B9)","v":327.75501946852506},"B5*B15*EXP(-B8*B9)-B6*B16*EXP(-B7*B9)"]
[]
["d1",{"$f":"(LN(B5/B6)+(B7-B8+B10^2/2)*B9)/(B10*SQRT(B9))","v":0.34103137107986436},"(LN(B5/B6)+(B7-B8+B10^2/2)*B9)/(B10*SQRT(B9))"]
["d2",{"$f":"B13-B10*SQRT(B9)","v":-0.36607541010668321},"B13-B10*SQRT(B9)"]
["N(d1)",{"$f":"NORMSDIST(B13)","v":0.63346001742384161},"NORMSDIST(B13)"]
["N(d2)",{"$f":"NORMSDIST(B14)","v":0.35715440288093858},"NORMSDIST(B14)"]
[]
["Assumption"]
["This investment opportunity is a European, not an American, call option."]

{"sheet":"Problem 2.6","index":6,"n_rows":28,"n_cols":3,"rows_kept":28,"cut":false,"hidden":false,"merged":[]}
["MARGRABE EXCHANGE"]
["Problem 2.6"," "]
["RESIDENTIAL TENANTS",1600000]
["RETAIL TENANTS",1750000]
["TENANT SWITCHING TIME",1]
[" "," "]
["BENEFIT YIELD",0.04]
["COST YIELD",0.04]
["BENEFIT VOLATILITY",0.2]
["COST VOLATILITY",0.2]
["EXCHANGE VOLATILITY",{"$f":"SQRT(B9^2 + B10^2 -2*B13*B10*B9)","v":0.2},"SQRT(B9^2 + B10^2 -2*B13*B10*B9)"]
[]
["CORRELATION ",0.5," "]
["EXCHANGE CALL OPTION VALUE",{"$f":"B3*B18*EXP(-B7*B5)-B4*B19*EXP(-B8*B5)","v":68736.540599974978},"B3*B18*EXP(-B7*B5)-B4*B19*EXP(-B8*B5)"]
[]
["d1",{"$f":"(LN(B3/B4)+(B8-B7+(B11^2)/2)*B5)/(B11*SQRT(B5))","v":-0.34806079344843577},"(LN(B3/B4)+(B8-B7+(B11^2)/2)*B5)/(B11*SQRT(B5))"]
["d2",{"$f":"B16-B11*SQRT(B5)","v":-0.54806079344843583},"B16-B11*SQRT(B5)"]
["N(d1)",{"$f":"NORMSDIST(B16)","v":0.36389726390554034},"NORMSDIST(B16)"]
["N(d2)",{"$f":"NORMSDIST(B17)","v":0.2918250801209703},"NORMSDIST(B17)"]
[]
["Margrabe Exchange Real Option is worth",null,{"$f":"B14","v":68736.540599974978}]
["ASSUMES: volatilities and correlation are constant, this a European option,"]
["Several assumptions required."," "]
[" "," "]
["Investment in facility for retail tenants worth ",null,{"$f":"B4-C28","v":50000}]
["Option to switch tenants in one year worth",null,{"$f":"B14","v":68736.540599974978}]
["So value of modular facility worth",null,{"$f":"C25+C26","v":118736.54059997498}]
["Investment cost ",null,1700000]

{"sheet":"Exercise 3.1","index":7,"n_rows":33,"n_cols":14,"rows_kept":33,"cut":false,"hidden":false,"merged":[]}
["REAL OPTION PAYOFFS"]
["Exercise 3.1"]
["OWN ASSET-DEBT",{"$f":"B12-$B$6","v":-150},{"$f":"C12-$B$6","v":-125},-100,-75,-50,-25,0,25,50,75,100,125,150]
["WRITE REAL CALL INTRINSIC",{"$f":"IF(B3>0,-B3+$B$7,$B$7)","v":50},{"$f":"IF(C3>0,-C3+$B$7,$B$7)","v":50},50,50,50,50,50,25,0,-25,-50,-75,-100]
["STRATEGY RESULT",{"$f":"B3+B4","v":-100},{"$f":"C3+C4","v":-75},-50,-25,0,25,50,50,50,50,50,50,50]
["Debt, K",150," "," ",{"$f":"D6","v":" "}," "," "," "," "," "," "," "," "," "]
["Option cost, y",{"$f":"$B$33","v":50},"Assumed"]
[" Own asset subject to debt K, give investor an option to buy net asset at nil cost, for immediate payment of option premium of y."]
["  STRATEGY RESULT equals write real put on net asset value."]
["WRITE REAL CALL INTRINSIC","IF(B3>0,-B3+$B$7,$B$7)"]
["STRATEGY RESULT","B3+B4","MIN(B12-$B$6+$B$7,$B$7)"]
["ASSET VALUE",0,{"$f":"B12+25","v":25},{"$f":"C12+25","v":50},75,100,125,150,175,200,225,250,275,300]
[{"$f":"A5","v":"STRATEGY RESULT"},{"$f":"MIN(B12-$B$6+$B$7,$B$7)","v":-100},{"$f":"MIN(C12-$B$6+$B$7,$B$7)","v":-75},-50,-25,0,25,50,50,50,50,50,50,50]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["Option cost, y",50]

{"sheet":"Exercise 3.2","index":8,"n_rows":33,"n_cols":14,"rows_kept":33,"cut":false,"hidden":false,"merged":[]}
["REAL OPTION PAYOFFS"]
["Exercise 3.2",0,{"$f":"B2+25","v":25},{"$f":"C2+25","v":50},75,100,125,150,175,200,225,250,275,300]
["OWN ASSET-DEBT",{"$f":"0-$B$6","v":-150},{"$f":"B3+25","v":-125},-100,-75,-50,-25,0,25,50,75,100,125,150]
["BUY REAL PUT INTRINSIC",{"$f":"IF(B3<0,-B3-$B$7,-$B$7)","v":75},{"$f":"IF(C3<0,-C3-$B$7,-$B$7)","v":50},25,0,-25,-50,-75,-75,-75,-75,-75,-75,-75]
["STRATEGY RESULT",{"$f":"B4+B3","v":-75},{"$f":"C4+C3","v":-75},-75,-75,-75,-75,-75,-50,-25,0,25,50,75]
["Debt, K",150," "," ",{"$f":"D6","v":" "}," "," "," "," "," "," "," "," "," "]
["Option cost, y",{"$f":"B33","v":75}]
["   Own asset subject to debt K, buy right to sell asset at debt amount K, for immediate payment of option premium of y."]
["  STRATEGY RESULT equals buy real call on net asset value at nil exercise cost."]
[{"$f":"A4","v":"BUY REAL PUT INTRINSIC"},"IF(B3<0,-B3-$B$7,-$B$7)"]
[{"$f":"A5","v":"STRATEGY RESULT"},"B3+B4"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["Option cost, y",75]

{"sheet":"Exercise 3.3","index":9,"n_rows":57,"n_cols":16,"rows_kept":57,"cut":false,"hidden":false,"merged":[]}
["SALFORD TRIATHLON ARRANGEMENT"]
["Exercise 3.3"]
["POUNDS"]
["REVENUE",100]
["FIXED COSTS",50000]
["VARIABLE COSTS",50]
["TRIATHLETES",0,{"$f":"B7+200","v":200},{"$f":"C7+200","v":400},600,800,1000,1200,1400,1600,1800,2000,2200,2400,2600]
[" "]
["NO ARRANGEMENT"]
["REVENUE",{"$f":"$B$4*B7","v":0},20000,40000,60000,80000,100000,120000,140000,160000,180000,200000,220000,240000,260000,"$B$4*P7"]
["FIXED COSTS",{"$f":"$B$5","v":50000},50000,50000,50000,50000,50000,50000,50000,50000,50000,50000,50000,50000,50000,"$B$5"]
["VARIABLE COSTS",{"$f":"$B$6*B7","v":0},10000,20000,30000,40000,50000,60000,70000,80000,90000,100000,110000,120000,130000,"$B$6*P7"]
["PROFIT",{"$f":"B10-B11-B12","v":-50000},{"$f":"C10-C11-C12","v":-40000},{"$f":"D10-D11-D12","v":-30000},-20000,-10000,0,10000,20000,30000,40000,50000,60000,70000,80000,"P10-P11-P12"]
[]
["WITH SALFORD COUNCIL ARRANGEMENT"]
["REVENUE",{"$f":"B4","v":100}]
["FIXED COSTS",{"$f":"B5-B19","v":10000}]
["VARIABLE COSTS",50]
["FEE",{"$f":"B55","v":40000}]
["SALFORD SHARE",{"$f":"B56","v":0.75}]
["SHARE START",{"$f":"B57","v":100000}]
[]
["REVENUE",{"$f":"$B$16*B26","v":0},20000,40000,60000,80000,100000,120000,140000,160000,180000,200000,220000,240000,260000,"$B$16*P26"]
["FIXED COSTS",{"$f":"$B$17","v":10000},10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,"$B$17"]
["VARIABLE COSTS",{"$f":"$B$6*B26","v":0},10000,20000,30000,40000,50000,60000,70000,80000,90000,100000,110000,120000,130000,"$B$6*P26"]
["TRIATHLETES",{"$f":"B7","v":0},{"$f":"C7","v":200},400,600,800,1000,1200,1400,1600,1800,2000,2200,2400,2600," "]
["SALFORD SHARE",{"$f":"IF(B23>$B$21,$B$20*B23,0)","v":0},0,0,0,0,0,90000,105000,120000,135000,150000,165000,180000,195000,"IF(P23>$B$21,$B$20*P23,0)"]
["PROFIT SHARING",{"$f":"B23-B24-B25-B27","v":-10000},{"$f":"C23-C24-C25-C27","v":0},10000,20000,30000,40000,-40000,-45000,-50000,-55000,-60000,-65000,-70000,-75000,"P23-P24-P25-P27"]
["PROFIT, NO SHARE",{"$f":"B13","v":-50000},-40000,-30000,-20000,-10000,0,10000,20000,30000,40000,50000,60000,70000,80000," "]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["FEE",40000]
["SALFORD SHARE",0.75]
["SHARE START",100000]

{"sheet":"Problem 3.4","index":10,"n_rows":33,"n_cols":22,"rows_kept":33,"cut":false,"hidden":false,"merged":[]}
["REAL OPTION PAYOFFS"]
["Problem 3.4",0,{"$f":"B2+25","v":25},{"$f":"C2+25","v":50},75,100,125,150,175,200,225,250,275,300,325,350,375,400,425,450,475,500]
["NET ASSET VALUE",{"$f":"B2-$B$7","v":-300},{"$f":"C2-$B$7","v":-275},-250,-225,-200,-175,-150,-125,-100,-75,-50,-25,0,25,50,75,100,125,150,175,200]
["REQUIRE USE OF NET ASSET",{"$f":"-B3","v":300},{"$f":"-C3","v":275},250,225,200,175,150,125,100,75,50,25,0,-25,-50,-75,-100,-125,-150,-175,-200]
["BUY REAL CALL INTRINSIC",{"$f":"IF(B3>0,B3-$B$8,-$B$8)","v":-75},{"$f":"IF(C3>0,C3-$B$8,-$B$8)","v":-75},-75,-75,-75,-75,-75,-75,-75,-75,-75,-75,-75,-50,-25,0,25,50,75,100,125]
["STRATEGY RESULT",{"$f":"B4+B5","v":225},{"$f":"C4+C5","v":200},175,150,125,100,75,50,25,0,-25,-50,-75,-75,-75,-75,-75,-75,-75,-75,-75]
["Debt, K",300," "," ",{"$f":"D7","v":" "}," "," "," "," "," "," "," "," "," "]
["Option cost, y",{"$f":"B33","v":75}]
["Require use of  asset subject to debt K, buy option to buy net asset at nil cost, for immediate payment of option premium of y."]
["  STRATEGY RESULT equals buy real put on net asset value."]
[{"$f":"A5","v":"BUY REAL CALL INTRINSIC"},"IF(B3>0,B3-$B$8,-$B$8)"]
["STRATEGY RESULT","B4+B5"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["Option cost, y",75]

{"sheet":"Problem 3.5","index":11,"n_rows":16,"n_cols":12,"rows_kept":16,"cut":false,"hidden":false,"merged":[]}
["Problem 3.5","REAL OPTION PAYOFFS"]
["OWN ASSET-DEBT",{"$f":"B16-$B$8","v":-500},-400,-300,-200,-100,0,100,200,300,400,500]
["WRITE REAL CALL AT K2 INTRINSIC ",{"$f":"IF(B2>$B$6,$B$6-B2+$B$9,$B$9)","v":25},{"$f":"IF(C2>$B$6,$B$6-C2+$B$9,$B$9)","v":25},25,25,25,25,25,-75,-175,-275,-375]
["BUY REAL PUT AT K1 INTRINSIC",{"$f":"IF(B2<$B$7,-B2-$B$7-$B$10,-$B$10)","v":475},{"$f":"IF(C2<$B$7,-C2-$B$7-$B$10,-$B$10)","v":375},275,175,75,-25,-25,-25,-25,-25,-25]
["STRATEGY RESULT",{"$f":"B2+B3+B4","v":0},{"$f":"C2+C3+C4","v":0},0,0,0,0,100,100,100,100,100]
["K2",100]
["K1",0]
["Debt, K",500," "," ",{"$f":"D8","v":" "}," "," "," "," "," "," "," "]
["Option cost, y2",25]
["Option cost, y1",25]
["   Own asset subject to debt K, buy a \"costless protective put\" (=protective collar)."]
["  STRATEGY RESULT equals real collar."]
[{"$f":"A3","v":"WRITE REAL CALL AT K2 INTRINSIC "},"IF(B2>$B$6,$B$6-B2+$B$9,$B$9)"]
[{"$f":"A4","v":"BUY REAL PUT AT K1 INTRINSIC"},"IF(B2<$B$7,-B2-$B$7-$B$10,-$B$10)"]
["STRATEGY RESULT","B2+B3+B4"]
["ASSET VALUE",0,{"$f":"B16+100","v":100},{"$f":"C16+100","v":200},300,400,500,600,700,800,900,1000]

{"sheet":"Problem 3.6","index":12,"n_rows":44,"n_cols":15,"rows_kept":44,"cut":false,"hidden":false,"merged":[]}
["MARIA KNOX:  INSURING HER EARLY CAREER EARNINGS IN A CONTINGENT CLAIM ARRANGEMENT"]
["Problem 3.6"]
["MARIA STARTING SALARY",30000,{"$f":"B3+10000","v":40000},{"$f":"C3+10000","v":50000},60000,70000,80000,90000,100000,110000,120000,130000,140000,150000,160000]
[" "]
["FUD BONUS INSURANCE PREMIUM",{"$f":"B41","v":20000}]
["BONUS",{"$f":"B42","v":30000}]
["LOW PAY BARRIER",{"$f":"B43","v":50000}]
["HIGH PAY BARRIER",{"$f":"B44","v":150000}]
[" "]
["LOW PAY  BONUS",{"$f":"IF(B3<$B$7,$B$6,0)","v":30000},{"$f":"IF(C3<$B$7,$B$6,0)","v":30000},0,0,0,0,0,0,0,0,0,0,0,0]
["HIGH PAY  BONUS",{"$f":"IF(B3>$B$8,$B$6,0)","v":0},{"$f":"IF(C3>$B$8,$B$6,0)","v":0},0,0,0,0,0,0,0,0,0,0,0,30000]
["TOTAL PAY + BONUS-FUD",{"$f":"B3+B10+B11-$B$5","v":40000},50000,30000,40000,50000,60000,70000,80000,90000,100000,110000,120000,130000,170000]
[{"$f":"A3","v":"MARIA STARTING SALARY"},{"$f":"B3","v":30000},40000,50000,60000,70000,80000,90000,100000,110000,120000,130000,140000,150000,160000]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[{"$f":"A5","v":"FUD BONUS INSURANCE PREMIUM"},20000]
[{"$f":"A6","v":"BONUS"},30000]
[{"$f":"A7","v":"LOW PAY BARRIER"},50000]
[{"$f":"A8","v":"HIGH PAY BARRIER"},150000]

{"sheet":"Exercise 4.1","index":13,"n_rows":18,"n_cols":3,"rows_kept":18,"cut":false,"hidden":false,"merged":[]}
["                                                       Perpetual American Option"]
["Exercise 4.1"]
["V",500]
["K",450]
["s",0.2]
["r",0.04]
["d",0.04]
["ROV",{"$f":"IF(B3<B12,(B12-B4)*(B3/B12)^B14,B10)","v":138.88888888888894},"IF(B3<B12,(B12-B4)*(B3/B12)^B14,B10)"]
["ROV",{"$f":"IF(B3<B12,B13*(B3^B14),B10)","v":138.88888888888874},"IF(B3<B12,B13*(B3^B14),B10)"]
["V-K",{"$f":"B3-B4","v":50},"B3-B4"]
["F'(V)",{"$f":"IF(B3<B12,B13*B14*(B3^(B14-1)),1)","v":0.55555555555555503},"IF(B3<B12,B13*B14*(B3^(B14-1)),1)"]
["V*",{"$f":"(B14/(B14-1))*B4","v":900},"(B14/(B14-1))*B4"]
["A",{"$f":"(B12-B4)/(B12^B14)","v":5.5555555555555631E-4},"(B12-B4)/(B12^B14)"]
["b1",{"$f":"0.5-(B6-B7)/(B5^2)+SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))","v":1.9999999999999998}]
["SF",100000]
[]
["ROV",{"$f":"B9*B15","v":13888888.888888875}]
["V* TOTAL",{"$f":"B12*B15","v":90000000}]

{"sheet":"Exercise 4.2","index":14,"n_rows":32,"n_cols":3,"rows_kept":32,"cut":false,"hidden":false,"merged":[]}
["                                                       Perpetual American Option"]
["Exercise 4.2"]
["V",750]
["K",850]
["s",0.5]
["r",0.04]
["d",0.04]
["ROV",{"$f":"IF(B3<B12,(B12-B4)*(B3/B12)^B14,B10)","v":385.5514036421655},"IF(B3<B12,(B12-B4)*(B3/B12)^B14,B10)"]
["ROV",{"$f":"IF(B3<B12,B13*(B3^B14),B10)","v":385.55140364216555},"IF(B3<B12,B13*(B3^B14),B10)"]
["V-K",{"$f":"B3-B4","v":-100},"B3-B4"]
["F'(V)",{"$f":"IF(B3<B12,B13*B14*(B3^(B14-1)),1)","v":0.64514750426605649},"IF(B3<B12,B13*B14*(B3^(B14-1)),1)"]
["V*",{"$f":"(B14/(B14-1))*B4","v":4183.549771868792},"(B14/(B14-1))*B4"]
["A",{"$f":"(B12-B4)/(B12^B14)","v":9.5044721811912397E-2},"(B12-B4)/(B12^B14)"]
["b1",{"$f":"0.5-(B6-B7)/(B5^2)+SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))","v":1.254983443527075},"0.5-(B6-B7)/(B5^2)+SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))"]
[" "," "]
["ODE",{"$f":"0.5*(B5^2)*(B3^2)*B17+(B6-B7)*B3*B11-B6*B9","v":0}]
["F''(V)",{"$f":"IF(B3<B12,B13*B14*(B14-1)*(B3^(B14-2)),0)","v":2.1933590962754321E-4}]
["F'(V*)",{"$f":"B13*B14*(B12^(B14-1))","v":1}]
["F(V*)",{"$f":"IF(B3<B12,B13*(B12^B14),B10)","v":3333.5497718687925}]
["V*-K",{"$f":"B12-B4","v":3333.549771868792}]
["SF",2000]
["TOTAL ROV",{"$f":"B9*B21","v":771102.80728433107}]
["COST",200000]
[" "," "]
["SECURITY ANALYSIS OF CITY LTD."]
["ASSETS","LIAB"]
[{"$f":"750000-B23","v":550000},500000]
[{"$f":"$B$22","v":771102.80728433107},{"$f":"A29-B27","v":821102.80728433095},"NET WORTH"]
[{"$f":"A27+A28","v":1321102.8072843309}]
[]
["SHARES",1000000]
[null,{"$f":"B28/B31","v":0.82110280728433094},"NET REAL OPTION VALUE/SHARE"]

{"sheet":"Exercise 4.3","index":15,"n_rows":32,"n_cols":3,"rows_kept":32,"cut":false,"hidden":false,"merged":[]}
["                                                       Perpetual American Option"]
["Exercise 4.3"]
["UMIT",1.1000000000000001]
["COST",1.7]
["s",0.2]
["r",0.04]
["d",0.04]
["ROV",{"$f":"IF(B3<B12,(B12-B4)*(B3/B12)^B14,B10)","v":0.1779411764705883},"IF(B3<B12,(B12-B4)*(B3/B12)^B14,B10)"]
["F(V)",{"$f":"IF(B3<B12,B13*(B3^B14),B10)","v":0.17794117647058838},"IF(B3<B12,B13*(B3^B14),B10)"]
["V-K",{"$f":"B3-B4","v":-0.59999999999999987},"B3-B4"]
["F'(V)",{"$f":"IF(B3<B12,B13*B14*(B3^(B14-1)),1)","v":0.32352941176470607},"IF(B3<B12,B13*B14*(B3^(B14-1)),1)"]
["V*",{"$f":"(B14/(B14-1))*B4","v":3.4},"(B14/(B14-1))*B4"]
["A",{"$f":"(B12-B4)/(B12^B14)","v":0.14705882352941185},"(B12-B4)/(B12^B14)"]
["b1",{"$f":"0.5-(B6-B7)/(B5^2)+SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))","v":1.9999999999999998}]
["b1=","0.5-(B6-B7)/(B5^2)+SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))"]
["ODE",{"$f":"0.5*(B5^2)*(B3^2)*B17+(B6-B7)*B3*B11-B6*B9","v":0}]
["F''(V)",{"$f":"IF(B3<B12,B13*B14*(B14-1)*(B3^(B14-2)),0)","v":0.29411764705882359}]
["F'(V*)",{"$f":"B13*B14*(B12^(B14-1))","v":1.0000000000000002}]
["F(V*)",{"$f":"IF(B3<B12,B13*(B12^B14),B10)","v":1.7}]
["V*-K",{"$f":"B12-B4","v":1.7}]
[]
["IT IS HARD TO IMAGINE THAT THERE IS ANOTHER"]
["TRADED ASSET CORRELATED WITH UMIT, THAT"]
["THE VOLATILITY OF UMIT CAN BE ESTIMATED"]
["ACCURATELY, OR THAT THIS ACQUISITION COULD"]
["BE PERPETUAL."]
[]
["BUT SOLVING THE PROBLEM INDICATES A THOUGHT"]
["PROCESS, WHEREBY UMAN MIGHT CONSIDER DEFERRAL"]
["UNTIL UMIT IS WORTH OVER 3 TIMES CURRENT VALUE,"]
["OR A GOVERNMENT REDUCES THE EFFECTIVE COST,"]
["UNLESS UMAN HAS OTHER OBJECTIVE FUNCTIONS."]

{"sheet":"Problem 4.4","index":16,"n_rows":25,"n_cols":3,"rows_kept":25,"cut":false,"hidden":false,"merged":[]}
["                                                       Perpetual American Option"]
["Problem 4.4"]
["V",500]
["K",450]
["s",0.2]
["r",0.04]
["d",0.04]
[]
["F(V)",{"$f":"IF(B3<B12,B13*(B3^B14),B10)","v":138.88888888888874},"IF(B3<B12,B13*(B3^B14),B10)"]
["V-K",{"$f":"B3-B4","v":50},"B3-B4"]
["F'(V)",{"$f":"IF(B3<B12,B13*B14*(B3^(B14-1)),1)","v":0.55555555555555503},"IF(B3<B12,B13*B14*(B3^(B14-1)),1)"]
["V*",{"$f":"(B14/(B14-1))*B4","v":900},"(B14/(B14-1))*B4"]
["A",{"$f":"(B12-B4)/(B12^B14)","v":5.5555555555555631E-4},"(B12-B4)/(B12^B14)"]
["b1",{"$f":"0.5-(B6-B7)/(B5^2)+SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))","v":1.9999999999999998}]
["b1=","0.5-(B6-B7)/(B5^2)+SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))"]
["ODE",{"$f":"0.5*(B5^2)*(B3^2)*B17+(B6-B7)*B3*B11-B6*B9","v":0},"0.5*(B5^2)*(B3^2)*B17+(B6-B7)*B3*B11-B6*B9"]
["F''(V)",{"$f":"IF(B3<B12,B13*B14*(B14-1)*(B3^(B14-2)),0)","v":1.1111111111111107E-3},"IF(B3<B12,B13*B14*(B14-1)*(B3^(B14-2)),0)"]
["F'(V*)",{"$f":"B13*B14*(B12^(B14-1))","v":0.99999999999999956},"B13*B14*(B12^(B14-1))"]
["F(V*)",{"$f":"IF(B3<B12,B13*(B12^B14),B10)","v":449.99999999999994},"IF(B3<B12,B13*(B12^B14),B10)"]
["V*-K",{"$f":"B12-B4","v":450},"B12-B4"]
[]
["INSERTING DELTA, GAMMA  AND THE F(V) FUNCTION"]
["INTO ODE RESULTS IN THE ODE EQUAL TO ZERO."]
["VALUE MATCHING AND SMOOTH PASTING CONDITIONS"]
["ARE MET."]

{"sheet":"Problem 4.5","index":17,"n_rows":71,"n_cols":6,"rows_kept":71,"cut":false,"hidden":false,"merged":[]}
[null,"                                                       Hedging a Perpetual American Option"]
["Problem 4.5","PER SF","TOTAL"]
["V",750,{"$f":"B3*C15","v":1500000}]
["K",850,{"$f":"B4*C15","v":1700000}]
["s",0.5,{"$f":"B5","v":0.5}]
["r",0.04,{"$f":"B6","v":0.04}]
["d",0.04,{"$f":"B7","v":0.04}]
[]
["F(V)",{"$f":"IF(B3<B12,B13*(B3^B14),B10)","v":385.55140364216555},{"$f":"B9*C15","v":771102.80728433107}]
["V-K",{"$f":"B3-B4","v":-100},{"$f":"C3-C4","v":-200000}]
["F'(V)",{"$f":"IF(B3<B12,B13*B14*(B3^(B14-1)),1)","v":0.64514750426605649},{"$f":"IF(C3<C12,C13*C14*(C3^(C14-1)),1)","v":0.64514750426605616}]
["V*",{"$f":"(B14/(B14-1))*B4","v":4183.549771868792},{"$f":"(C14/(C14-1))*C4","v":8367099.5437375847}]
["A",{"$f":"(B12-B4)/(B12^B14)","v":9.5044721811912397E-2},{"$f":"(C12-C4)/(C12^C14)","v":1.3684218762133868E-2}]
["b1",{"$f":"0.5-(B6-B7)/(B5^2)+SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))","v":1.254983443527075},{"$f":"0.5-(C6-C7)/(C5^2)+SQRT(((C6-C7)/(C5^2)-0.5)^2 + 2*C6/(C5^2))","v":1.254983443527075}]
["SF",null,2000]
["CITY OTHER NET ASSETS",null,250000,null," "," "]
["COST CITY'S ROV",null,200000]
[]
["CITY LTD VALUE",null,{"$f":"C9+C16-C17","v":821102.80728433107},null," "," "]
["CITY LTD ISSSED FOR "," ",900000,null," "," "]
["DELTA HEDGE POSITION: V",null,{"$f":"C11*C3","v":967721.25639908423},"C11*C3"," "," "]
[" "," "]
[]
["INITIAL PROFITS",null,{"$f":"C20-C19","v":78897.192715668934},"C20-C19"]
["EVENTUAL PROFITS DEPEND ON HEDGING INACCURACY & TRANSACTION COSTS."]
[]
[null,"ROV NUMERICAL DELTA",null,null,"10% DECREASE","10% INCREASE"]
[{"$f":"A3","v":"V"},675,{"$f":"B3","v":750},825,{"$f":"-1+B28/C28","v":-9.9999999999999978E-2},{"$f":"D28/C28-1","v":0.10000000000000009}]
[{"$f":"A4","v":"K"},850,{"$f":"B4","v":850},850]
["s",0.5,{"$f":"B5","v":0.5},0.5]
["r",0.04,{"$f":"B6","v":0.04},0.04]
["d",0.04,{"$f":"B7","v":0.04},0.04]
[" "," "," "," ","AS % V"]
[{"$f":"A9","v":"F(V)"},{"$f":"IF(B28<B37,B38*(B28^B39),B35)","v":337.79825012267383},{"$f":"B9","v":385.55140364216555},{"$f":"IF(D28<D37,D38*(D28^D39),D35)","v":434.53966290232796},{"$f":"(B34-C34)/(B28-C28)","v":0.6367087135932229},{"$f":"(D34-C34)/(D28-C28)","v":0.65317679013549879}]
[{"$f":"A10","v":"V-K"},{"$f":"B28-B29","v":-175},-100,{"$f":"D28-D29","v":-25}]
[{"$f":"A11","v":"F'(V)"},{"$f":"IF(B28<B37,B38*B39*(B28^(B39-1)),1)","v":0.62804623875018295},0.64514750426605649,{"$f":"IF(D28<D37,D38*D39*(D28^(D39-1)),1)","v":0.66101828181607036}]
[{"$f":"A12","v":"V*"},{"$f":"(B39/(B39-1))*B29","v":4183.549771868792},4183.549771868792,{"$f":"(D39/(D39-1))*D29","v":4183.549771868792}]
[{"$f":"A13","v":"A"},{"$f":"(B37-B29)/(B37^B39)","v":9.5044721811912397E-2},9.5044721811912397E-2,{"$f":"(D37-D29)/(D37^D39)","v":9.5044721811912397E-2}]
["b1",{"$f":"0.5-(B31-B32)/(B30^2)+SQRT(((B31-B32)/(B30^2)-0.5)^2 + 2*B31/(B30^2))","v":1.254983443527075},1.254983443527075,{"$f":"0.5-(D31-D32)/(D30^2)+SQRT(((D31-D32)/(D30^2)-0.5)^2 + 2*D31/(D30^2))","v":1.254983443527075}]
[]
["                                                                                  Hedging a Perpetual American WRITTEN CALL Option (per SF)"]
["MONTH",0,{"$f":"B42+1","v":1},{"$f":"C42+1","v":2},{"$f":"D42+1","v":3},{"$f":"E42+1","v":4}]
["V",750,800,750,700,750]
["K",850,{"$f":"B44","v":850},850,850,850]
["s",0.5,0.5,0.5,0.5,0.5]
["r",0.04,0.04,0.04,0.04,0.04]
["d",0.04,0.04,0.04,0.04,0.04]
["OUTPUT"]
["WRITE ROV CALL",{"$f":"IF(B43<B57,-B58*(B43^B59),-B61)","v":-385.55140364216555},{"$f":"IF(C43<C57,-C58*(C43^C59),-C61)","v":-418.07853698190758},{"$f":"IF(D43<D57,-D58*(D43^D59),-D61)","v":-385.55140364216555},{"$f":"IF(E43<E57,-E58*(E43^E59),-E61)","v":-353.57287450837214},{"$f":"IF(F43<F57,-F58*(F43^F59),-F61)","v":-385.55140364216555}]
["HEDGE LONG VD",{"$f":"B56*B43","v":483.86062819954236},{"$f":"B50+C51","v":492.42426679301366},{"$f":"C50+D51","v":484.39585561163432},{"$f":"D50+E51","v":476.52070621367847},{"$f":"E50+F51","v":484.95836628291693}]
["ALTER HEDGE",null,{"$f":"(C56-B56)*C43","v":8.5636385934712678},{"$f":"(D56-C56)*D43","v":-8.0284111813793135},{"$f":"(E56-D56)*E43","v":-7.8751493979558713},{"$f":"(F56-E56)*F43","v":8.4376600692384347}]
["GAIN ROV",null,{"$f":"-B49+C49","v":-32.527133339742022},{"$f":"-C49+D49","v":32.527133339742022},{"$f":"-D49+E49","v":31.978529133793415},{"$f":"-E49+F49","v":-31.978529133793415}]
["GAIN V",null,{"$f":"(B50/B43)*(C43-B43)","v":32.257375213302822},{"$f":"(C50/C43)*(D43-C43)","v":-30.776516674563354},{"$f":"(D50/D43)*(E43-D43)","v":-32.293057040775622},{"$f":"(E50/E43)*(F43-E43)","v":34.03719330097703}]
["NET GAIN",null,{"$f":"C52+C53","v":-0.26975812643919994},{"$f":"D52+D53","v":1.7506166651786685},{"$f":"E52+E53","v":-0.31452790698220667},{"$f":"F52+F53","v":2.0586641671836148}]
["CUM GAIN",null,{"$f":"SUM($C$54:C54)","v":-0.26975812643919994},{"$f":"SUM($C$54:D54)","v":1.4808585387394686},{"$f":"SUM($C$54:E54)","v":1.1663306317572619},{"$f":"SUM($C$54:F54)","v":3.2249947989408767}]
["F'(V)",{"$f":"IF(B43<B57,B58*B59*(B43^(B59-1)),1)","v":0.64514750426605649},{"$f":"IF(C43<C57,C58*C59*(C43^(C59-1)),1)","v":0.65585205250789558},{"$f":"IF(D43<D57,D58*D59*(D43^(D59-1)),1)","v":0.64514750426605649},{"$f":"IF(E43<E57,E58*E59*(E43^(E59-1)),1)","v":0.63389729084040525},{"$f":"IF(F43<F57,F58*F59*(F43^(F59-1)),1)","v":0.64514750426605649}]
["V*",{"$f":"(B59/(B59-1))*B44","v":4183.549771868792},{"$f":"(C59/(C59-1))*C44","v":4183.549771868792},{"$f":"(D59/(D59-1))*D44","v":4183.549771868792},{"$f":"(E59/(E59-1))*E44","v":4183.549771868792},{"$f":"(F59/(F59-1))*F44","v":4183.549771868792}]
["A",{"$f":"(B57-B44)/(B57^B59)","v":9.5044721811912397E-2},{"$f":"(C57-C44)/(C57^C59)","v":9.5044721811912397E-2},{"$f":"(D57-D44)/(D57^D59)","v":9.5044721811912397E-2},{"$f":"(E57-E44)/(E57^E59)","v":9.5044721811912397E-2},{"$f":"(F57-F44)/(F57^F59)","v":9.5044721811912397E-2}]
["b1",{"$f":"0.5-(B46-B47)/(B45^2)+SQRT(((B46-B47)/(B45^2)-0.5)^2 + 2*B46/(B45^2))","v":1.254983443527075},{"$f":"0.5-(C46-C47)/(C45^2)+SQRT(((C46-C47)/(C45^2)-0.5)^2 + 2*C46/(C45^2))","v":1.254983443527075},{"$f":"0.5-(D46-D47)/(D45^2)+SQRT(((D46-D47)/(D45^2)-0.5)^2 + 2*D46/(D45^2))","v":1.254983443527075},{"$f":"0.5-(E46-E47)/(E45^2)+SQRT(((E46-E47)/(E45^2)-0.5)^2 + 2*E46/(E45^2))","v":1.254983443527075},{"$f":"0.5-(F46-F47)/(F45^2)+SQRT(((F46-F47)/(F45^2)-0.5)^2 + 2*F46/(F45^2))","v":1.254983443527075}]
["F''(V)",{"$f":"IF(B43<B57,B58*B59*(B59-1)*(B43^(B59-2)),0)","v":2.1933590962754321E-4},{"$f":"IF(C43<C57,C58*C59*(C59-1)*(C43^(C59-2)),0)","v":2.0903926849095414E-4},{"$f":"IF(D43<D57,D58*D59*(D59-1)*(D43^(D59-2)),0)","v":2.1933590962754321E-4},{"$f":"IF(E43<E57,E58*E59*(E59-1)*(E43^(E59-2)),0)","v":2.3090473437281488E-4},{"$f":"IF(F43<F57,F58*F59*(F59-1)*(F43^(F59-2)),0)","v":2.1933590962754321E-4}]
["V-K",{"$f":"B43-B44","v":-100},{"$f":"C43-C44","v":-50},{"$f":"D43-D44","v":-100},{"$f":"E43-E44","v":-150},{"$f":"F43-F44","v":-100}]
[null,null,null," "," "," "]
[{"$f":"A50","v":"HEDGE LONG VD"},"B56*B43","B50+C51"]
["ALTER HEDGE",null,"(C56-B56)*C43"]
["GAIN ROV",null,"-B49+C49"]
["GAIN V",null,"(B50/B43)*(C43-B43)"]
["NET GAIN",null,"C52+C53"]
["CUM GAIN",null,"SUM($C$54:C54)"]
[]
["ISSUE A PERPETUAL AMERICAN REAL CALL OPTION"]
["HEDGE BY BUYING DELTA OF V BEGINNING OF EACH MONTH."]

{"sheet":"Problem 4.6","index":18,"n_rows":74,"n_cols":7,"rows_kept":74,"cut":false,"hidden":false,"merged":[]}
["                                                       Perpetual American Option"]
["Problem 4.6","MONTH",1,2,3,4]
["V",750,800,750,700,750]
["K",850,850,850,850,850]
["s",0.5,0.5,0.5,0.5,0.5]
["r",0.04,0.04,0.02,0.05,0.04]
["d",0.04,0.04,0.04,0.04,0.04]
[]
["F(V)",{"$f":"IF(B3<B12,B13*(B3^B14),B10)","v":385.55140364216555},{"$f":"IF(C3<C12,C13*(C3^C14),C10)","v":418.07853698190758},{"$f":"IF(D3<D12,D13*(D3^D14),D10)","v":366.92206183363351},{"$f":"IF(E3<E12,E13*(E3^E14),E10)","v":361.94124131739443},{"$f":"IF(F3<F12,F13*(F3^F14),F10)","v":385.55140364216555}]
["V-K",{"$f":"B3-B4","v":-100},{"$f":"C3-C4","v":-50},{"$f":"D3-D4","v":-100},{"$f":"E3-E4","v":-150},{"$f":"F3-F4","v":-100}]
["F'(V)",{"$f":"IF(B3<B12,B13*B14*(B3^(B14-1)),1)","v":0.64514750426605649},{"$f":"IF(C3<C12,C13*C14*(C3^(C14-1)),1)","v":0.65585205250789558},{"$f":"IF(D3<D12,D13*D14*(D3^(D14-1)),1)","v":0.62844287404807353},{"$f":"IF(E3<E12,E13*E14*(E3^(E14-1)),1)","v":0.64221229872477104},{"$f":"IF(F3<F12,F13*F14*(F3^(F14-1)),1)","v":0.64514750426605649}]
["V*",{"$f":"(B14/(B14-1))*B4","v":4183.549771868792},{"$f":"(C14/(C14-1))*C4","v":4183.549771868792},{"$f":"(D14/(D14-1))*D4","v":3837.1034638421597},{"$f":"(E14/(E14-1))*E4","v":4361.6915720768257},{"$f":"(F14/(F14-1))*F4","v":4183.549771868792}]
["A",{"$f":"(B12-B4)/(B12^B14)","v":9.5044721811912397E-2},{"$f":"(C12-C4)/(C12^C14)","v":9.5044721811912397E-2},{"$f":"(D12-D4)/(D12^D14)","v":7.4369508155089262E-2},{"$f":"(E12-E4)/(E12^E14)","v":0.10589807296022138},{"$f":"(F12-F4)/(F12^F14)","v":9.5044721811912397E-2}]
["b1",{"$f":"0.5-(B6-B7)/(B5^2)+SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))","v":1.254983443527075},{"$f":"0.5-(C6-C7)/(C5^2)+SQRT(((C6-C7)/(C5^2)-0.5)^2 + 2*C6/(C5^2))","v":1.254983443527075},{"$f":"0.5-(D6-D7)/(D5^2)+SQRT(((D6-D7)/(D5^2)-0.5)^2 + 2*D6/(D5^2))","v":1.2845565981523412},{"$f":"0.5-(E6-E7)/(E5^2)+SQRT(((E6-E7)/(E5^2)-0.5)^2 + 2*E6/(E5^2))","v":1.2420485918406858},{"$f":"0.5-(F6-F7)/(F5^2)+SQRT(((F6-F7)/(F5^2)-0.5)^2 + 2*F6/(F5^2))","v":1.254983443527075}]
[" "," "," "," "," "," "]
["SF",2000,2000,2000,2000,2000]
["TOTAL ROV",{"$f":"B9*B16","v":771102.80728433107},{"$f":"C9*C16","v":836157.07396381511},{"$f":"D9*D16","v":733844.12366726703},{"$f":"E9*E16","v":723882.48263478884},{"$f":"F9*F16","v":771102.80728433107}]
["COST",200000,200000,200000,200000,200000]
["RO WORTH",{"$f":"B17-B18","v":571102.80728433107},{"$f":"C17-C18","v":636157.07396381511},{"$f":"D17-D18","v":533844.12366726703},{"$f":"E17-E18","v":523882.48263478884},{"$f":"F17-F18","v":571102.80728433107}]
["SECURITY ANALYSIS OF CITY LTD."]
["FUNDAMENTALS",null," "," "," "," "]
["OTHER NET ASSETS",250000,{"$f":"B22","v":250000},{"$f":"C22","v":250000},{"$f":"D22","v":250000},{"$f":"E22","v":250000}]
["ROV",{"$f":"B19","v":571102.80728433107},{"$f":"C19","v":636157.07396381511},{"$f":"D19","v":533844.12366726703},{"$f":"E19","v":523882.48263478884},{"$f":"F19","v":571102.80728433107}]
["TOTAL EQUITY VALUE",{"$f":"B22+B23","v":821102.80728433107},{"$f":"C22+C23","v":886157.07396381511},{"$f":"D22+D23","v":783844.12366726703},{"$f":"E22+E23","v":773882.48263478884},{"$f":"F22+F23","v":821102.80728433107}]
["SHARES",1000000,1000000,1000000,1000000,1000000]
["NET REAL OPTION VALUE/SHARE",{"$f":"B24/B25","v":0.82110280728433105},{"$f":"C24/C25","v":0.88615707396381516},{"$f":"D24/D25","v":0.78384412366726708},{"$f":"E24/E25","v":0.77388248263478887},{"$f":"F24/F25","v":0.82110280728433105}]
["MP/SHARE",{"$f":"B26","v":0.82110280728433105},1,0.82,0.8,0.8]
["PHF SHARES",{"$f":"0.1*B25","v":100000}]
["PHF MARKET POSITION","$B$28*B27"]
["PHF MARKET POSITION",{"$f":"$B$28*B27","v":82110.280728433107},{"$f":"$B$28*C27","v":100000},{"$f":"$B$28*D27","v":82000},{"$f":"$B$28*E27","v":80000},{"$f":"$B$28*F27","v":80000}]
["PHF HEDGE: SHORT VD",{"$f":"B16*B51*0.1","v":-96772.125639908481},{"$f":"C16*C51*0.1","v":-95059.397921214229},{"$f":"D16*D51*0.1","v":-99170.774690187536},{"$f":"E16*E51*0.1","v":-97243.055235449865},{"$f":"F16*F51*0.1","v":-96802.774404257056}]
["PHF HEDGE","B16*B51*0.1"]
["GAINS/LOSSES"]
["PHF POSITION",null,{"$f":"C30-B30","v":17889.719271566893},{"$f":"D30-C30","v":-18000},{"$f":"E30-D30","v":-2000},{"$f":"F30-E30","v":0}]
["PHF HEDGE",null,{"$f":"2000*0.1*C54","v":-6451.4750426605642},{"$f":"2000*0.1*D54","v":5941.2123700758875},{"$f":"2000*0.1*E54","v":6611.3849793458339},{"$f":"2000*0.1*F54","v":-6945.9325168178484}]
[]
["CUM £ GAIN/LOSS"]
[{"$f":"A34","v":"PHF POSITION"},null,{"$f":"SUM($C$34:C34)","v":17889.719271566893},{"$f":"SUM($C$34:D34)","v":-110.28072843310656},{"$f":"SUM($C$34:E34)","v":-2110.2807284331066},{"$f":"SUM($C$34:F34)","v":-2110.2807284331066}]
[{"$f":"A35","v":"PHF HEDGE"},null,{"$f":"SUM($C$35:C35)","v":-6451.4750426605642},{"$f":"SUM($C$35:D35)","v":-510.26267258467669},{"$f":"SUM($C$35:E35)","v":6101.1223067611572},{"$f":"SUM($C$35:F35)","v":-844.81021005669118}]
["NET CUM GAIN",null,{"$f":"C38+C39","v":11438.244228906329},{"$f":"D38+D39","v":-620.54340101778325},{"$f":"E38+E39","v":3990.8415783280507},{"$f":"F38+F39","v":-2955.0909384897977}]
[" "]
[null,"                                                       Hedging a Perpetual American Option"]
["MONTH",0,{"$f":"B43+1","v":1},{"$f":"C43+1","v":2},{"$f":"D43+1","v":3},{"$f":"E43+1","v":4}]
["V",{"$f":"B3","v":750},{"$f":"C3","v":800},{"$f":"D3","v":750},{"$f":"E3","v":700},{"$f":"F3","v":750}]
["K",{"$f":"B4","v":850},{"$f":"B45","v":850},850,850,850]
["s",{"$f":"B5","v":0.5},0.5,0.5,0.5,0.5]
["r",{"$f":"B6","v":0.04},{"$f":"C6","v":0.04},{"$f":"D6","v":0.02},{"$f":"E6","v":0.05},{"$f":"F6","v":0.04}]
["d",{"$f":"B7","v":0.04},{"$f":"B48","v":0.04},{"$f":"C48","v":0.04},{"$f":"D48","v":0.04},{"$f":"E48","v":0.04}]
["OUTPUT"]
["ROV",{"$f":"IF(B44<B58,B59*(B44^B60),B62)","v":385.55140364216555},{"$f":"IF(C44<C58,C59*(C44^C60),C62)","v":418.07853698190758},{"$f":"IF(D44<D58,D59*(D44^D60),D62)","v":366.92206183363351},{"$f":"IF(E44<E58,E59*(E44^E60),E62)","v":361.94124131739443},{"$f":"IF(F44<F58,F59*(F44^F60),F62)","v":385.55140364216555}]
["HEDGE",{"$f":"-B57*B44","v":-483.86062819954236},{"$f":"B51+C52","v":-475.29698960607107},{"$f":"C51+D52","v":-495.85387345093761},{"$f":"D51+E52","v":-486.21527617724934},{"$f":"E51+F52","v":-484.01387202128524}]
["ALTER HEDGE",null,{"$f":"(C57-B57)*C44","v":8.5636385934712678},{"$f":"(D57-C57)*D44","v":-20.556883844866537},{"$f":"(E57-D57)*E44","v":9.638597273688255},{"$f":"(F57-E57)*F44","v":2.2014041559640929}]
["GAIN ROV",null,{"$f":"-B50+C50","v":32.527133339742022},{"$f":"-C50+D50","v":-51.156475148274069},{"$f":"-D50+E50","v":-4.9808205162390777},{"$f":"-E50+F50","v":23.610162324771125}]
["GAIN V",null,{"$f":"-(B51/B44)*(-C44+B44)","v":-32.257375213302822},{"$f":"-(C51/C44)*(-D44+C44)","v":29.706061850379438},{"$f":"-(D51/D44)*(-E44+D44)","v":33.056924896729171},{"$f":"-(E51/E44)*(-F44+E44)","v":-34.72966258408924}]
["NET GAIN",null,{"$f":"C53+C54","v":0.26975812643919994},{"$f":"D53+D54","v":-21.450413297894631},{"$f":"E53+E54","v":28.076104380490094},{"$f":"F53+F54","v":-11.119500259318116}]
["CUM GAIN",null,{"$f":"SUM($C$55:C55)","v":0.26975812643919994},{"$f":"SUM($C$55:D55)","v":-21.180655171455431},{"$f":"SUM($C$55:E55)","v":6.8954492090346626},{"$f":"SUM($C$55:F55)","v":-4.2240510502834532}]
["F'(V)",{"$f":"IF(B44<B58,B59*B60*(B44^(B60-1)),1)","v":0.64514750426605649},{"$f":"IF(C44<C58,C59*C60*(C44^(C60-1)),1)","v":0.65585205250789558},{"$f":"IF(D44<D58,D59*D60*(D44^(D60-1)),1)","v":0.62844287404807353},{"$f":"IF(E44<E58,E59*E60*(E44^(E60-1)),1)","v":0.64221229872477104},{"$f":"IF(F44<F58,F59*F60*(F44^(F60-1)),1)","v":0.64514750426605649}]
["V*",{"$f":"(B60/(B60-1))*B45","v":4183.549771868792},{"$f":"(C60/(C60-1))*C45","v":4183.549771868792},{"$f":"(D60/(D60-1))*D45","v":3837.1034638421597},{"$f":"(E60/(E60-1))*E45","v":4361.6915720768257},{"$f":"(F60/(F60-1))*F45","v":4183.549771868792}]
["A",{"$f":"(B58-B45)/(B58^B60)","v":9.5044721811912397E-2},{"$f":"(C58-C45)/(C58^C60)","v":9.5044721811912397E-2},{"$f":"(D58-D45)/(D58^D60)","v":7.4369508155089262E-2},{"$f":"(E58-E45)/(E58^E60)","v":0.10589807296022138},{"$f":"(F58-F45)/(F58^F60)","v":9.5044721811912397E-2}]
["b1",{"$f":"0.5-(B47-B48)/(B46^2)+SQRT(((B47-B48)/(B46^2)-0.5)^2 + 2*B47/(B46^2))","v":1.254983443527075},{"$f":"0.5-(C47-C48)/(C46^2)+SQRT(((C47-C48)/(C46^2)-0.5)^2 + 2*C47/(C46^2))","v":1.254983443527075},{"$f":"0.5-(D47-D48)/(D46^2)+SQRT(((D47-D48)/(D46^2)-0.5)^2 + 2*D47/(D46^2))","v":1.2845565981523412},{"$f":"0.5-(E47-E48)/(E46^2)+SQRT(((E47-E48)/(E46^2)-0.5)^2 + 2*E47/(E46^2))","v":1.2420485918406858},{"$f":"0.5-(F47-F48)/(F46^2)+SQRT(((F47-F48)/(F46^2)-0.5)^2 + 2*F47/(F46^2))","v":1.254983443527075}]
["F''(V)",{"$f":"IF(B44<B58,B59*B60*(B60-1)*(B44^(B60-2)),0)","v":2.1933590962754321E-4},{"$f":"IF(C44<C58,C59*C60*(C60-1)*(C44^(C60-2)),0)","v":2.0903926849095414E-4},{"$f":"IF(D44<D58,D59*D60*(D60-1)*(D44^(D60-2)),0)","v":2.3843675516293353E-4},{"$f":"IF(E44<E58,E59*E60*(E60-1)*(E44^(E60-2)),0)","v":2.2206654652728676E-4},{"$f":"IF(F44<F58,F59*F60*(F60-1)*(F44^(F60-2)),0)","v":2.1933590962754321E-4}]
["V-K",{"$f":"B44-B45","v":-100},{"$f":"C44-C45","v":-50},{"$f":"D44-D45","v":-100},{"$f":"E44-E45","v":-150},{"$f":"F44-F45","v":-100}]
[null,null,null," "," "," "]
[{"$f":"A51","v":"HEDGE"},"-B57*B44","B51+C52"]
["ALTER HEDGE",null,"(C57-B57)*C44"]
["GAIN ROV",null,"-B50+C50"]
["GAIN V",null,"-(B51/B44)*(-C44+B44)"]
["NET GAIN",null,"C53+C54"]
["CUM GAIN",null,"SUM($C$55:C55)"]
[]
["BUY A FIRM OWNING A PERPETUAL AMERICAN REAL CALL OPTION"]
["HEDGE BY SHORTING DELTA OF V BEGINNING OF EACH MONTH.",null,null,null,null,null,"RISK"]
["RISK BUYING CITY SHS",null,{"$f":"C34/$B$30","v":0.21787429190181845},-0.21921737254232732,-2.4357485838036368E-2,0,{"$f":"STDEV(C73:F73)","v":0.17884222174223935}]
["RISK CITY SHS HEDGED",null,-7.8570855993024893E-2,7.2356498082444959E-2,8.0518358002111268E-2,-8.4592726455173531E-2,{"$f":"STDEV(C74:F74)","v":9.1326361835198877E-2}]

{"sheet":"Exercise 5.1","index":19,"n_rows":22,"n_cols":3,"rows_kept":22,"cut":false,"hidden":false,"merged":[]}
[null,"                           American Perpetual Exchange Option"]
["INPUT"," "," "]
["V",300]
["K",273]
["sV",0.2]
["sk",0.2]
["r",0.04]
["dV",0.04]
["dk",0.04]
["r",0.5]
["OUTPUT"]
["W(V,K)",{"$f":"IF(B18<B17,B4*B14*(B18^B15),B13)","v":82.417582417582452},"IF(B18<B17,B4*B14*(B18^B15),B13)"]
["V-K",{"$f":"B3-B4","v":27},"B3-B4"]
["A",{"$f":"(B17-1)/(B17^B15)","v":0.25000000000000006},"(B17-1)/(B17^B15)"]
["b1",{"$f":"0.5-(B9-B8)/(B16^2)+SQRT(((B9-B8)/(B16^2)-0.5)^2 + (2*B9)/(B16^2))","v":1.9999999999999998},"0.5-(B9-B8)/(B16^2)+SQRT(((B9-B8)/(B16^2)-0.5)^2 + (2*B9)/(B16^2))"]
["h",{"$f":"SQRT(B5^2+B6^2-2*B10*B5*B6)","v":0.2},"SQRT(B5^2+B6^2-2*B10*B5*B6)"]
["z*",{"$f":"(B15/(B15-1))","v":2},"(B15/(B15-1))"]
["z",{"$f":"B3/B4","v":1.098901098901099},"B3/B4"]
[{"$f":"A12","v":"W(V,K)"},{"$f":"B20*(B4*(B17-1)*(B18/B17)^B15)","v":247252.74725274736},"B20*(B4*(B17-1)*(B18/B17)^B15)"]
["Sq Feet",3000]
["ROV",{"$f":"B20*B12","v":247252.74725274736},"B20*B12"]
["Z*",{"$f":"B20*B17*B4","v":1638000}]

{"sheet":"Exercise 5.2","index":20,"n_rows":22,"n_cols":3,"rows_kept":22,"cut":false,"hidden":false,"merged":[]}
[null,"                           American Perpetual Exchange Option"]
["Exercise 5.2"," "]
["V",300000000]
["K",300000000]
["sV",1.1200000000000001]
["sK",0.95]
["dV",0.02]
["dK",0.02]
["r",0]
["OUTPUT"]
["W(V,K)",{"$f":"IF(B17<B16,B4*(B16-1)*(B17/B16)^B14,B13)","v":273813887.03764677},"IF(B17<B16,B4*(B16-1)*(B17/B16)^B14,B13)"]
["V-K",{"$f":"B3-B4","v":0},"B3-B4"]
["A",{"$f":"(B16-1)/(B16^B14)","v":0.91271295679215581},"(B16-1)/(B16^B14)"]
["b1",{"$f":"0.5-(B8-B7)/(B15^2)+SQRT(((B8-B7)/(B15^2)-0.5)^2 + (2*B8)/(B15^2))","v":1.0182134060600989},"0.5-(B8-B7)/(B15^2)+SQRT(((B8-B7)/(B15^2)-0.5)^2 + (2*B8)/(B15^2))"]
["h",{"$f":"SQRT(B5^2+B6^2-2*B9*B5*B6)","v":1.468638825579659},"SQRT(B5^2+B6^2-2*B9*B5*B6)"]
["z*",{"$f":"(B14/(B14-1))","v":55.904612388275559},"(B14/(B14-1))"]
["z",{"$f":"B3/B4","v":1},"B3/B4"]
[]
["THE OPTION TO ACQUIRE IS WORTH $273 MILLION, DUE TO THE HIGH"]
["VOLALILITY OF BOTH COMPANIES.  DON'T MAKE THE ACQUISITION"]
["UNTIL BLOCKBUSTER IS WORTH $16770 MILLION (WHILE BIOSURGERY"]
["IS WORTH THE CURRENT VALUE OF $300 MILLION)."]

{"sheet":"Exercise 5.3","index":21,"n_rows":27,"n_cols":3,"rows_kept":27,"cut":false,"hidden":false,"merged":[]}
["American Multi-factor Perpetual Real Option"]
["Exercise 5.3","Stochastic P & Q"]
["DSP",1]
["DS",2]
["X",{"$f":"B3*B4","v":2},"B3*B4"]
["K",{"$f":"100*B4","v":200},"100*B4"]
["s",0.2]
["a",0.2]
["r",-0.5]
["r",0.04]
["m",0.01]
["w",0.01]
["OUTPUT"]
["n",{"$f":"B10-B11-B12","v":1.9999999999999997E-2},"B10-B11-B12"]
["V",{"$f":"B5/B14","v":100.00000000000001},"B5/B14"]
["P(P,Q)",{"$f":"IF(B5<B20,(B6/(B18-1))*((B5/B20)^B18),B17)","v":12.5},"IF(B5<B20,(B6/(B18-1))*((B5/B20)^B18),B17)"]
["V-K",{"$f":"B15-B6","v":-99.999999999999986},"B15-B6"]
["b1",{"$f":"(1/B19^2)*(-(B9*B7*B8+B11+B12-0.5*(B19^2))+SQRT((B9*B7*B8+B11+B12-0.5*(B19^2))^2+(2*B10)*(B19^2)))","v":2}]
["z",{"$f":"SQRT(B7^2+B8^2+2*B9*B7*B8)","v":0.2},"SQRT(B7^2+B8^2+2*B9*B7*B8)"]
["X*",{"$f":"B6*B14*(B18/(B18-1))","v":7.9999999999999991},"B6*B14*(B18/(B18-1))"]
["b1","(1/B19^2)*(-(B9*B7*B8+B11+B12-0.5*(B19^2))+SQRT((B9*B7*B8+B11+B12-0.5*(B19^2))^2+(2*B10)*(B19^2)))"]
["V*-K",{"$f":"B20/B14-B6","v":200},"B20/B14-B6"]
[]
["THE VALUE OF THIS OPPORTUNITY IS 12.50, EVEN THOUGH"]
["THE NET PRESENT VALUE IS VERY NEGATIVE."]
["ROGroupie SHOULD NOT START THIS VENTURE UNTIL"]
["DS*DSP ARE OVER FOUR TIMES CURRENT EXPECTATIONS."]

{"sheet":"Problem 5.4","index":22,"n_rows":24,"n_cols":3,"rows_kept":24,"cut":false,"hidden":false,"merged":[]}
[null,"                           American Perpetual Exchange Option"]
["Problem 5.4"," "]
["V",300]
["K",273]
["sV",0.3]
["sK",0.2]
["dV",0.03]
["dK",0.02]
["r",0]
["SQ FT",3000]
["W(V,K)",{"$f":"IF(B17<B16,B4*(B16-1)*(B17/B16)^B14,B13)*B10","v":415450.3471642377},"IF(B17<B16,B4*(B16-1)*(B17/B16)^B14,B13)"]
["V-K",{"$f":"(B3-B4)*B10","v":81000},"B3-B4"]
["A",{"$f":"(B16-1)/(B16^B14)","v":0.44547644219851407},"(B16-1)/(B16^B14)"]
["b1",{"$f":"0.5-(B8-B7)/(B15^2)+SQRT(((B8-B7)/(B15^2)-0.5)^2 + (2*B8)/(B15^2))","v":1.3772558479494157},"0.5-(B8-B7)/(B15^2)+SQRT(((B8-B7)/(B15^2)-0.5)^2 + (2*B8)/(B15^2))"]
["h",{"$f":"SQRT(B5^2+B6^2-2*B9*B5*B6)","v":0.36055512754639896},"SQRT(B5^2+B6^2-2*B9*B5*B6)"]
["z*",{"$f":"(B14/(B14-1))","v":3.6507210038904021},"(B14/(B14-1))"]
["z",{"$f":"B3/B4","v":1.098901098901099},"B3/B4"]
[]
["THE OPTION TO BUILD IS WORTH £415,000, DUE TO THE LOW CORRELATION"]
["OF VALUE AND CONSTRUCTION COSTS.  DON'T START CONSTRUCTION"]
["UNTIL HOUSE VALUE IS WORTH £2,989,350 (EVEN THOUGH THE "]
["CURRENT NET PRESENT VALUE IS POSITIVE). NOTE THAT THE"]
["OPTION TO BUILD IS WORTH ALMOST HALF THE CURRENT GROSS VALUE"]
["OF THE HOUSE WERE IT TO BE BUILT TODAY."]

{"sheet":"Problem 5.5","index":23,"n_rows":26,"n_cols":3,"rows_kept":26,"cut":false,"hidden":false,"merged":[]}
[null,"                           American Perpetual Exchange Option"]
["Problem 5.5"," "]
["V",200000]
["K",250000]
["sV",0.3]
["sK",0.3]
["dV",0.02]
["dK",0.02]
["r",0.6]
[" "," "]
["W(V,K)",{"$f":"IF(B17<B16,B4*(B16-1)*(B17/B16)^B14,B13)","v":79450.741132652038},"IF(B17<B16,B4*(B16-1)*(B17/B16)^B14,B13)"]
["V-K",{"$f":"(B3-B4)","v":-50000},"B3-B4"]
["A",{"$f":"(B16-1)/(B16^B14)","v":0.43410256218739263},"(B16-1)/(B16^B14)"]
["b1",{"$f":"0.5-(B8-B7)/(B15^2)+SQRT(((B8-B7)/(B15^2)-0.5)^2 + (2*B8)/(B15^2))","v":1.3975274678557508},"0.5-(B8-B7)/(B15^2)+SQRT(((B8-B7)/(B15^2)-0.5)^2 + (2*B8)/(B15^2))"]
["h",{"$f":"SQRT(B5^2+B6^2-2*B9*B5*B6)","v":0.26832815729997478},"SQRT(B5^2+B6^2-2*B9*B5*B6)"]
["z*",{"$f":"(B14/(B14-1))","v":3.5155494421403506},"(B14/(B14-1))"]
["z",{"$f":"B3/B4","v":0.8},"B3/B4"]
[]
["THE INVESTMENT OPTION IS WORTH $79,451 DUE TO THE HIGH VOLATILITY"]
["OF VALUE AND COSTS, EVEN THOUGH THE NPV IS NEGATIVE.  YM MA"]
["SHOULD TAKE UP THE OPTION ESPECIALLY IF THERE IS NO PREMIUM"]
["BUT NOT CONSTRUCT THE GENERATING PLANT "]
["UNTIL HER CONSUMPTION RISES TO $880,000 (PERHAPS DUE TO HIGHER "]
["ELECTRICITY PRICES) OR THE COST OF THE PLANT FALLS."]
["THERE IS AN IMPLICIT ASSUMPTION THAT YM MA WILL LIVE FOREVER."]
[" "]

{"sheet":"Problem 5.6","index":24,"n_rows":25,"n_cols":3,"rows_kept":25,"cut":false,"hidden":false,"merged":[]}
[null,"                           American Perpetual Exchange Option"]
["Problem 5.6"," "]
["V",200000]
["K",250000]
["sV",0.3]
["sK",1]
["dV",0.02," "]
["dK",0]
["r",0]
[" "," "]
["W(V,K)",{"$f":"IF(B17<B16,B4*(B16-1)*(B17/B16)^B14,B13)","v":169267.4048507257},"IF(B17<B16,B4*(B16-1)*(B17/B16)^B14,B13)"]
["V-K",{"$f":"(B3-B4)","v":-50000},"B3-B4"]
["A",{"$f":"(B16-1)/(B16^B14)","v":0.85329592356765638},"(B16-1)/(B16^B14)"]
["b1",{"$f":"0.5-(B8-B7)/(B15^2)+SQRT(((B8-B7)/(B15^2)-0.5)^2 + (2*B8)/(B15^2))","v":1.036697247706422},"0.5-(B8-B7)/(B15^2)+SQRT(((B8-B7)/(B15^2)-0.5)^2 + (2*B8)/(B15^2))"]
["h",{"$f":"SQRT(B5^2+B6^2-2*B9*B5*B6)","v":1.0440306508910551},"SQRT(B5^2+B6^2-2*B9*B5*B6)"]
["z*",{"$f":"(B14/(B14-1))","v":28.25},"(B14/(B14-1))"]
["z",{"$f":"B3/B4","v":0.8},"B3/B4"]
[]
["THE INVESTMENT OPTION IS WORTH $169,267 DUE TO THE HIGH VOLATILITY"]
["OF THE INVESTMENT COSTS, EVEN THOUGH THE NPV IS NEGATIVE.  YM MA"]
["SHOULD TAKE UP THE OPTION ESPECIALLY IF THERE IS NO PREMIUM"]
["BUT NOT CONSTRUCT THE GENERATING PLANT "]
["UNTIL HER CONSUMPTION RISES TO $5,650,000 (VERY HIGH "]
["ELECTRICITY PRICES OR USAGE) OR THE COST OF THE PLANT FALLS."]
["THERE IS AN IMPLICIT ASSUMPTION THAT YM MA WILL LIVE FOREVER."]

{"sheet":"Exercise 6.1","index":25,"n_rows":27,"n_cols":3,"rows_kept":27,"cut":false,"hidden":false,"merged":[]}
["EXERCISE 6.1"]
["SPOT GAS PRICE -OP COST",{"$f":"3.25*0.7","v":2.2749999999999999},"3.25*0.7"]
["I TRADITIONAL PRESENT VALUE",{"$f":"B7*(B2-B5)","v":209000.00000000009},"B7*(B1-B5)"]
["II EUROPEAN OPTION VALUE",{"$f":"B17*B7","v":245705.7409370027},"B17*B7"]
["I    V(BE)",{"$f":"B8/B7","v":2.0659999999999998},"B8/B7"]
["INPUT"]
["RESERVES (DISCOUNTED BBLS)",1000000," "]
["PV DEVELOPMENT & OPS COST",2066000," "]
["CONVENIENCE YIELD",0.08," "]
["DISCOUNT RATE",0.05," "]
["COST ESCALATION",0," "]
["TIME TO DEVELOPMENT",4," "]
["VOLATILITY",0.2," "]
["NET DISCOUNT RATE",{"$f":"B15-B9","v":-0.03}," "]
["NET RATE",{"$f":"B10-B11","v":0.05}," "]
["OUTPUT"]
["REAL EUROPEAN OPTION PRICE",{"$f":"EXP(-B9*B12)*B2*B20-B5*B21*EXP(-B15*B12)","v":0.2457057409370027},"EXP(-B9*B12)*B1*B20-B5*B21*EXP(-B15*B12)"]
["d1",{"$f":"(LN(B2/B5)+(B15-B9+0.5*(B13^2))*B12)/(B13*SQRT(B12))","v":0.14091420426366735},"(LN(B1/B5)+(B15-B9+0.5*(B13^2))*B12)/(B13*SQRT(B12))"]
["d2",{"$f":"B18-B13*SQRT(B12)","v":-0.25908579573633267},"B18-B13*SQRT(B12)"]
["N(d1)",{"$f":"NORMSDIST(B18)","v":0.55603113963037809},"NORMSDIST(B18)"]
["N(d2)",{"$f":"NORMSDIST(B19)","v":0.39778452203748571},"NORMSDIST(B19)"]
[]
["IF THE PURCHASE PRICE (REAL OPTION PREMIUM) IS $250,000"]
["W W SHOULD ATTEMPT TO RENEGOTIATE (DOWNWARDS) "]
["THIS OFFER, OTHERWISE POLITELY DECLINE.  ADARKO"]
["PROBABLY KNOWS HOW TO VALUE REAL OPTIONS IN THIS EXERCISE,"]
["AND BELIEVES WW IS A MOTLEY FOOL."]

{"sheet":"Exercise 6.2","index":26,"n_rows":42,"n_cols":3,"rows_kept":42,"cut":false,"hidden":false,"merged":[]}
["EXERCISE 6.2",null," "]
["SPOT GAS PRICE -OP COST",{"$f":"3.25*0.7","v":2.2749999999999999}," "]
["I TRADITIONAL PRESENT VALUE",{"$f":"B11*(B2-B7)","v":209000.00000000009}," "]
["II EUROPEAN OPTION VALUE",{"$f":"B21*B11","v":245705.7409370027}," "]
["III FINITE AMERICAN OPTION",{"$f":"B29*B11","v":406485.28047519951}," "]
[]
["I    V(BE)",{"$f":"B12/B11","v":2.0659999999999998},"B12/B11"]
["III  V(AF)",{"$f":"B40","v":2.4907078199895509},"B40"]
["IV V(AP)",{"$f":"(B27/(B27-1))*B7","v":2.9779140317490498},"(B27/(B27-1))*B6"]
["INPUT"]
["RESERVES (DISCOUNTED BBLS)",1000000," "]
["PV DEVELOPMENT & OPS COST",2066000," "]
["CONVENIENCE YIELD",0.08," "]
["DISCOUNT RATE",0.05," "]
["COST ESCALATION",0," "]
["TIME TO DEVELOPMENT",4," "]
["VOLATILITY",0.2," "]
["NET DISCOUNT RATE",{"$f":"B19-B13","v":-0.03}," "]
["NET RATE",{"$f":"B14-B15","v":0.05}," "]
["OUTPUT"]
["REAL EUROPEAN OPTION PRICE",{"$f":"EXP(-B13*B16)*B2*B24-B7*B25*EXP(-B19*B16)","v":0.2457057409370027},"EXP(-B13*B16)*B1*B24-B6*B25*EXP(-B19*B16)"]
["d1",{"$f":"(LN(B2/B7)+(B19-B13+0.5*(B17^2))*B16)/(B17*SQRT(B16))","v":0.14091420426366735},"(LN(B1/B6)+(B19-B13+0.5*(B17^2))*B16)/(B17*SQRT(B16))"]
["d2",{"$f":"B22-B17*SQRT(B16)","v":-0.25908579573633267},"B22-B17*SQRT(B16)"]
["N(d1)",{"$f":"NORMSDIST(B22)","v":0.55603113963037809},"NORMSDIST(B22)"]
["N(d2)",{"$f":"NORMSDIST(B23)","v":0.39778452203748571},"NORMSDIST(B23)"]
["AMERICAN PERPETUITY",{"$f":"IF(B2<B9,B28*(B2^B27),B2-B7)","v":0.37853756381660658},"IF(B1<B9,B28*(B1^B27),B1-B6)"]
["b1",{"$f":"0.5-(B19-B13)/(B17^2)+SQRT(((B19-B13)/(B17^2)-0.5)^2 + 2*B14/(B17^2))","v":3.2655644370746373},"0.5-(B19-B13)/(B17^2)+SQRT(((B19-B13)/(B17^2)-0.5)^2 + 2*B14/(B17^2))"]
["A",{"$f":"(B9-B7)/(B9^B27)","v":2.5844207245074868E-2},"(B9-B6)/(B9^B27)"]
["AMERICAN FINITE CALL OPTION",{"$f":"IF(B2>=B40,B2-B7,(B21+B32*(B2/B40)^B31))","v":0.4064852804751995},"IF(B1>=B40,B1-B6,(B21+B32*(B1/B40)^B31))"]
["c(V*)",{"$f":"EXP(-B13*B16)*B40*B37-B7*B39*EXP(-B19*B16)","v":0.33980629592107492},"EXP(-B13*B16)*B40*B37-B6*B39*EXP(-B19*B16)"]
["g2",{"$f":"((-(B35-1)+SQRT((B35-1)^2+(4*B34)/B33)))/2","v":5.1684357740452347},"((-(B35-1)+SQRT((B35-1)^2+(4*B34)/B33)))/2"]
["A2",{"$f":"(B40/B31)*(1-EXP(-B13*B16)*NORMSDIST(B36))","v":0.25678177312087597},"(B40/B31)*(1-EXP(-B13*B16)*NORMSDIST(B36))"]
["h",{"$f":"1-EXP(-B19*B16)","v":0.18126924692201818},"1-EXP(-B19*B16)"]
["a",{"$f":"(2*B19)/(B17^2)","v":2.4999999999999996},"(2*B19)/(B17^2)"]
["b",{"$f":"(2*(B19-B13))/(B17^2)","v":-1.4999999999999996},"(2*(B19-B13))/(B17^2)"]
["d1(V*)",{"$f":"(LN(B40/B7)+(B19-B13+(B17^2)/2)*B16)/(B17*SQRT(B16))","v":0.36738141109889555},"(LN(B40/B6)+(B19-B13+(B17^2)/2)*B16)/(B17*SQRT(B16))"]
["N(d1(V*)",{"$f":"NORMSDIST(B36)","v":0.64333273227456633},"NORMSDIST(B36)"]
["d2(V*)",{"$f":"B36-B17*SQRT(B16)","v":-3.2618588901104473E-2},"B36-B17*SQRT(B16)"]
["N(d2(V*)",{"$f":"NORMSDIST(B38)","v":0.48698937295910472},"NORMSDIST(B38)"]
["V*",2.4907078199895509," "]
["V* solver=0",{"$f":"B30+((1-EXP(-B13*B16))*B37)*(B40/B31)+B7-B40","v":-3.7241515649100165E-7},"B30+((1-EXP(-B13*B16))*B37)*(B40/B31)+B6-B40"]
["Use Tools/Solver, set B41=0, changing B40."]

{"sheet":"Exercise 6.3","index":27,"n_rows":38,"n_cols":3,"rows_kept":38,"cut":false,"hidden":false,"merged":[]}
[null,"AMERICAN FINITE CALL APPROXIMATION (BAW)"]
["EXERCISE 6.3",null," "]
["I TRADITIONAL PRESENT VALUE",{"$f":"B9-B10","v":100}," "]
["II EUROPEAN OPTION VALUE",{"$f":"B17","v":111.89031057781148}," "]
["III FINITE AMERICAN OPTION",{"$f":"B22","v":165.18105494510107}," "]
["V*(AF)",{"$f":"B33","v":1159.0647854992999}," "]
[]
["INPUT"]
["ASSET VALUE",1100]
["INVESTMENT COST",1000," "]
["CONVENIENCE YIELD",0.08," "]
["INTEREST RATE",0.04," "]
["TIME TO DEVELOPMENT",2," "]
["VOLATILITY",0.2," "]
[" "," "," "]
["OUTPUT"]
["REAL EUROPEAN OPTION PRICE",{"$f":"EXP(-B11*B13)*B9*B20-B10*B21*EXP(-B12*B13)","v":111.89031057781148},"EXP(-B11*B13)*B9*B20-B10*B21*EXP(-B12*B13)"]
["d1",{"$f":"(LN(B9/B10)+(B12-B11+0.5*(B14^2))*B13)/(B14*SQRT(B13))","v":0.19555101604142694},"(LN(B9/B10)+(B12-B11+0.5*(B14^2))*B13)/(B14*SQRT(B13))"]
["d2",{"$f":"B18-B14*SQRT(B13)","v":-8.7291696433192123E-2},"B18-B14*SQRT(B13)"]
["N(d1)",{"$f":"NORMSDIST(B18)","v":0.5775191982712119},"NORMSDIST(B18)"]
["N(d2)",{"$f":"NORMSDIST(B19)","v":0.46521982705680842},"NORMSDIST(B19)"]
["AMERICAN FINITE CALL OPTION",{"$f":"IF(B9>=B33,B9-B10,(B17+B25*(B9/B33)^B24))","v":165.18105494510107},"IF(B9>=B33,B9-B10,(B17+B25*(B9/B33)^B24))"]
["c(V*)",{"$f":"EXP(-B11*B13)*B33*B30-B10*B32*EXP(-B12*B13)","v":142.76790651745142},"EXP(-B11*B13)*B33*B30-B10*B32*EXP(-B12*B13)"]
["g2",{"$f":"((-(B28-1)+SQRT((B28-1)^2+(4*B27)/B26)))/2","v":6.8163269191545943},"((-(B28-1)+SQRT((B28-1)^2+(4*B27)/B26)))/2"]
["A2",{"$f":"(B33/B24)*(1-EXP(-B11*B13)*NORMSDIST(B29))","v":76.117555257897394},"(B33/B24)*(1-EXP(-B11*B13)*NORMSDIST(B29))"]
["h",{"$f":"1-EXP(-B12*B13)","v":7.6883653613364245E-2},"1-EXP(-B12*B13)"]
["a",{"$f":"(2*B12)/(B14^2)","v":1.9999999999999996},"(2*B12)/(B14^2)"]
["b",{"$f":"(2*(B12-B11))/(B14^2)","v":-1.9999999999999996},"(2*(B12-B11))/(B14^2)"]
["d1(V*)",{"$f":"(LN(B33/B10)+(B12-B11+(B14^2)/2)*B13)/(B14*SQRT(B13))","v":0.38047103851449871},"(LN(B33/B10)+(B12-B11+(B14^2)/2)*B13)/(B14*SQRT(B13))"]
["N(d1(V*)",{"$f":"NORMSDIST(B29)","v":0.6482021045439994},"NORMSDIST(B29)"]
["d2(V*)",{"$f":"B29-B14*SQRT(B13)","v":9.7628326039879643E-2},"B29-B14*SQRT(B13)"]
["N(d2(V*)",{"$f":"NORMSDIST(B31)","v":0.5388862844910044},"NORMSDIST(B31)"]
["V*",1159.0647854992999," "]
["V* solver=0",{"$f":"B23+((1-EXP(-B11*B13))*B30)*(B33/B24)+B10-B33","v":1.076513287898706E-4},"B23+((1-EXP(-B11*B13))*B30)*(B33/B24)+B10-B33"]
["Use Tools/Solver, set B34=0, changing B33."]
[]
["Alfred should wait until the asset value increases to about $1160 before investing in this new model,"]
["assuming that the opportunity to acquire the model is proprietary, and only the benefit is stochastic."]

{"sheet":"Problem 6.4","index":28,"n_rows":38,"n_cols":3,"rows_kept":38,"cut":false,"hidden":false,"merged":[]}
[null,"                            LEE-PAXSON REAL AMERICAN PUT OPTION APPROXIMATION, CEA"]
["PROBLEM 6.4"]
["ASSET VALUE, V",1100]
["GUARANTEE , K",800]
["T/2",{"$f":"B6/2","v":1}," "]
["T",2," "]
["INTEREST RATE",0.04," "]
["DIVIDEND",0.08," "]
["VALUE VOLATILITY",0.2," "]
["AMERICAN PUT APPROX(CEA)",{"$f":"MAX(B29-((B29-B12)^2)/(B29-B11), B4-B3)","v":26.0468932265033},"MAX(B29-((B29-B12)^2)/(B29-B11), B4-B3)"]
["P1 EQ 6.13",{"$f":"B4*EXP(-B7*B6)*NORMSDIST(-B16)-B3*EXP(-B8*B6)*NORMSDIST(-B15)","v":26.046889576747873},"B4*EXP(-B7*B6)*NORMSDIST(-B16)-B3*EXP(-B8*B6)*NORMSDIST(-B15)"]
["P2 EQ 6.14",{"$f":"B4*EXP(-B7*B6)*B28-B3*EXP(-B8*B6)*B27+B4*EXP(-B7*B5)*B26-B3*EXP(-B8*B5)*B25","v":26.046891401625597},"B4*EXP(-B7*B6)*B28-B3*EXP(-B8*B6)*B27+B4*EXP(-B7*B5)*B26-B3*EXP(-B8*B5)*B25"]
["t2-t1",{"$f":"B6-B5","v":1},"B6-B5"]
["V*",407.93685949794269," "]
["d1",{"$f":"(LN(B3/B4)+((B7-B8+0.5*B9^2)*B6))/(B9*SQRT(B6))","v":0.98448260760305673},"(LN(B3/B4)+((B7-B8+0.5*B9^2)*B6))/(B9*SQRT(B6))"]
["d2",{"$f":"B15-B9*SQRT(B6)","v":0.70163989512843772},"B15-B9*SQRT(B6)"]
["N1",{"$f":"NORMSDIST(B15)","v":0.83756086055945067},"NORMSDIST(B15)"]
["N2",{"$f":"NORMSDIST(B16)","v":0.75854811745843409},"NORMSDIST(B16)"]
["Value Match EQ 6.15",{"$f":"B4-B14-B4*EXP(-B7*B13)*NORMSDIST(-B24)+B14*EXP(-B8*B13)*NORMSDIST(-B22)","v":-7.1130422156784334E-6},"B4-B14-B4*EXP(-B7*B13)*NORMSDIST(-B24)+B14*EXP(-B8*B13)*NORMSDIST(-B22)"]
["r(t1/t2)",{"$f":"SQRT(B5/B6)","v":0.70710678118654757},"SQRT(B5/B6)"]
["d1,t1",{"$f":"(LN(B3/B14)+(B7-B8+0.5*B9^2)*B5)/B9*SQRT(B5)","v":4.8597652624537968},"(LN(B3/B14)+(B7-B8+0.5*B9^2)*B5)/B9*SQRT(B5)"]
["d1,t2",{"$f":"(LN(B14/B4)+(B7-B8+0.5*B9^2)*B13)/B9*SQRT(B13)","v":-3.4674966068611237},"(LN(B14/B4)+(B7-B8+0.5*B9^2)*B13)/B9*SQRT(B13)"]
["d2,t1",{"$f":"B21-B9*SQRT(B5)","v":4.6597652624537966},"B21-B9*SQRT(B5)"]
["d2,t2",{"$f":"B22-B9*SQRT(B13)","v":-3.6674966068611239},"B22-B9*SQRT(B13)"]
["N(-d1,t1)",{"$f":"NORMSDIST(-B21)","v":5.876252329173326E-7},"NORMSDIST(-B21)"]
["N(-d2,t1)",{"$f":"NORMSDIST(-B23)","v":1.5828509993820461E-6},"NORMSDIST(-B23)"]
["B1",{"$f":"BiVariateNormalCDF(B21,-B15,-B20)","v":0.16243855190408071},"BiVariateNormalCDF(B21,-B15,-B20)"]
["B2",{"$f":"BiVariateNormalCDF(B23,-B16,-B20)","v":0.24145029979775751},"BiVariateNormalCDF(B23,-B16,-B20)"]
["P (∞)    EQ 6.17",{"$f":"(-B4/(B31-1))*((B3/B30)^B31)","v":241.23834196625748},"(-B4/(B31-1))*((B3/B30)^B31)"]
["V* (∞)   EQ 6.18",{"$f":"(B31/(B31-1))*B4","v":287.68943743823394},"(B31/(B31-1))*B4"]
["h              EQ 6.19",{"$f":"(-(B7-B8-0.5*B9^2)-SQRT((B7-B8-0.5*B9^2)^2+2*(B9^2)*B7))/(B9^2)","v":-0.56155281280883029},"(-(B7-B8-0.5*B9^2)-SQRT((B7-B8-0.5*B9^2)^2+2*(B9^2)*B7))/(B9^2)"]
[" "," "," "]
["Use Tools/Solver, set B19=0, changing B14."]
[]
["At $55, PHF is charging too much for this put option, so Alfred Marshall should wait.  "]
["But if PHF lowers the quarantee premium to below $26, or raises the guarantee to $900,  "]
["Alfred should take up the guarantee but not exercise it until the asset value falls below $407 (if X=800), a sharp"]
["decline from the current value.  "]

{"sheet":"Problem 6.5","index":29,"n_rows":38,"n_cols":3,"rows_kept":38,"cut":false,"hidden":false,"merged":[]}
[null,"                            LEE-PAXSON REAL AMERICAN PUT OPTION APPROXIMATION, CEA"]
["PROBLEM 6.5"]
["RENT, V",42]
["TAKE BACK RENT, K",40]
["T/2",{"$f":"B6/2","v":0.5}," "]
["T",1," "]
["INTEREST RATE",0.05," "]
["YIELD",0," "]
["RENT VOLATILITY",0.4," "]
["AMERICAN PUT APPROX(CEA)",{"$f":"MAX(B29-((B29-B12)^2)/(B29-B11), B4-B3)","v":4.1946901329592077},"MAX(B29-((B29-B12)^2)/(B29-B11), B4-B3)"]
["P1 EQ 6.13",{"$f":"B4*EXP(-B7*B6)*NORMSDIST(-B16)-B3*EXP(-B8*B6)*NORMSDIST(-B15)","v":4.5590418140149591},"B4*EXP(-B7*B6)*NORMSDIST(-B16)-B3*EXP(-B8*B6)*NORMSDIST(-B15)"]
["P2 EQ 6.14",{"$f":"B4*EXP(-B7*B6)*B28-B3*EXP(-B8*B6)*B27+B4*EXP(-B7*B5)*B26-B3*EXP(-B8*B5)*B25","v":4.3787597321718881},"B4*EXP(-B7*B6)*B28-B3*EXP(-B8*B6)*B27+B4*EXP(-B7*B5)*B26-B3*EXP(-B8*B5)*B25"]
["t2-t1",{"$f":"B6-B5","v":0.5},"B6-B5"]
["V*",31.073118431287813," "]
["d1",{"$f":"(LN(B3/B4)+((B7-B8+0.5*B9^2)*B6))/(B9*SQRT(B6))","v":0.44697541042358013},"(LN(B3/B4)+((B7-B8+0.5*B9^2)*B6))/(B9*SQRT(B6))"]
["d2",{"$f":"B15-B9*SQRT(B6)","v":4.6975410423580111E-2},"B15-B9*SQRT(B6)"]
["N1",{"$f":"NORMSDIST(B15)","v":0.67255359286272476},"NORMSDIST(B15)"]
["N2",{"$f":"NORMSDIST(B16)","v":0.51873358723653595},"NORMSDIST(B16)"]
["Value Match EQ 6.15",{"$f":"B4-B14-B4*EXP(-B7*B13)*NORMSDIST(-B24)+B14*EXP(-B8*B13)*NORMSDIST(-B22)","v":4.1608758039046734E-6},"B4-B14-B4*EXP(-B7*B13)*NORMSDIST(-B24)+B14*EXP(-B8*B13)*NORMSDIST(-B22)"]
["r(t1/t2)",{"$f":"SQRT(B5/B6)","v":0.70710678118654757},"SQRT(B5/B6)"]
["d1,t1",{"$f":"(LN(B3/B14)+(B7-B8+0.5*B9^2)*B5)/B9*SQRT(B5)","v":0.6475799372546599},"(LN(B3/B14)+(B7-B8+0.5*B9^2)*B5)/B9*SQRT(B5)"]
["d1,t2",{"$f":"(LN(B14/B4)+(B7-B8+0.5*B9^2)*B13)/B9*SQRT(B13)","v":-0.3315205935205065},"(LN(B14/B4)+(B7-B8+0.5*B9^2)*B13)/B9*SQRT(B13)"]
["d2,t1",{"$f":"B21-B9*SQRT(B5)","v":0.36473722478004084},"B21-B9*SQRT(B5)"]
["d2,t2",{"$f":"B22-B9*SQRT(B13)","v":-0.61436330599512556},"B22-B9*SQRT(B13)"]
["N(-d1,t1)",{"$f":"NORMSDIST(-B21)","v":0.25862833849475553},"NORMSDIST(-B21)"]
["N(-d2,t1)",{"$f":"NORMSDIST(-B23)","v":0.3576537843421449},"NORMSDIST(-B23)"]
["B1",{"$f":"BiVariateNormalCDF(B21,-B15,-B20)","v":0.14453721168404396},"BiVariateNormalCDF(B21,-B15,-B20)"]
["B2",{"$f":"BiVariateNormalCDF(B23,-B16,-B20)","v":0.19340186006678867},"BiVariateNormalCDF(B23,-B16,-B20)"]
["P (∞)    EQ 6.17",{"$f":"(-B4/(B31-1))*((B3/B30)^B31)","v":13.140290653808901},"(-B4/(B31-1))*((B3/B30)^B31)"]
["V* (∞)   EQ 6.18",{"$f":"(B31/(B31-1))*B4","v":15.384615384615385},"(B31/(B31-1))*B4"]
["h              EQ 6.19",{"$f":"(-(B7-B8-0.5*B9^2)-SQRT((B7-B8-0.5*B9^2)^2+2*(B9^2)*B7))/(B9^2)","v":-0.625},"(-(B7-B8-0.5*B9^2)-SQRT((B7-B8-0.5*B9^2)^2+2*(B9^2)*B7))/(B9^2)"]
[" "," "," "]
["Use Tools/Solver, set B19=0, changing B14."]
[]
["This right is worth over £4 per SF or around 10% of the current rent.  If Global can exercise this right"]
["anytime over the next year, it should do so if rent falls to £31 (when the intrinsic value would be £9)."]
["Also, the put with any positive intrinsic value just before the end of the year should be exercised."]
["Per square foot calculations should be multiplied by 10,000 to figure the total value of this arrangement."]

{"sheet":"Problem 6.6","index":30,"n_rows":72,"n_cols":9,"rows_kept":72,"cut":false,"hidden":false,"merged":[]}
[null,"                            LEE-PAXSON REAL AMERICAN PUT OPTION APPROXIMATION, CEAM"]
["PROBLEM 6.6"]
["N",1,{"$f":"B3+1","v":2},{"$f":"C3+1","v":3},4,5,6,7,8]
["BJ T/N",{"$f":"(B3*B5)/8","v":0.5},1,1.5,2,2.5,3,3.5,{"$f":"(I3*I5)/8.01","v":3.9950062421972534}]
["T",4,{"$f":"B5","v":4},4,4,4,4,4,4]
["INTEREST RATE",0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05]
["YIELD",0,0,0,0,0,0,0,0]
["VALUE VARIANCE",{"$f":"B9^2","v":0.16000000000000003},0.16000000000000003,0.16000000000000003,0.16000000000000003,0.16000000000000003,0.16000000000000003,0.16000000000000003,0.16000000000000003]
["VALUE VOLATILITY",0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4]
["ASSET VALUE, V",42,42,42,42,42,42,42,42]
["PUT EXERCISE PRICE, K",40,{"$f":"B11","v":40},{"$f":"C11","v":40},40,40,40,40,40]
["P1 EQ 6.13",{"$f":"B11*EXP(-B6*B5)*NORMSDIST(-B23)-B10*EXP(-B7*B5)*NORMSDIST(-B22)","v":7.5171025331236194},7.5171025331236194,7.5171025331236194,7.5171025331236194,7.5171025331236194,7.5171025331236194,7.5171025331236194,7.5171025331236194]
["P2 EQ 6.14",{"$f":"B11*EXP(-B6*B5)*B36-B10*EXP(-B7*B5)*B35+B11*EXP(-B6*B4)*B34-B10*EXP(-B7*B4)*B33","v":7.6471145218298471},7.8724783380396701,8.0135416285812848,8.0668750580826121,8.0434323802897953,7.9502143181580998,7.785820996542224,7.5206969631340206]
["AMERICAN PUT APPROX, CEAM",{"$f":"MAX(B16-((B16-B13)^2)/(B16-B12), B11-B10)","v":7.771797258877803},8.1880365375108557,8.4322788707565195,8.5213535976946275,8.4824217777818411,8.3241836372692255,8.0317730558191833,7.524287319721628]
["P1(s*)   EQ A3",{"$f":"B11*EXP(-B6*B5)*NORMSDIST(-B40)-B10*EXP(-B7*B5)*NORMSDIST(-B39)","v":10.688864403500391},10.688864403500391,10.688864403500391,10.688864403500391,10.688864403500391,10.688864403500391,10.688864403500391,10.688864403500391]
["U*   EQ A6",{"$f":"MIN(B17,B15)","v":10.688864403500391},10.688864403500391,10.688864403500391,10.688864403500391,10.688864403500391,10.688864403500391,10.688864403500391,10.688864403500391]
["P (∞)    EQ  6.17",{"$f":"(-B11/(B19-1))*((B10/B18)^B19)","v":13.140290653808901},13.140290653808901,13.140290653808901,13.140290653808901,13.140290653808901,13.140290653808901,13.140290653808901,13.140290653808901]
["V* (∞)   EQ  6.18",{"$f":"(B19/(B19-1))*B11","v":15.384615384615385},15.384615384615385,15.384615384615385,15.384615384615385,15.384615384615385,15.384615384615385,15.384615384615385,15.384615384615385]
["h",{"$f":"(-(B6-B7-0.5*B8)-SQRT((B6-B7-0.5*B8)^2+2*B8*B6))/B8","v":-0.625},{"$f":"(-(C6-C7-0.5*C8)-SQRT((C6-C7-0.5*C8)^2+2*C8*C6))/C8","v":-0.625},{"$f":"(-(D6-D7-0.5*D8)-SQRT((D6-D7-0.5*D8)^2+2*D8*D6))/D8","v":-0.625},-0.625,-0.625,-0.625,-0.625,-0.625]
["t2-t1",{"$f":"B5-B4","v":3.5},{"$f":"C5-C4","v":3},2.5,2,1.5,1,0.5,4.993757802746579E-3]
["V*",27.961324092802744,27.943193082093554,27.988265133605736,28.12814917216074,28.425955825262786,29.017788258916713,30.323369233469084,33]
["d1",{"$f":"(LN(B10/B11)+((B6-B7+0.5*B8)*B5))/(SQRT(B8*B5))","v":0.71098770521179},{"$f":"(LN(C10/C11)+((C6-C7+0.5*C8)*C5))/(SQRT(C8*C5))","v":0.71098770521179},0.71098770521179,0.71098770521179,0.71098770521179,0.71098770521179,0.71098770521179,0.71098770521179]
["d2",{"$f":"B22-SQRT(B8*B5)","v":-8.9012294788210045E-2},-8.9012294788210045E-2,-8.9012294788210045E-2,-8.9012294788210045E-2,-8.9012294788210045E-2,-8.9012294788210045E-2,-8.9012294788210045E-2,-8.9012294788210045E-2]
["N1",{"$f":"NORMSDIST(B22)","v":0.76145407266321063},{"$f":"NORMSDIST(C22)","v":0.76145407266321063},0.76145407266321063,0.76145407266321063,0.76145407266321063,0.76145407266321063,0.76145407266321063,0.76145407266321063]
["N2",{"$f":"NORMSDIST(B23)","v":0.46453606953986881},0.46453606953986881,0.46453606953986881,0.46453606953986881,0.46453606953986881,0.46453606953986881,0.46453606953986881,0.46453606953986881]
["Value Match EQ 6.15",{"$f":"B11-B21-B11*EXP(-B6*B20)*NORMSDIST(-B32)+B21*EXP(-B7*B20)*NORMSDIST(-B30)","v":-4.2987455975307398E-5},6.8112080853666157E-5,-1.0440758999585853E-4,6.4493485018246588E-5,-3.6514624138561658E-5,4.0391718606258564E-5,7.9506893676750678E-5,9.9862688276388667E-3]
["SSE",{"$f":"B26^2","v":1.8479213712289917E-9},4.6392555582163559E-9,1.0900944848743299E-8,4.1594096097987973E-9,1.3333177759804297E-9,1.6314909319671744E-9,6.3213461421261367E-9,9.9725565097871747E-5]
["r(t1/t2)",{"$f":"SQRT(B4/B5)","v":0.35355339059327379},{"$f":"SQRT(C4/C5)","v":0.5},0.61237243569579447,0.70710678118654757,0.79056941504209488,0.8660254037844386,0.93541434669348533,0.99937558532781523]
["d1,t1",{"$f":"(LN(B10/B21)+(B6-B7+0.5*B8)*B4)/(SQRT(B8*B4))","v":1.6682322879374922},1.3437399686123035,1.2265499377935569,1.1683150463362399,1.1310944671371124,1.0966199501538678,1.0433223308563171,0.95123505050039259]
["d1,t2",{"$f":"(LN(B21/B11)+(B6-B7+0.5*B8)*B20)/(SQRT(B8*B20))","v":0.12954529075019905},4.5169253389909819E-2,-5.0745281734987949E-2,-0.16282659094520269,-0.29919861729564318,-0.47742605983656938,-0.74939451394399093,-6.7826564001694685]
["d2,t1",{"$f":"B29-SQRT(B8*B4)","v":1.3853895754628731},0.94373996861230347,0.73665198923692121,0.60262962138700182,0.49863893510343649,0.40379962712631678,0.29499085350152876,0.15173458223814029]
["d2,t2",{"$f":"B30-SQRT(B8*B20)","v":-0.61878618660458928},-0.64765106963764119,-0.68320081376866382,-0.72851201589444081,-0.78909656585227883,-0.87742605983656941,-1.0322372264186099,-6.8109230103029716]
["N(-d1,t1)",{"$f":"NORMSDIST(-B29)","v":4.7634811831384072E-2},{"$f":"NORMSDIST(-C29)","v":8.9516243920762739E-2},0.10999589754059325,0.12133985416267357,0.12900766640447026,0.13640378135304831,0.14839951602092827,0.17074253462762357]
["N(-d2,t1)",{"$f":"NORMSDIST(-B31)","v":8.2966688418506518E-2},{"$f":"NORMSDIST(-C31)","v":0.17265127206174313},0.23066700516608596,0.27337755511820461,0.30901688542256078,0.34318003535482822,0.38400043341412005,0.43969814014187558]
["B1",{"$f":"BiVariateNormalCDF(B29,-B22,-B28)","v":0.21422918753723949},{"$f":"BiVariateNormalCDF(C29,-C22,-C28)","v":0.18620408056856064},0.16647111353202637,0.15055602753634886,0.13591997506237918,0.12036207934310661,9.9533323717742733E-2,6.7803427672955996E-2]
["B2",{"$f":"BiVariateNormalCDF(B31,-B23,-B28)","v":0.47050489718611355},{"$f":"BiVariateNormalCDF(C31,-C23,-C28)","v":0.39339835201169637},0.33787553447462071,0.29289276140218357,0.25228487880681139,0.21128034736067269,0.16198627733558035,9.5765790318256938E-2]
["VOL*  EQ A2",{"$f":"B9+(B11/B10)*(10*(B6-B7)*(B6-B7)+B38*B9)*SQRT(B5)","v":0.52380952380952384},0.52380952380952384,0.52380952380952384,0.52380952380952384,0.52380952380952384,0.52380952380952384,0.52380952380952384,0.52380952380952384]
["a",0.1,{"$f":"B38","v":0.1},0.1,0.1,0.1,0.1,0.1,0.1]
["d1",{"$f":"(LN(B10/B11)+((B6-B7+0.5*B37^2)*B5))/(B37*SQRT(B5))","v":0.76129104415307247},{"$f":"(LN(C10/C11)+((C6-C7+0.5*C37^2)*C5))/(C37*SQRT(C5))","v":0.76129104415307247},0.76129104415307247,0.76129104415307247,0.76129104415307247,0.76129104415307247,0.76129104415307247,0.76129104415307247]
["d2",{"$f":"B39-B37*SQRT(B5)","v":-0.2863280034659752},{"$f":"C39-C37*SQRT(C5)","v":-0.2863280034659752},-0.2863280034659752,-0.2863280034659752,-0.2863280034659752,-0.2863280034659752,-0.2863280034659752,-0.2863280034659752]
[" "," "]
[" "," ",null,null,null,null,null,"MAX",{"$f":"MAX(B14:I14)","v":8.5213535976946275}]
["Use Tools/Solver, set I43=0, changing B21:I21",null,"CEAM is Max B14:I14",null,null,null,null,null,{"$f":"SUM(B27:I27)","v":9.9756398784109804E-5}]
["AN ACCURATE VALUE IS £8,521,400.  THE PUTBACK SHOULD BE EXECUTED WHEN RENTS=£28 OR AT YEAR END,"]
["IF THE THEN RENTS <£40 PER SQUARE FOOT."]
[]
[{"$f":"A12","v":"P1 EQ 6.13"},"J11*EXP(-J6*J5)*NORMSDIST(-J23)-J10*EXP(-J7*J5)*NORMSDIST(-J22)"]
[{"$f":"A13","v":"P2 EQ 6.14"},"J11*EXP(-J6*J5)*J36-J10*EXP(-J7*J5)*J35+J11*EXP(-J6*J4)*J34-J10*EXP(-J7*J4)*J33"]
["AMERICAN PUT APPROX, CEAM","MAX(J16-((J16-J13)^2)/(J16-J12), J11-J10)"]
["P1(s*)   EQ A3","J11*EXP(-J6*J5)*NORMSDIST(-J41)-J10*EXP(-J7*J5)*NORMSDIST(-J40)"]
["U*   EQ A6","MIN(J17,J15)"]
["P (∞)    EQ  6.17","(-J11/(J19-1))*((J10/J18)^J19)"]
["V* (∞)   EQ  6.18","(J19/(J19-1))*J11"]
["h","(-(J6-J7-0.5*J8)-SQRT((J6-J7-0.5*J8)^2+2*J8*J6))/J8"]
[{"$f":"A22","v":"d1"},"(LN(J10/J11)+((J6-J7+0.5*J8)*J5))/(SQRT(J8*J5))"]
["d2","J22-SQRT(J8*J5)"]
["N1","NORMSDIST(J22)"]
["N2","NORMSDIST(J23)"]
["Value Match EQ 6.15","J11-J21-J11*EXP(-J6*J20)*NORMSDIST(-J32)+J21*EXP(-J7*J20)*NORMSDIST(-J30)"]
["SSE","J26^2"]
["r(t1/t2)","SQRT(J4/J5)"]
[{"$f":"A29","v":"d1,t1"},"(LN(J10/J21)+(J6-J7+0.5*J8)*J4)/(SQRT(J8*J4))"]
["d1,t2","(LN(J21/J11)+(J6-J7+0.5*J8)*J20)/(SQRT(J8*J20))"]
["d2,t1","J29-SQRT(J8*J4)"]
["d2,t2","J30-SQRT(J8*J20)"]
["N(-d1,t1)","NORMSDIST(-J29)"]
["N(-d2,t1)","NORMSDIST(-J31)"]
["B1","BiVariateNormalCDF(J29,-J22,-J28)"]
["B2","BiVariateNormalCDF(J31,-J23,-J28)"]
["VOL*  EQ A2","J9+(J11/J10)*(10*(J6-J7)*(J6-J7)+J38*J9)*SQRT(J5)"]
[{"$f":"A39","v":"d1"},"(LN(J10/J11)+((J6-J7+0.5*J37^2)*J5))/(J37*SQRT(J5))"]
[{"$f":"A40","v":"d2"},"J39-J37*SQRT(J5)"]

{"sheet":"Exercise 7.1","index":31,"n_rows":41,"n_cols":10,"rows_kept":41,"cut":false,"hidden":false,"merged":[]}
["STAGE ONE"," ","STAGE TWO"," ","Exercise 7.1"]
["INPUT"," "," ","INPUT"," ",null," "]
["V",100,{"$f":"B3","v":100},"V","STAGE","VOLATILITY","f"," ","V^","V^-SKN"]
["K1",90,{"$f":"B4","v":90},"K1",1,{"$f":"B33","v":0.2},{"$f":"B27","v":3.00000000000523}," ",{"$f":"B29","v":134.99999996656956},{"$f":"I4-B4","v":44.999999966569561}]
["K2",10,10,"K2",2,{"$f":"C33","v":0.44721359550089362},{"$f":"C34","v":1.3660254037822379}," ",{"$f":"C29","v":126.83685009645247},{"$f":"I5-B5-B4","v":26.836850096452466}]
["sV",0.2,0.2,"sV"]
["sK1",0.2,0.2,"sK1","STAGE","ROV","A","b","h1","h2"]
["sK2",{"$f":"B7","v":0.2},0.2,"sK2",1,{"$f":"B35","v":18.289894577216028},{"$f":"B26","v":0.14814814705475093},{"$f":"B27","v":3.00000000000523},{"$f":"B28","v":-2.0000000014743669}]
["r VK1",0.5,0.5,"r VK1",2,{"$f":"C35","v":10.312906066335906},{"$f":"C26","v":3.3292304811496573E-2},{"$f":"C27","v":4.0980762113538578},{"$f":"C28","v":-2.7320508045926193},{"$f":"C30","v":-0.36602540257963467}]
["r VK2",0.5,0.5,"r VK2"]
["r K1K2",0,0,"r K1K2","CALCULATOR RESULT"]
["r",0.04,0.04,"r","STEP 1","V1^",{"$f":"(G4/(G4-1))*B4","v":134.99999999988233},"(G4/(G4-1))*B4"]
["qV",0,0,"qV","STEP 2","A1",{"$f":"(G4^-G4)*(G4-1)^(G4-1)","v":0.14814814814783397},"(G4^-G4)*(G4-1)^(G4-1)"]
["qK1",0.04,0.04,"qK1","STEP 3","ROV1",{"$f":"G13*(B3^G4)*B4^(1-G4)","v":18.289894833076019},"G13*(B3^G4)*B4^(1-G4)"]
["qK2",0.04,0.04,"qK2","STEP 4","V2^",{"$f":"(G4/(G4-1))*((G5*(G4-1)/(G5-1))^(1/G4))*(B4^((G4-1)/G4))*(B5^(1/G4))","v":126.83684960657395},"(G4/(G4-1))*((G5*(G4-1)/(G5-1))^(1/G4))*(B4^((G4-1)/G4))*(B5^(1/G4))"]
["l1",0,0,"l1","STEP 5","B",{"$f":"((G5-1)^(G5-1))/(G5^G5)","v":0.45205772181688819},"((G5-1)^(G5-1))/(G5^G5)"]
["l2",0.05,0.05,"l2","STEP 6","ROV2",{"$f":"G16*(G14^G5)*(B5^(1-G5))","v":10.312906105758509},"G16*(G14^G5)*(B4^(1-G5))"]
["s1^2",{"$f":"B6^2+B7^2-2*B9*B6*B7","v":4.0000000000000008E-2},{"$f":"(B27^2)*(C6^2)+((1-B27)^2)*(C7^2)+(C8^2)+2*B27*(1-B27)*C9*C6*C7-2*B27*C10*C6*C8-2*(1-B27)*C11*C7*C8","v":0.2000000000008369},"s2^2"," "]
["Q(b,h)",{"$f":"0.5*(B18)*B27*(B27-1)+B27*(B13-B14)-(B12+B16-B14)","v":3.1383229348591613E-13},{"$f":"0.5*(C18)*C34*(C34-1)+C34*(C12+C16-C15)-(C12+C17-C15)","v":-1.7194579093882112E-13},"Q(b,h)","0.5*(C18)*C34*(C34-1)+C34*(C12+C16-C15)-(C12+C17-C15)"]
["SP1",{"$f":"B27*B26*(B29^(B27-1))*(B31^B28)-1","v":-1.4482668619919536E-8},{"$f":"C27*C26*(C29^(C27-1))*(C31^C28)*(C32^C30)-B27*B26*(C29^(B27-1))*(C31^(1-B27))","v":6.8823367005421687E-9},"SP1","C27*C26*(C29^(C27-1))*(C31^C28)*(C32^C30)-B27*B26*(C29^(B27-1))*(C31^(1-B27))"]
["SP2",{"$f":"B28*B26*(B29^B27)*(B31^(B28-1))+1","v":1.3994860603716575E-8},{"$f":"C28*C26*(C29^C27)*(C31^(C28-1))*(C32^C30)-(1-B27)*B26*(C29^B27)*(C31^(-B27))","v":-5.5618678551638823E-9},"SP2","C28*C26*(C29^C27)*(C31^(C28-1))*(C32^C30)-(1-B27)*B26*(C29^B27)*(C31^(-B27))"]
["VM1",{"$f":"B26*(B29^B27)*(B31^B28)-(B29-B31)","v":-6.295115468901713E-7},{"$f":"C30*C26*(C29^C27)*(C31^C28)*(C32^(C30-1))+1","v":-8.7196647680087835E-9},"SP3","C30*C26*(C29^C27)*(C31^C28)*(C32^(C30-1))+1"]
[" "," ",{"$f":"C26*(C29^C27)*(C31^C28)*(C32^C30)-B26*(C29^B27)*(C31^(1-B27))+C32","v":1.7092559545517361E-7},"VM1","C26*(C29^C27)*(C31^C28)*(C32^C30)-B26*(C29^B27)*(C31^(1-B27))+C32"]
["SOLVER: SET D25=0, CHANGING B26:C30"]
["SOLVER",{"$f":"SUM(ABS(B19:B22))","v":6.579893899461009E-7},{"$f":"SUM(ABS(C19:C23))","v":1.9208963672467938E-7},{"$f":"SUM(ABS(B25:C25))","v":8.5007902667078028E-7}]
["A12",0.14814814705475093,3.3292304811496573E-2,"A24"]
["b12",3.00000000000523,4.0980762113538578,"b24"]
["h1,12",-2.0000000014743669,-2.7320508045926193,"h2,14"]
["V1*",134.99999996656956,126.83685009645247,"V2*"]
[null," ",-0.36602540257963467,"h2,24"]
["K1*",{"$f":"B4","v":90},{"$f":"C4","v":90},"K1*"]
[null,null,{"$f":"C5","v":10},"K2*"]
["VOLATILITY",{"$f":"SQRT(B18)","v":0.2},{"$f":"SQRT(C18)","v":0.44721359550089362},"VOLATILITY"]
["b12",{"$f":"B27","v":3.00000000000523},{"$f":"C27/B34","v":1.3660254037822379},"f2"]
["ROV 1",{"$f":"IF(B3<B29,B26*(B3^B27)*(B4^B28),B29-B31)","v":18.289894577216028},{"$f":"IF(C3<C29,C26*(C3^C27)*(C4^C28)*(C5^C30),C3-C31-C32)","v":10.312906066335906},"ROV 2","IF(C3<C29,C26*(C3^C27)*(C4^C28)*(C5^C30),C3-C31-C32)"]
["Q(b,h)","0.5*(B18)*B27*(B27-1)+B27*(B13-B14)-(B12+B16-B14)"]
["SP1","B27*B26*(B29^(B27-1))*(B31^B28)-1"]
["SP2","B28*B26*(B29^B27)*(B31^(B28-1))+1"]
["VM1","B26*(B29^B27)*(B31^B28)-(B29-B31)"]
["ROV 1","IF(B3<B29,B26*(B3^B27)*(B4^B28),B27-B31)"]
["s2^2","(B27^2)*(C6^2)+((1-B27)^2)*(C7^2)+(C8^2)+2*B27*(1-B27)*C9*C6*C7-2*B27*C10*C6*C8-2*(1-B27)*C11*C7*C8"]

{"sheet":"Problem 7.2","index":32,"n_rows":38,"n_cols":3,"rows_kept":38,"cut":false,"hidden":false,"merged":[]}
[null,"                                       GESKE EUROPEAN COMPOUND CALL OPTION"]
["Problem 7.2"]
["DEVELOPMENT TIME t' ",1]
["INVESTMENT TIME    t ",5]
["INTEREST RATE",0.04]
["V YIELD",0.04]
["VALUE VOLATILITY",0.2]
["V ",900000," "]
["D",150000]
["K",819000]
["REAL OPTION VALUE ",{"$f":"B8*EXP(-B6*B4)*B26-B10*EXP(-B5*B4)*B27-B9*EXP(-B5*B3)*B25","v":46884.589858220977},"B8*EXP(-B6*B4)*B26-B10*EXP(-B5*B4)*B27-B9*EXP(-B5*B3)*B25"]
["t-t' ",{"$f":"B4-B3","v":4},"B4-B3"]
["V*",893329.08626343647," "]
["d1",{"$f":"(LN(B13/B10)+((B5-B6+0.5*B7^2)*B12))/(B7*SQRT(B12))","v":0.41717736697425456},"(LN(B13/B10)+((B5-B6+0.5*B7^2)*B12))/(B7*SQRT(B12))"]
["d2",{"$f":"B14-B7*SQRT(B12)","v":1.7177366974254538E-2},"B14-B7*SQRT(B12)"]
["N1",{"$f":"NORMSDIST(B14)","v":0.66172566066787608},"NORMSDIST(B14)"]
["N2",{"$f":"NORMSDIST(B15)","v":0.5068524409679277},"NORMSDIST(B15)"]
["EQ 7.4",{"$f":"B13*EXP(-B6*B12)*B16-B10*EXP(-B5*B12)*B17","v":149999.99999999849},"B13*EXP(-B6*B12)*B16-B10*EXP(-B5*B12)*B17"]
["EQ 7.4-D",{"$f":"B18-B9","v":-1.5133991837501526E-9},"B18-B9"]
["r(t'/t)",{"$f":"SQRT(B3/B4)","v":0.44721359549995793},"SQRT(B3/B4)"]
["d1,t1",{"$f":"(LN(B8/B13)+(B5-B6+0.5*B7^2)*B3)/(B7*SQRT(B3))","v":0.13719866340769818},"(LN(B8/B13)+(B5-B6+0.5*B7^2)*B3)/(B7*SQRT(B3))"]
["d1,t2",{"$f":"(LN(B8/B10)+(B5-B6+0.5*B7^2)*B4)/(B7*SQRT(B4))","v":0.43449188805186867},"(LN(B8/B10)+(B5-B6+0.5*B7^2)*B4)/(B7*SQRT(B4))"]
["d2,t1",{"$f":"B21-B7*SQRT(B3)","v":-6.2801336592301832E-2},"B21-B7*SQRT(B3)"]
["d2,t2",{"$f":"B22-B7*SQRT(B4)","v":-1.2721707448089314E-2},"B22-B7*SQRT(B4)"]
["N2",{"$f":"NORMSDIST(B23)","v":0.47496235076264615},"NORMSDIST(B23)"]
["B1",{"$f":"BiVariateNormalCDF(B21,B22,B20)","v":0.43745315090886272},"BiVariateNormalCDF(B21,B22,B20)"]
["B2",{"$f":"BiVariateNormalCDF(B23,B24,B20)","v":0.30871409787566351},"BiVariateNormalCDF(B23,B24,B20)"]
["V-D-K",{"$f":"B8-B9-B10","v":-69000},"B8-B9-B10"]
["USE TOOLS/SOLVER, SETTING B19=0 BY CHANGING B13."]
[" "]
["This is an out-of-the-money call option, with 150,000 paid at t=1 in order to maintain the"]
["option to pay 819,000 at T=5 to receive V.  Using solver V* (the Putney house value"]
["that would justify paying D) is slightly below the current value, so the European part of K is costly."]
["The RO value of the bungalow site is £46,884, even thoughy the net present value of paying D "]
["and K for V is negative, due to the volatility of Putney house prices."]
[" "]
[" "]
[" "]

{"sheet":"Problem 7.3","index":33,"n_rows":44,"n_cols":3,"rows_kept":44,"cut":false,"hidden":false,"merged":[]}
[null,"        EUROPEAN COMPOUND EXCHANGE OPTION"]
["Problem 7.3"]
["DEVELOPMENT TIME t' ",1]
["INVESTMENT TIME    t ",5]
["V YIELD",0.04]
["K YIELD",0.04]
["VALUE VOLATILITY",0.2]
["K VOLATILITY",0.2]
["CORRELATION",0.5]
["EXCHANGE VOLATILITY",{"$f":"SQRT(B7^2+B8^2-2*B9*B7*B8)","v":0.2},"SQRT(B7^2+B8^2-2*B9*B7*B8)"]
["V ",900000," "]
["D",{"$f":"0.18*B13","v":148500}," "]
["K",825000," "]
["X=V/K",{"$f":"B11/B13","v":1.0909090909090908},"B11/B13"]
["REAL OPTION VALUE ",{"$f":"B11*EXP(-B5*B4)*B30-B13*EXP(-B6*B4)*B31-B12*EXP(-B6*B3)*B29","v":46049.435109123689},"B11*EXP(-B5*B4)*B30-B13*EXP(-B6*B4)*B31-B12*EXP(-B6*B3)*B29"]
["t-t' ",{"$f":"B4-B3","v":4},"B4-B3"]
["X*",1.0907972073385004," "]
["d1",{"$f":"(LN(B11/B13)+((B5-B6+0.5*B10^2)*B16))/(B10*SQRT(B16))","v":0.41752844247407422},"(LN(B11/B13)+((B5-B6+0.5*B10^2)*B16))/(B10*SQRT(B16))"]
["d2",{"$f":"B18-B10*SQRT(B16)","v":1.7528442474074202E-2},"B18-B10*SQRT(B16)"]
["N1",{"$f":"NORMSDIST(B18)","v":0.66185403764105366},"NORMSDIST(B18)"]
["N2",{"$f":"NORMSDIST(B19)","v":0.50699247874179398},"NORMSDIST(B19)"]
["EQ 7.10",{"$f":"B17*EXP(-B5*B16)*B20-EXP(-B6*B16)*B21","v":0.18317346902897008},"B17*EXP(-B5*B16)*B20-EXP(-B6*B16)*B21"]
["EQ 7.10-D/K",{"$f":"B22-(B12/B13)","v":3.1734690289700884E-3},"B22-(B12/B13)"]
["r(t'/t)",{"$f":"SQRT(B3/B4)","v":0.44721359549995793},"SQRT(B3/B4)"]
["d1,t1",{"$f":"(LN(B14/B17)+(B6-B5+0.5*B10^2)*B3)/(B10*SQRT(B3))","v":0.1005128259966908},"(LN(B14/B17)+(B6-B5+0.5*B10^2)*B3)/(B10*SQRT(B3))"]
["d1,t2",{"$f":"(LN(B14)+(B6-B5+0.5*B10^2)*B4)/(B10*SQRT(B4))","v":0.41817015151465198},"(LN(B14)+(B6-B5+0.5*B10^2)*B4)/(B10*SQRT(B4))"]
["d2,t1",{"$f":"B25-B7*SQRT(B3)","v":-9.9487174003309212E-2},"B25-B7*SQRT(B3)"]
["d2,t2",{"$f":"B26-B7*SQRT(B4)","v":-2.9043443985306006E-2},"B26-B7*SQRT(B4)"]
["N2",{"$f":"NORMSDIST(B27)","v":0.46037573551967359},"NORMSDIST(B27)"]
["B1",{"$f":"BiVariateNormalCDF(B25,B26,B24)","v":0.42505427916376681},"BiVariateNormalCDF(B25,B26,B24)"]
["B2",{"$f":"BiVariateNormalCDF(B27,B28,B24)","v":0.29827386488844898},"BiVariateNormalCDF(B27,B28,B24)"]
["V-D-K",{"$f":"B11-B12-B13","v":-73500}]
["The first five inputs are the D and K timing estimates, the "]
["value and cost yields and volatilities, and correlation."]
["After calculating the exchange volatility, the next three inputs are V, D and K estimates."]
["Real call option value assumes X* is the value above which D should be paid at t,."]
["USE TOOLS/SOLVER, SETTING B23=0 BY CHANGING B17."]
[]
["This is an out-of-the-money European exchange option, with 148,500 paid at t=1 in order to maintain the"]
["option to pay 825,000 at T=5, in order to receive V, but both the house value and the construction"]
["cost (and by assumption the architect and demolition costs) are variable.  If construction costs are 825,000 at t=1,"]
["then V should be greater than 900,000 before paying the earlier costs at t=1. V* depends on K at t=1."]
["The RO value of the bungalow site is £46,049, similar to the previous exercise, since the "]
["parameters are quite similar."]

{"sheet":"Problem 7.4","index":34,"n_rows":39,"n_cols":3,"rows_kept":39,"cut":false,"hidden":false,"merged":[]}
[null,"                                       GESKE EUROPEAN COMPOUND CALL OPTION"]
["Problem 7.4"]
["DEVELOPMENT TIME t' ",{"$f":"B4/2","v":1}]
["INVESTMENT TIME    t ",2]
["INTEREST RATE",0.04]
["V YIELD",0.04]
["VALUE VOLATILITY",0.2]
["V ",{"$f":"5/B5","v":125},"5/B5"]
["D",50]
["K",50]
["REAL OPTION VALUE ",{"$f":"B8*EXP(-B6*B4)*B26-B10*EXP(-B5*B4)*B27-B9*EXP(-B5*B3)*B25","v":22.877990958893797},"B8*EXP(-B6*B4)*B26-B10*EXP(-B5*B4)*B27-B9*EXP(-B5*B3)*B25"]
["t-t' ",{"$f":"B4-B3","v":1},"B4-B3"]
["V*",102.03990310430456," "]
["d1",{"$f":"(LN(B13/B10)+((B5-B6+0.5*B7^2)*B12))/(B7*SQRT(B12))","v":3.6667046912980084},"(LN(B13/B10)+((B5-B6+0.5*B7^2)*B12))/(B7*SQRT(B12))"]
["d2",{"$f":"B14-B7*SQRT(B12)","v":3.4667046912980082},"B14-B7*SQRT(B12)"]
["N1",{"$f":"NORMSDIST(B14)","v":0.99987715187087378},"NORMSDIST(B14)"]
["N2",{"$f":"NORMSDIST(B15)","v":0.999736559800953},"NORMSDIST(B15)"]
["EQ 7.4",{"$f":"B13*EXP(-B6*B12)*B16-B10*EXP(-B5*B12)*B17","v":50.000000954491377},"B13*EXP(-B6*B12)*B16-B10*EXP(-B5*B12)*B17"]
["EQ 7.4-D",{"$f":"B18-B9","v":9.544913766035279E-7},"B18-B9"]
["r(t'/t)",{"$f":"SQRT(B3/B4)","v":0.70710678118654757},"SQRT(B3/B4)"]
["d1,t1",{"$f":"(LN(B8/B13)+(B5-B6+0.5*B7^2)*B3)/(B7*SQRT(B3))","v":1.1147489680727667},"(LN(B8/B13)+(B5-B6+0.5*B7^2)*B3)/(B7*SQRT(B3))"]
["d1,t2",{"$f":"(LN(B8/B10)+(B5-B6+0.5*B7^2)*B4)/(B7*SQRT(B4))","v":3.3809983064703073},"(LN(B8/B10)+(B5-B6+0.5*B7^2)*B4)/(B7*SQRT(B4))"]
["d2,t1",{"$f":"B21-B7*SQRT(B3)","v":0.91474896807276673},"B21-B7*SQRT(B3)"]
["d2,t2",{"$f":"B22-B7*SQRT(B4)","v":3.0981555939956884},"B22-B7*SQRT(B4)"]
["N2",{"$f":"NORMSDIST(B23)","v":0.81983828457438424},"NORMSDIST(B23)"]
["B1",{"$f":"BiVariateNormalCDF(B21,B22,B20)","v":0.86751305282551727},"BiVariateNormalCDF(B21,B22,B20)"]
["B2",{"$f":"BiVariateNormalCDF(B23,B24,B20)","v":0.81981747758028334},"BiVariateNormalCDF(B23,B24,B20)"]
[]
["USE TOOLS/SOLVER, SETTING B19=0 BY CHANGING B13."]
[]
["Assume that the current value of the research is price/yield less cost/rate, so V=5/.04. "]
["This is thus an in-the-money call option, with 50 paid at T/2 in order to maintain the"]
["option to pay 50 at T to receive V.  Using solver V* (the net value of the research at the end"]
["of the year that would justify paying 50) is way below the current value."]
["The ROV is actually less than the current present value if D and K could be paid today "]
["(that is the research yield is high, so it would pay to exercise the option immediately)."]
["However, WW must delay enjoying the fruits of his research, so even the optionality"]
["does not add to value in this case (perhaps WW is a slow worker, or his research"]
["supervisor enjoys testing WW's endurance)."]

{"sheet":"Problem 7.5","index":35,"n_rows":102,"n_cols":10,"rows_kept":102,"cut":false,"hidden":false,"merged":[]}
["SEQUENTIAL MATRIX","PROB 7.5",null,"STAGE","VOLATILITY","f","V^","V^-SKN","ROV"]
["Project value  V",81,null,1,{"$f":"B37","v":0.2},{"$f":"B42","v":1.5811388300841895},{"$f":"B46","v":163.24555320336762},{"$f":"B46-B19","v":103.24555320336762},{"$f":"B49","v":34.091155886190897}]
["q  theta_V",0.02,null,2,{"$f":"B59","v":0.31622776601683794},{"$f":"B64","v":1.4142135623730951},{"$f":"B69","v":162.42520818147082},{"$f":"B69-B19-B20","v":72.425208181470822},{"$f":"B71","v":15.28367617696084}]
["sigma_V",0.2,null,3,{"$f":"B86","v":0.44721359549995804},{"$f":"B91","v":1.2247448713915889},{"$f":"B97","v":143.02243649195117},{"$f":"B97-B19-B20-B21","v":43.022436491951169},{"$f":"B99","v":9.3776551670997499}]
["Stage 1 "]
["theta_K1",0]
["sigma_K1",0,null,"Input the correlations:"]
["Failure probability: lambda",0,null,null,"V","K1","K2","K3","Volatility"]
["Stage 2",null,null,"V",1,{"$f":"E10","v":0},{"$f":"E10","v":0},{"$f":"E10","v":0},{"$f":"B23","v":0.2}]
["theta_K2",0,null,"K1",0,{"$f":"E9","v":1},0,0,{"$f":"C23","v":0}]
["sigma_K2",0,null,"K2",{"$f":"E10","v":0},0,{"$f":"E9","v":1},0,{"$f":"D23","v":0}]
["Failure probability: lambda",0.05,null,"K3",{"$f":"E10","v":0},0,0,{"$f":"E9","v":1},{"$f":"E23","v":0}]
["Stage 3",null,"Assumes all V, K correlations are the same as in D10, Ks are not correlated."]
["theta_K3",0]
["sigma_K3",0]
["Risk-free rate",0.05]
["Failure probability: lambda",0.1]
["Threshold Levels"]
["K1^",60]
["K2^",30]
["K3^",10]
["Calculations"]
["Volatility",{"$f":"B4","v":0.2},{"$f":"B7","v":0},{"$f":"B11","v":0},{"$f":"B15","v":0}," "]
["Variance-Covariance Matrix",null,null,null,null,null,null," "," "," "]
["V",{"$f":"E9*B$23*$I9","v":4.0000000000000008E-2},0,0,0," ",null," "," "," "]
["K1",0,0,0,0," "]
["K2",0,0,0,0," "]
["K3",0,0,0,0," "]
["Analysis"]
["Stage 1 "]
["w",1,"column vector with 2 elements"]
[null,-1]
["wT (w transpose)",{"$f":"TRANSPOSE(B31:B32)","v":1},-1,"TRANSPOSE(B31:B32)"]
["Var-Covar*w",{"$f":"MMULT(B25:C26,B31:B32)","v":4.0000000000000008E-2},"MMULT(B25:C26,B31:B32)"]
[null,0]
["sigma^2_1=wT*Var-Covar*w",{"$f":"MMULT(B33:C33,B34:B35)","v":4.0000000000000008E-2},"MMULT(B33:C33,B34:B35)"]
["vol_1",{"$f":"SQRT(B36)","v":0.2},"SQRT(B36)"]
["theta_V - theta_K1",{"$f":"B3-B6","v":0.02},"B3-B6"]
["r + Lamda_1 - theta_K1",{"$f":"B16+B8-B6","v":0.05},"B16+B8-B6"]
["T1",{"$f":"0.5-B38/B36","v":0},"0.5-B38/B36"]
["T2",{"$f":"B40^2+2*B39/B36","v":2.4999999999999996},"B40^2+2*B39/B36"]
["phi_1",{"$f":"B40+SQRT(B41)","v":1.5811388300841895},"B40+SQRT(B41)"]
["phi_1/(phi_1 - 1)",{"$f":"B42/(B42-1)","v":2.7207592200561268},"B42/(B42-1)"]
["beta_1",{"$f":"B42","v":1.5811388300841895},"B42"]
["eta_11",{"$f":"1-B44","v":-0.58113883008418954},"1-B44"]
["V1^",{"$f":"B43*B19","v":163.24555320336762},"B43*B19"]
["A1",{"$f":"((B42-1)^(B42-1))/(B42^B42)","v":0.35352057418829869},"((B42-1)^(B42-1))/(B42^B42)"]
["Mark-up Factor  MEF",{"$f":"B42/(B42-1)","v":2.7207592200561268},"B42/(B42-1)"]
["ROV 1",{"$f":"IF(B2<B46,B47*(B2^B44)*(B19^B45),MAX(B46-B19,0))","v":34.091155886190897},"IF(B2<B46,B47*(B2^B44)*(B19^B45),MAX(B46-B19,0))"]
["Stage 2"]
["w",{"$f":"B42","v":1.5811388300841895},"column vector with 3 elements"]
[null,{"$f":"1-B42","v":-0.58113883008418954}]
[null,-1]
["wT",{"$f":"TRANSPOSE(B51:B53)","v":1.5811388300841895},-0.58113883008418954,-1]
["Var-Covar*w",{"$f":"MMULT(B25:D27,B51:B53)","v":6.3245553203367597E-2}]
[null,0]
[null,0]
["sigma^2_2=wT*Var-Covar*w",{"$f":"MMULT(B54:D54,B55:B57)","v":0.1},"MMULT(B54:D54,B55:B57)"]
["vol_2",{"$f":"SQRT(B58)","v":0.31622776601683794},"SQRT(B58)"]
["r + lambda_1 - theta_K2",{"$f":"B16+B8-B10","v":0.05},"B16+B8-B10"]
["r + lambda_2 - theta_K2",{"$f":"B16+B12-B10","v":0.1},"B16+B12-B10"]
["T1",{"$f":"0.5-B60/B58","v":0},"0.5-B60/B58"]
["T2",{"$f":"B62^2+2*B61/B58","v":2},"B62^2+2*B61/B58"]
["phi_2",{"$f":"B62+SQRT(B63)","v":1.4142135623730951},"B62+SQRT(B63)"]
["B2",{"$f":"((B64-1)^(B64-1))/(B64^B64)","v":0.42519560665184075},"((B64-1)^(B64-1))/(B64^B64)"]
["beta_2",{"$f":"B64*B44","v":2.2360679774997898},"B64*B44"]
["eta_21",{"$f":"B64*B45","v":-0.82185441512669455},"B64*B45"]
["eta_22",{"$f":"1-B64","v":-0.41421356237309515},"1-B64"]
["V2^",{"$f":"((B64*(B19^(B42-1))*B20)/(B47*(B64-1)))^(1/B42)","v":162.42520818147082},"((B64*(B19^(B42-1))*B20)/(B47*(B64-1)))^(1/B42)"]
["A2",{"$f":"B65*B47^B64","v":9.771263030219135E-2},"B65*B47^B64"]
["ROV 2",{"$f":"IF($B$2<B69,B70*($B$2^B66)*($B$19^B67)*($B$20^B68),MAX(B49-B20,0))","v":15.28367617696084},"IF($B$2<B69,B70*($B$2^B66)*($B$19^B67)*($B$20^B68),MAX(B49-B20,0))"]
["Mark-up Factor_2",{"$f":"(B64/(B47*(B64-1)))^(1/B44)","v":4.1965293779944632},"(B64/(B47*(B64-1)))^(1/B44)"]
["V2^/(K1^+K2^)  MEF",{"$f":"B69/(B19+B20)","v":1.8047245353496757},"B69/(B19+B20)"]
["Check: V2^/K2^",{"$f":"B69/B20","v":5.4141736060490278},"B69/B20"]
["Stage 3"]
["w",{"$f":"B42*B64","v":2.2360679774997898},"column vector with 4 elements"]
[null,{"$f":"B64*(1-B42)","v":-0.82185441512669455}]
[null,{"$f":"1-B64","v":-0.41421356237309515}]
[null,-1]
["wT",{"$f":"TRANSPOSE(B76:B79)","v":2.2360679774997898},-0.82185441512669455,-0.41421356237309515,-1]
["Var-Covar*w",{"$f":"MMULT(B25:E28,B76:B79)","v":8.9442719099991616E-2}]
[null,0]
[null,0]
[null,0]
["sigma^2_3=wT*Var-Covar*w",{"$f":"MMULT(B80:E80,B81:B84)","v":0.20000000000000007},"MMULT(B80:E80,B81:B84)"]
["vol_3",{"$f":"SQRT(B85)","v":0.44721359549995804},"SQRT(B85)"]
["r + lambda_2 - theta_K3",{"$f":"B16+B12-B14","v":0.1},"B16+B12-B14"]
["r + lambda_3 - theta_K3",{"$f":"B16+B17-B14","v":0.15000000000000002},"B16+B17-B14"]
["T1",{"$f":"0.5-B87/B85","v":0},"0.5-B87/B85"]
["T2",{"$f":"B89^2+2*B88/B85","v":1.4999999999999998},"B89^2+2*B88/B85"]
["phi_3",{"$f":"B89+SQRT(B90)","v":1.2247448713915889},"B89+SQRT(B90)"]
["B3",{"$f":"((B91-1)^(B91-1))/(B91^B91)","v":0.55777901629166915},"((B91-1)^(B91-1))/(B91^B91)"]
["beta_3",{"$f":"B91*B66","v":2.7386127875258306},"B91*B66"]
["eta_31",{"$f":"B91*B67","v":-1.006561979956953},"B91*B67"]
["eta_32",{"$f":"B91*B68","v":-0.50730593617728836},"B91*B68"]
["eta_33",{"$f":"1-B91","v":-0.22474487139158894},"1-B91"]
["V3^",{"$f":"((B91*(B19^(-B67))*(B20^(-B68))*B21)/(B70*(B91-1)))^(1/B66)","v":143.02243649195117},"((B91*(B19^(-B67))*(B20^(-B68))*B21)/(B70*(B91-1)))^(1/B66)"]
["A3",{"$f":"B92*B70^B91","v":3.2315395613262916E-2},"B92*B70^B91"]
["ROV 3",{"$f":"IF($B$2<B97,B98*($B$2^B93)*($B$19^B94)*($B$20^B95)*($B$21^B96),MAX(B71-$B$20,0))","v":9.3776551670997499},"IF($B$2<B97,B98*($B$2^B93)*($B$19^B94)*($B$20^B95)*($B$21^B96),MAX(B71-$B$20,0))"]
["Mark-up Factor_3",{"$f":"(B91/(B70*(B91-1)))^(1/B66)","v":6.0397104666340438},"(B91/(B70*(B91-1)))^(1/B66)"]
["V2^/(K1^+K2^+K3^)  MEF",{"$f":"B97/(B19+B20+B21)","v":1.4302243649195117},"B97/(B19+B20+B21)"]
["Check: V2^/K2^",{"$f":"B97/B21","v":14.302243649195116},"B97/B21"]

{"sheet":"Problem 7.6","index":36,"n_rows":102,"n_cols":10,"rows_kept":102,"cut":false,"hidden":false,"merged":[]}
["SEQUENTIAL MATRIX","Prob 7.6",null,"STAGE","VOLATILITY","f","V^","V^-SKN","ROV"]
["Project value  V",87,null,1,{"$f":"B37","v":0.40968280413021979},{"$f":"B42","v":1.2415617255303812},{"$f":"B46","v":308.38372001301917},{"$f":"B46-B19","v":248.38372001301917},{"$f":"B49","v":51.617305523221056}]
["q  theta_V",0.02,null,2,{"$f":"B59","v":0.45041334355143148},{"$f":"B64","v":1.2782952894266286},{"$f":"B69","v":191.86641446088859},{"$f":"B69-B19-B20","v":101.86641446088859},{"$f":"B71","v":30.724495853199556}]
["sigma_V",0.2,null,3,{"$f":"B86","v":0.51687440665453543},{"$f":"B91","v":1.1928016103500558},{"$f":"B97","v":135.22237150956232},{"$f":"B97-B19-B20-B21","v":35.222371509562322},{"$f":"B99","v":22.506610983426192}]
["Stage 1 ",null,null,null,null,null,null,null,null," "]
["theta_K1",0,null,"Input the correlations:",null," "," "," "," "]
["sigma_K1",0.34,null,"V","K1","K2","K3"," ","Volatility"]
["Failure probability: lambda",0,"V",1,{"$f":"D9","v":-0.09},{"$f":"D9","v":-0.09},{"$f":"D9","v":-0.09}," ",{"$f":"B23","v":0.2}]
["Stage 2",null,"K1",-0.09,{"$f":"D8","v":1},0,0," ",{"$f":"C23","v":0.34}]
["theta_K2",0,"K2",{"$f":"D9","v":-0.09},0,{"$f":"D8","v":1},0," ",{"$f":"D23","v":0.34}]
["sigma_K2",{"$f":"B7","v":0.34},"K3",{"$f":"D9","v":-0.09},0,0,{"$f":"D8","v":1}," ",{"$f":"E23","v":0.34}]
["Failure probability: lambda",0.05,"Assumes all V, K correlations are the same , Ks are not correlated."]
["Stage 3"]
["theta_K3",0]
["sigma_K3",{"$f":"B7","v":0.34}]
["Failure probability: lambda",0.1]
["Risk-free rate",0.05]
["Threshold Levels"]
["K1^",60]
["K2^",30]
["K3^",10]
["Calculations"]
["Volatility",{"$f":"B4","v":0.2},{"$f":"B7","v":0.34},{"$f":"B11","v":0.34},{"$f":"B15","v":0.34}," "]
["Variance-Covariance Matrix",null,null,null,null," ",null," "," "," "]
["V",{"$f":"D8*B$23*$I8","v":4.0000000000000008E-2},-6.1200000000000004E-3,-6.1200000000000004E-3,-6.1200000000000004E-3," ",null," "," "," "]
["K1",-6.1199999999999996E-3,0.11560000000000002,0,0," "]
["K2",-6.1199999999999996E-3,0,0.11560000000000002,0," "]
["K3",-6.1199999999999996E-3,0,0,0.11560000000000002," "]
["Analysis"]
["Stage 1 "]
["w",1,"column vector with 2 elements"]
[null,-1]
["wT (w transpose)",{"$f":"TRANSPOSE(B31:B32)","v":1},-1,"TRANSPOSE(B44:B45)"]
["Var-Covar*w",{"$f":"MMULT(B25:C26,B31:B32)","v":4.6120000000000008E-2},"MMULT(B37:C38,B44:B45)"]
[null,-0.12172000000000002]
["sigma^2_1=wT*Var-Covar*w",{"$f":"MMULT(B33:C33,B34:B35)","v":0.16784000000000004},"MMULT(B46:C46,B47:B48)"]
["vol_1",{"$f":"SQRT(B36)","v":0.40968280413021979},"SQRT(B49)"]
["theta_V - theta_K1",{"$f":"B3-B6","v":0.02},"B3-B6"]
["r + Lamda_1 - theta_K1",{"$f":"B17+B8-B6","v":0.05},"B21+B8-B6"]
["T1",{"$f":"0.5-B38/B36","v":0.38083889418493805},"0.5-B51/B49"]
["T2",{"$f":"B40^2+2*B39/B36","v":0.74084379239931608},"B53^2+2*B52/B49"]
["phi_1",{"$f":"B40+SQRT(B41)","v":1.2415617255303812},"B53+SQRT(B54)"]
["phi_1/(phi_1 - 1)",{"$f":"B42/(B42-1)","v":5.139728666883653},"B55/(B55-1)"]
["beta_1",{"$f":"B42","v":1.2415617255303812},{"$f":"C42","v":"B53+SQRT(B54)"}]
["eta_11",{"$f":"1-B44","v":-0.24156172553038124},"1-B57"]
["V1^",{"$f":"B43*B19","v":308.38372001301917},"B56*B23"]
["A1",{"$f":"((B42-1)^(B42-1))/(B42^B42)","v":0.54237010616744552},"((B55-1)^(B55-1))/(B55^B55)"]
["Mark-up Factor  MEF",{"$f":"B42/(B42-1)","v":5.139728666883653},"B55/(B55-1)"]
["F",{"$f":"IF(B2<B46,B47*(B2^B44)*(B19^B45),MAX(B46-B19,0))","v":51.617305523221056},"IF(B2<B59,B60*(B2^B57)*(B23^B58),MAX(B59-B23,0))"]
["Stage 2"]
["w",{"$f":"B42","v":1.2415617255303812},"column vector with 3 elements"]
[null,{"$f":"1-B42","v":-0.24156172553038124}]
[null,-1]
["wT",{"$f":"TRANSPOSE(B51:B53)","v":1.2415617255303812},-0.24156172553038124,-1]
["Var-Covar*w",{"$f":"MMULT(B25:D27,B51:B53)","v":5.7260826781461195E-2}]
[null,-3.5522893231558009E-2]
[null,-0.12319835776024596]
["sigma^2_2=wT*Var-Covar*w",{"$f":"MMULT(B54:D54,B55:B57)","v":0.20287218004917984},"MMULT(B67:D67,B68:B70)"]
["vol_2",{"$f":"SQRT(B58)","v":0.45041334355143148},"SQRT(B71)"]
["r + lambda_1 - theta_K2",{"$f":"B17+B8-B10","v":0.05},"B21+B8-B10"]
["r + lambda_2 - theta_K2",{"$f":"B17+B12-B10","v":0.1},"B21+B12-B10"]
["T1",{"$f":"0.5-B60/B58","v":0.25353939614648441},"0.5-B73/B71"]
["T2",{"$f":"B62^2+2*B61/B58","v":1.0501246408123863},"B75^2+2*B74/B71"]
["phi_2",{"$f":"B62+SQRT(B63)","v":1.2782952894266286},"B75+SQRT(B76)"]
["B2",{"$f":"((B64-1)^(B64-1))/(B64^B64)","v":0.51180255570553301},"((B77-1)^(B77-1))/(B77^B77)"]
["beta_2",{"$f":"B64*B44","v":1.5870825052778832},"B77*B57"]
["eta_21",{"$f":"B64*B45","v":-0.30878721585125452},"B77*B58"]
["eta_22",{"$f":"1-B64","v":-0.27829528942662862},"1-B77"]
["V2^",{"$f":"((B64*(B19^(B42-1))*B20)/(B47*(B64-1)))^(1/B42)","v":191.86641446088859},"((B77*(B23^(B55-1))*B24)/(B60*(B77-1)))^(1/B55)"]
["A2",{"$f":"B65*B47^B64","v":0.23412832172192308},"B78*B60^B77"]
["F",{"$f":"IF($B$2<B69,B70*($B$2^B66)*($B$19^B67)*($B$20^B68),MAX(B69-B19-B20,0))","v":30.724495853199556},"IF($B$2<B82,B83*($B$2^B79)*($B$23^B80)*($B$24^B81),MAX(B82-B23-B24,0))"]
["Mark-up Factor_2",{"$f":"(B64/(B47*(B64-1)))^(1/B44)","v":5.5886700001861875},"(B77/(B60*(B77-1)))^(1/B57)"]
["V2^/(K1^+K2^)  MEF",{"$f":"B69/(B19+B20)","v":2.131849049565429},"B82/(B23+B24)"]
["Check: V2^/K2^",{"$f":"B69/B20","v":6.395547148696286},"B82/B24"]
["Stage 3"]
["w",{"$f":"B42*B64","v":1.5870825052778832},"column vector with 4 elements"]
[null,{"$f":"B64*(1-B42)","v":-0.30878721585125452}]
[null,{"$f":"1-B64","v":-0.27829528942662862}]
[null,-1]
["wT",{"$f":"TRANSPOSE(B76:B79)","v":1.5870825052778832},-0.30878721585125452,-0.27829528942662862,-1]
["Var-Covar*w",{"$f":"MMULT(B25:E28,B76:B79)","v":7.3196245143415994E-2}]
[null,-4.5408747084705672E-2]
[null,-4.1883880390018918E-2]
[null,-0.12531294493230066]
["sigma^2_3=wT*Var-Covar*w",{"$f":"MMULT(B80:E80,B81:B84)","v":0.26715915225447806},"MMULT(B93:E93,B94:B97)"]
["vol_3",{"$f":"SQRT(B85)","v":0.51687440665453543},"SQRT(B98)"]
["r + lambda_2 - theta_K3",{"$f":"B17+B12-B14","v":0.1},"B21+B12-B14"]
["r + lambda_3 - theta_K3",{"$f":"B17+B16-B14","v":0.15000000000000002},"B21+B16-B14"]
["T1",{"$f":"0.5-B87/B85","v":0.12569128118528144},"0.5-B100/B98"]
["T2",{"$f":"B89^2+2*B88/B85","v":1.1387244546101531},"B102^2+2*B101/B98"]
["phi_3",{"$f":"B89+SQRT(B90)","v":1.1928016103500558},"B102+SQRT(B103)"]
["B3",{"$f":"((B91-1)^(B91-1))/(B91^B91)","v":0.58998027391539554},"((B104-1)^(B104-1))/(B104^B104)"]
["beta_3",{"$f":"B91*B66","v":1.8930745680538601},"B104*B79"]
["eta_31",{"$f":"B91*B67","v":-0.36832188832288665},"B104*B80"]
["eta_32",{"$f":"B91*B68","v":-0.33195106938091751},"B104*B81"]
["eta_33",{"$f":"1-B91","v":-0.19280161035005583},"1-B104"]
["V3^",{"$f":"((B91*(B19^(-B67))*(B20^(-B68))*B21)/(B70*(B91-1)))^(1/B66)","v":135.22237150956232},"((B104*(B23^(-B80))*(B24^(-B81))*B25)/(B83*(B104-1)))^(1/B79)"]
["A3",{"$f":"B92*B70^B91","v":0.10440496443199589},"B105*B83^B104"]
["F",{"$f":"IF($B$2<B97,B98*($B$2^B93)*($B$19^B94)*($B$20^B95)*($B$21^B96),MAX(B97-$B$19-$B$20-$B$21,0))","v":22.506610983426192},"IF($B$2<B110,B111*($B$2^B106)*($B$23^B107)*($B$24^B108)*($B$25^B109),MAX(B110-$B$23-$B$24-$B$25,0))"]
["Mark-up Factor_3",{"$f":"(B91/(B70*(B91-1)))^(1/B66)","v":7.870203070689997},"(B104/(B83*(B104-1)))^(1/B79)"]
["V2^/(K1^+K2^+K3^)  MEF",{"$f":"B97/(B19+B20+B21)","v":1.3522237150956231},"B110/(B23+B24+B25)"]
["Check: V2^/K2^",{"$f":"B97/B21","v":13.522237150956233},"B110/B25"]

{"sheet":"Exercise 8.1","index":37,"n_rows":34,"n_cols":3,"rows_kept":34,"cut":false,"hidden":false,"merged":[]}
["Exercise 8.1","                                                                                   MARSHALLIAN & SIMPLE OPTION  ENTER PRICES"]
["INPUT"]
["P",2]
["Investment K",5]
["Operating cost C",1]
["Abandon  A",25]
["Interest Rate",0.04]
["Asset Yield",0.04]
["Asset Volatility",0.2]
[]
["b1",{"$f":"0.5-(B7-B8)/(B9^2)+SQRT(((B7-B8)/(B9^2)-0.5)^2 + 2*B7/(B9^2))","v":1.9999999999999998},"0.5-(B7-B8)/(B9^2)+SQRT(((B7-B8)/(B9^2)-0.5)^2 + 2*B7/(B9^2))"]
["b2",{"$f":"0.5-(B7-B8)/(B9^2)-SQRT(((B7-B8)/(B9^2)-0.5)^2 + 2*B7/(B9^2))","v":-0.99999999999999978},"0.5-(B7-B8)/(B9^2)-SQRT(((B7-B8)/(B9^2)-0.5)^2 + 2*B7/(B9^2))"]
[]
["OUTPUT"]
[" WK",{"$f":"B5+B7*B4","v":1.2},"B5+B7*B4"]
[" WA",{"$f":"IF((B5-B7*B6)>0,B5-B7*B6,0)","v":0},"IF((B5-B7*B6)>0,B5-B7*B6,0)"]
["WK-WA",{"$f":"B15-B16","v":1.2},"B15-B16"]
[]
[" PK",{"$f":"(B8/B7)*B11/(B11-1)*B15","v":2.4},"(B8/B7)*B11/(B11-1)*B15"]
[" PA",{"$f":"(B8/B7)*(-B12/(-B12+1))*B16","v":0},"(B8/B7)*(-B12/(-B12+1))*B16"]
["PK-PA",{"$f":"B19-B20","v":2.4},"B19-B20"]
[]
["(PK-PA)/(WK-WA)",{"$f":"B21/B17","v":2},"B21/B17"]
[]
["ROV",{"$f":"B26*(B3^B11)","v":20.833333333333336},"B26*(B3^B11)"]
["A1",{"$f":"(B19/B8-B5/B7-B4)/(B19^B11)","v":5.2083333333333348},"(B19/B8-B5/B7-B4)/(B19^B11)"]
["ROV",{"$f":"(B19/B8-B5/B7-B4)*(B3/B19)^B11","v":20.833333333333336},"(B19/B8-B5/B7-B4)*(B3/B19)^B11"]
["NPV",{"$f":"(B3/B8-B5/B7-B4)","v":20},"(B3/B8-B5/B7-B4)"]
["C-rA",{"$f":"B5-B7*B6","v":0},"B5-B7*B6"]
["Following Professor Marshall you would enter the class now, since P>=WK.  With the advantage"]
["of a stochastic real options model, you would wait until the perceived benefits P>2.400."]
["Note that Professor Marshall class value is less than the RO value."]
["Perhaps it is only a dream of teachers, that students \"once committed, are forever comitted\","]
["but this class appears to be valuable if viewed as a real option."]

{"sheet":"Problem 8.2","index":38,"n_rows":33,"n_cols":6,"rows_kept":33,"cut":false,"hidden":false,"merged":[]}
["PROBLEM 8.2"," ",null,"                                                       Perpetual American Option"]
["INPUT",null,null,"INPUT"]
["P",2,null,"P",2]
["Investment K",5,null,"K",5]
["Operating cost C",1,null,"C",1]
["Abandon  A",25]
["Interest Rate",0.04,null,"r",0.04]
["Asset Yield",0.04,null,"d",0.04]
["Asset Volatility",0.2,null,"s",0.2]
[]
["b1",{"$f":"0.5-(B7-B8)/(B9^2)+SQRT(((B7-B8)/(B9^2)-0.5)^2 + 2*B7/(B9^2))","v":1.9999999999999998},null,"b1",{"$f":"0.5-(E7-E8)/(E9^2)+SQRT(((E7-E8)/(E9^2)-0.5)^2 + (2*E7)/(E9^2))","v":1.9999999999999998}]
[" "," ",null,null,null," "]
[]
["OUTPUT"]
[" WK",{"$f":"B5+B7*B4","v":1.2},null,"Vo(P)",{"$f":"E17*(E3^E11)","v":20.833333333333336},"E17*(E3^E11)"]
[" "," ",null,"PV-K",{"$f":"E3/E8-E5/E7-E4","v":20},"E3/E8-E5/E7-E4"]
["A1",{"$f":"(B19/B8-B5/B7-B4)/(B19^B11)","v":5.2083333333333348},null,"A1",{"$f":"B17","v":5.2083333333333348}," "]
[null,null,null,"B"]
[" PK",{"$f":"(B8/B7)*B11/(B11-1)*B15","v":2.4},null," PK",{"$f":"B19","v":2.4}," "]
[" "," "]
[" "," ",null,"ODE(0)",{"$f":"0.5*(E9^2)*(E3^2)*E23+(E7-E8)*E3*E22-E7*E15","v":0},"0.5*(E9^2)*(E3^2)*E23+(E7-E8)*E3*E22-E7*E15"]
["ROV",{"$f":"(B19/B8-B5/B7-B4)*(B3/B19)^B11","v":20.833333333333336},null,"V'o(P)",{"$f":"E11*E17*(E3^(E11-1))","v":20.833333333333332},"E11*E17*(E3^(E11-1))"]
["NPV",{"$f":"(B3/B8-B5/B7-B4)","v":20},null,"V''o(P)",{"$f":"E11*(E11-1)*E17*(E3^(E11-2))","v":10.416666666666664},"E11*(E11-1)*E17*(E3^(E11-2))"]
[null,null,null,"VALUE MATCH"]
[" ",null,null,"Vo(P*)",{"$f":"E17*(E19^E11)","v":29.999999999999996},"E17*(E19^E11)"]
[" ",null,null,"P*-K",{"$f":"(E19/E8)-(E5/E7)-E4","v":30},"(E19/E8)-(E5/E7)-E4"]
[null,null,null,"SMOOTH PASTE"]
[null,null,null,"V'o(P*)",{"$f":"E11*E17*(E19^(E11-1))","v":24.999999999999996},"E11*E17*(E19^(E11-1))"]
[null," ",null,"'NPV(P*)",{"$f":"(1/E8)","v":25},"(1/E8)"]
[null,null,null,null,null," "]
[null,null,null,"ODE (8.2)=0",null,"VALUE MATCHING & SMOOTH PASTING CONDITIONS MET."]
[]
[null,null,null,null,null," "]

{"sheet":"Problem 8.3","index":39,"n_rows":27,"n_cols":6,"rows_kept":27,"cut":false,"hidden":false,"merged":[]}
["PROBLEM 8.3","MARSHALLIAN AND OPTION ENTER TRIGGERS"]
["INPUT"]
["P",2,2,2,2,2]
["Investment K",5,5,5,5,5]
["Operating cost C",0.8,{"$f":"B5+0.05","v":0.85000000000000009},{"$f":"C5+0.05","v":0.90000000000000013},{"$f":"D5+0.05","v":0.95000000000000018},{"$f":"E5+0.05","v":1.0000000000000002}]
["Abandon  A",25,25,25,25,25]
["Interest Rate",0.04,0.04,0.04,0.04,0.04]
["Asset Yield",0.04,0.04,0.04,0.04,0.04]
["Asset Volatility",0.2,0.2,0.2,0.2,0.2]
[]
["b1",{"$f":"0.5-(B7-B8)/(B9^2)+SQRT(((B7-B8)/(B9^2)-0.5)^2 + 2*B7/(B9^2))","v":1.9999999999999998},{"$f":"0.5-(C7-C8)/(C9^2)+SQRT(((C7-C8)/(C9^2)-0.5)^2 + 2*C7/(C9^2))","v":1.9999999999999998},{"$f":"0.5-(D7-D8)/(D9^2)+SQRT(((D7-D8)/(D9^2)-0.5)^2 + 2*D7/(D9^2))","v":1.9999999999999998},{"$f":"0.5-(E7-E8)/(E9^2)+SQRT(((E7-E8)/(E9^2)-0.5)^2 + 2*E7/(E9^2))","v":1.9999999999999998},{"$f":"0.5-(F7-F8)/(F9^2)+SQRT(((F7-F8)/(F9^2)-0.5)^2 + 2*F7/(F9^2))","v":1.9999999999999998}]
["b2",{"$f":"0.5-(B7-B8)/(B9^2)-SQRT(((B7-B8)/(B9^2)-0.5)^2 + 2*B7/(B9^2))","v":-0.99999999999999978},{"$f":"0.5-(C7-C8)/(C9^2)-SQRT(((C7-C8)/(C9^2)-0.5)^2 + 2*C7/(C9^2))","v":-0.99999999999999978},{"$f":"0.5-(D7-D8)/(D9^2)-SQRT(((D7-D8)/(D9^2)-0.5)^2 + 2*D7/(D9^2))","v":-0.99999999999999978},{"$f":"0.5-(E7-E8)/(E9^2)-SQRT(((E7-E8)/(E9^2)-0.5)^2 + 2*E7/(E9^2))","v":-0.99999999999999978},{"$f":"0.5-(F7-F8)/(F9^2)-SQRT(((F7-F8)/(F9^2)-0.5)^2 + 2*F7/(F9^2))","v":-0.99999999999999978}]
[]
["OUTPUT"]
[" WK",{"$f":"B5+B7*B4","v":1},{"$f":"C5+C7*C4","v":1.05},{"$f":"D5+D7*D4","v":1.1000000000000001},{"$f":"E5+E7*E4","v":1.1500000000000001},{"$f":"F5+F7*F4","v":1.2000000000000002}]
[" WA",{"$f":"IF((B5-B7*B6)>0,B5-B7*B6,0)","v":0},{"$f":"IF((C5-C7*C6)>0,C5-C7*C6,0)","v":0},{"$f":"IF((D5-D7*D6)>0,D5-D7*D6,0)","v":0},{"$f":"IF((E5-E7*E6)>0,E5-E7*E6,0)","v":0},{"$f":"IF((F5-F7*F6)>0,F5-F7*F6,0)","v":2.2204460492503131E-16}]
["WK-WA",{"$f":"B15-B16","v":1},{"$f":"C15-C16","v":1.05},{"$f":"D15-D16","v":1.1000000000000001},{"$f":"E15-E16","v":1.1500000000000001},{"$f":"F15-F16","v":1.2}]
["PK-PA",{"$f":"B19-B20","v":2},{"$f":"C19-C20","v":2.1},{"$f":"D19-D20","v":2.2000000000000002},{"$f":"E19-E20","v":2.3000000000000003},{"$f":"F19-F20","v":2.4000000000000004}]
[" PK",{"$f":"(B8/B7)*B11/(B11-1)*B15","v":2},{"$f":"(C8/C7)*C11/(C11-1)*C15","v":2.1},{"$f":"(D8/D7)*D11/(D11-1)*D15","v":2.2000000000000002},{"$f":"(E8/E7)*E11/(E11-1)*E15","v":2.3000000000000003},{"$f":"(F8/F7)*F11/(F11-1)*F15","v":2.4000000000000004}]
[" PA",{"$f":"(B8/B7)*(-B12/(-B12+1))*B16","v":0},{"$f":"(C8/C7)*(-C12/(-C12+1))*C16","v":0},{"$f":"(D8/D7)*(-D12/(-D12+1))*D16","v":0},{"$f":"(E8/E7)*(-E12/(-E12+1))*E16","v":0},{"$f":"(F8/F7)*(-F12/(-F12+1))*F16","v":1.1102230246251564E-16}]
[]
["(PK-PA)/(WK-WA)",{"$f":"B18/B17","v":2},{"$f":"C18/C17","v":2},{"$f":"D18/D17","v":2},{"$f":"E18/E17","v":2},{"$f":"F18/F17","v":2.0000000000000004}]
[]
["Following Professor Marshall & RO theory you might have entered this class now when C=.8.  With the advantage"]
["of a stochastic real options model, this would be a marginal decision highly dependent on this remaining a low."]
["cost (low mental and physical stress) class, while Professor Marshall could increase class requirements without"]
["losing his popularity."]

{"sheet":"Problem 8.4","index":40,"n_rows":34,"n_cols":3,"rows_kept":34,"cut":false,"hidden":false,"merged":[]}
["Entry - Exit (STOCHASTIC MODEL)"]
["PROBLEM 8.4"," "]
["P=",2]
["K=",5]
["C=",0.4]
["A=",2]
["r=",0.04]
["d=",0.04]
["s=",0.2]
[]
["b1=",{"$f":"0.5-((B7-B8)/(B9^2))+SQRT(((((B7-B8)/(B9^2))-0.5)^2)+(2*(B7/(B9^2))))","v":1.9999999999999998},"0.5-((B7-B8)/(B9^2))+SQRT(((((B7-B8)/(B9^2))-0.5)^2)+(2*(B7/(B9^2))))"]
["b2=",{"$f":"0.5-((B7-B8)/(B9^2))-SQRT(((((B7-B8)/(B9^2))-0.5)^2)+(2*(B7/(B9^2))))","v":-0.99999999999999978},"0.5-((B7-B8)/(B9^2))-SQRT(((((B7-B8)/(B9^2))-0.5)^2)+(2*(B7/(B9^2))))"]
[]
["Vo(P)",{"$f":"B17*(B3^B11)","v":43.429394874150589},"B17*(B3^B11)"]
["VK(P)",{"$f":"B18*(B3^B12)+(B3/B8)-(B5/B7)","v":40.346680977355668},"B18*(B3^B12)+(B3/B8)-(B5/B7)"]
[]
["A1",10.857348718537649," "]
["B2",0.69336195471133166," "]
[" PK",1.1261146747824857," "]
[" PA",0.1814475087805251," "]
["PK-PA",{"$f":"B19-B20","v":0.94466716600196066}]
["Eq.8.14",{"$f":"(B17*(B19^B11))-(B18*(B19^B12))-(B19/B8)+(B5/B7)+B4","v":-2.6553891814273811E-6},"(B17*(B19^B11))-(B18*(B19^B12))-(B19/B8)+(B5/B7)+B4"]
["Eq.8.15",{"$f":"(B11*B17*(B19^(B11-1)))-(B12*B18*(B19^(B12-1)))-(1/B8)","v":-3.0287600907286105E-6},"(B11*B17*(B19^(B11-1)))-(B12*B18*(B19^(B12-1)))-(1/B8)"]
["Eq.8.16",{"$f":"(-B17*(B20^B11))+(B18*(B20^B12))+(B20/B8)-(B5/B7)+B6","v":1.0276516665186364E-5},"(-B17*(B20^B11))+(B18*(B20^B12))+(B20/B8)-(B5/B7)+B6"]
["Eq.8.17",{"$f":"(-B11*B17*(B20^(B11-1)))+(B12*B18*(B20^(B12-1)))+(1/B8)","v":-5.9393238117877445E-5},"(-B11*B17*(B20^(B11-1)))+(B12*B18*(B20^(B12-1)))+(1/B8)"]
["SUM",{"$f":"SUM(ABS(B22:B25))","v":7.53539040552198E-5}]
["SOLVER","Set B26=0, and B23=B24=B25=B22, CHANGING B17:B20."]
[]
["Note that the annualized value of the abandonment cost is not above the perpetual operating cost "]
["value, so the simple stochastic entry model is inappropriate.  Now the optimal entry price is"]
["below the Marshallian trigger, and the hysteresis range is narrower, because of the"]
["flexibility of exiting and then re-entering. Teachers offering this flexibility should attract"]
["larger numbers of students initially, but those student will come and go as the "]
["perceived benefits vary from class to class over time."]

{"sheet":"Problem 8.5","index":41,"n_rows":36,"n_cols":3,"rows_kept":36,"cut":false,"hidden":false,"merged":[]}
[null,"          Entry - Exit (STOCHASTIC MODEL)"]
["PROBLEM 8.5"," "]
["P=",9]
["K=",100]
["C=",3]
["A=",-55]
["r=",0.1]
["d=",0.05]
["s=",0.3]
[]
["b1=",{"$f":"0.5-((B7-B8)/(B9^2))+SQRT(((((B7-B8)/(B9^2))-0.5)^2)+(2*(B7/(B9^2))))","v":1.436191286899728},"0.5-((B7-B8)/(B9^2))+SQRT(((((B7-B8)/(B9^2))-0.5)^2)+(2*(B7/(B9^2))))"]
["b2=",{"$f":"0.5-((B7-B8)/(B9^2))-SQRT(((((B7-B8)/(B9^2))-0.5)^2)+(2*(B7/(B9^2))))","v":-1.5473023980108391},"0.5-((B7-B8)/(B9^2))-SQRT(((((B7-B8)/(B9^2))-0.5)^2)+(2*(B7/(B9^2))))"]
[]
["Vo(P)",{"$f":"B17*(B3^B11)","v":86.636353321028409},"B17*(B3^B11)"]
["VK(P)",{"$f":"B18*(B3^B12)+(B3/B8)-(B5/B7)","v":159.25244340737885},"B18*(B3^B12)+(B3/B8)-(B5/B7)"]
["NPV",{"$f":"(B3/B8)-(B5/B7)-B4","v":50},"(B3/B8)-(B5/B7)-B4"]
["A1",3.6916913684137636," "]
["B2",277.17761948621154," "]
[" PK",20.51758095103024," "]
[" PA",4.3924557617718323," "]
["PK-PA",{"$f":"B19-B20","v":16.125125189258409}]
["Eq.8.14",{"$f":"(B17*(B19^B11))-(B18*(B19^B12))-(B19/B8)+(B5/B7)+B4","v":-1.4225309428184119E-6},"(B17*(B19^B11))-(B18*(B19^B12))-(B19/B8)+(B5/B7)+B4"]
["Eq.8.15",{"$f":"(B11*B17*(B19^(B11-1)))-(B12*B18*(B19^(B12-1)))-(1/B8)","v":1.2535013027559216E-7},"(B11*B17*(B19^(B11-1)))-(B12*B18*(B19^(B12-1)))-(1/B8)"]
["Eq.8.16",{"$f":"(-B17*(B20^B11))+(B18*(B20^B12))+(B20/B8)-(B5/B7)+B6","v":-6.5975531725825931E-5},"(-B17*(B20^B11))+(B18*(B20^B12))+(B20/B8)-(B5/B7)+B6"]
["Eq.8.17",{"$f":"(-B11*B17*(B20^(B11-1)))+(B12*B18*(B20^(B12-1)))+(1/B8)","v":5.6307200107852395E-5},"(-B11*B17*(B20^(B11-1)))+(B12*B18*(B20^(B12-1)))+(1/B8)"]
["SUM",{"$f":"SUM(ABS(B22:B25))","v":1.2383061290677233E-4}]
["SOLVER","Set B26=0, and B23=B24=B25=B22, CHANGING B17:B20."]
[]
["This analysis, stated on a per room basis, times 100 rooms is transformed into hotel."]
["Consider the switching opportunity as a \"negative\" abandonment cost A."]
["This is an in-the-money investment opportunity, since the NPV is positive, but"]
["the current investment should not be made yet until the price per room times"]
["the vacancy rate is above $20,500.  Once the suite-hotel is constructed"]
["the switching-refurbishment alternative is quite valuable.  "]
["Change P to 20.518, so that VK(P)=383, which is 103 over the then NPV, "]
["representing the switching-refurbishment option."]

{"sheet":"Problem 8.6","index":42,"n_rows":46,"n_cols":11,"rows_kept":46,"cut":false,"hidden":false,"merged":[]}
["Problem 8.6",null,"Invest, Revert, Contract and Abandonment"]
[null,"INPUT"]
["P","Gross Profits",9," "," "," "," "," "," "," "," "]
["K","Initial Investment",100]
["C","Operating Cost",3]
["r","Riskless Rate",0.1]
["δ","Cost of Carry",0.05]
["σ","Volatility ",0.3]
["E","Cost of Contracting",15]
["A","Abandonment Cost",5]
["R","Cost for Reversion:FS from Contraction",10]
["C1","Reduced Operating Cost in Contraction",1]
["ς","Contraction Multiplier",0.5]
["β1","Eq. 8.6",{"$f":"0.5-((C6-C7)/(C8^2))+SQRT(((((C6-C7)/(C8^2))-0.5)^2)+(2*(C6/(C8^2))))","v":1.436191286899728}]
["β2","Eq. 8.7",{"$f":"0.5-((C6-C7)/(C8^2))-SQRT(((((C6-C7)/(C8^2))-0.5)^2)+(2*(C6/(C8^2))))","v":-1.5473023980108391}]
[]
["V0(P)","Eq. 8.4",{"$f":"C21*(C3^C14)","v":85.895817772323312},"C21*(C3^C14)"," "," "," "," "," "," "," "]
["VK(P)","Eq. 8.12",{"$f":"C22*(C3^C15)+(C3/C7)-(C5/C6)","v":150.02528386362508},"C22*(C3^C15)+(C3/C7)-(C5/C6)"," "," "," "," "," "," "," "]
["VC(P)","Eq.8.23",{"$f":"C23*(C3^C14)+C24*(C3^C15)+(C13*C3/C7)-(C12/C6)","v":140.19500832327822},"C23*(C3^C14)+C24*(C3^C15)+(C13*C3/C7)-(C12/C6)"," "," "," "," "," "," "," "]
[null,"NPV",{"$f":"(C3/C7)-(C5/C6)-C4","v":50},"(C3/C7)-(C5/C6)-C4"]
["A1","Value Coefficient of the Option to Invest",3.6601361541375113]
["B2","Value Coefficient of the Option to Contract",0.75743463887828022]
["D1","Value Coefficient of the Option to Revert:FS1",2.5644981277606513]
["D2","Value Coefficient of the Option to Abandon",0.34590645738000736]
["P(K)","Price Trigger for New Entry",21.399455280848354]
["P(R)","Price Trigger to Revert ",9.8695700381186917]
["'P'('C)","Price Trigger to Contract",0.37798498176865331]
["P(A)","Price Trigger to Abandon",0.32980116963751815]
[null," "," "," "," "," "," "," "," "," "," "]
[null,"Eq.8.16",{"$f":"(C21)*(C25^C14)-C22*(C25^C15)-(C25/C7)+(C5/C6)+C4","v":1.1368683772161603E-13},"(C24)*(C28^C17)-C25*(C28^C18)-(C28/C10)+(C8/C9)+C7"]
[null,"Eq.8.17",{"$f":"C14*(C21)*(C25^(C14-1))-C15*C22*(C25^(C15-1))-(1/C7)","v":1.1013412404281553E-13},"C17*(C24)*(C28^(C17-1))-C18*C25*(C28^(C18-1))-(1/C10)"]
[null,"Eq.8.26",{"$f":"(-C23)*(C27^C14)+(C22-C24)*(C27^C15)+((1-C13)*C27)/C7-((C5-C12)/C6)+C9","v":1.4388490399142029E-13},"(-C26)*(C30^C17)+(C25-C27)*(C30^C18)+((1-C16)*C30)/C10-((C8-C15)/C9)+C12"]
[null,"Eq.8.27",{"$f":"C14*(-C23)*(C27^(C14-1))+C15*(C22-C24)*(C27^(C15-1))+(1-C13)/C7","v":1.4770407119613083E-11},"C17*(-C26)*(C30^(C17-1))+C18*(C25-C27)*(C30^(C18-1))+(1-C16)/C10"]
[null,"Eq.8.28",{"$f":"(C23)*(C26^C14)+(C24-C22)*(C26^C15)-(1-C13)*C26/C7+(C5-C12)/C6+C11","v":-8.5265128291212022E-14},"(C26)*(C29^C17)+(C27-C25)*(C29^C18)-(1-C16)*C29/C10+(C8-C15)/C9+C14"]
[null,"Eq.8.29",{"$f":"C14*(C23)*(C26^(C14-1))+C15*(C24-C22)*(C26^(C15-1))-(1-C13)/C7","v":-2.8421709430404007E-14},"C17*(C26)*(C29^(C17-1))+C18*(C27-C25)*(C29^(C18-1))-(1-C16)/C10"]
[null,"Eq.8.30",{"$f":"(C23-C21)*(C28^C14)+C24*(C28^C15)+((C13*C28)/C7)-C12/C6+C10","v":1.306028047487473E-6},"(C26-C24)*(C31^C17)+C27*(C31^C18)+((C16*C31)/C10)-C15/C9+C13"]
[null,"Eq.8.31",{"$f":"C14*(C23-C21)*(C28^(C14-1))+C15*C24*(C28^(C15-1))+(C13/C7)","v":-1.2767421141646196E-5},"C17*(C26-C24)*(C31^(C17-1))+C18*C27*(C31^(C18-1))+(C16/C10)"]
[null,"SOLVER: SET C38=0, CHANGING C30:C37",{"$f":"SUM(ABS(C30:C37))","v":1.4073464440933492E-5}]
[]
["Note it costs $5000 per room to abandon the hotel, and there is"]
["no switching-refurbishing alternative.  Even so this contracting option is very valuable, increasing"]
["the option to invest from the previous problem, and the value of the full operating state is also"]
["increased.  Note that the investment trigger for the room rent times the occupancy rate has decreased."]
["If P rises to the investment trigger, the NPV is still 100 less than than the value of the full service"]
["state, representing the value of the contracting and reversion alternative.  The contracting trigger"]
["is hardly greater than the abandonment trigger, but the reversion option is quite valuable."]

{"sheet":"Exercise 9.1 A","index":43,"n_rows":33,"n_cols":3,"rows_kept":33,"cut":false,"hidden":false,"merged":[]}
["Duopoly Competition with Permanent First-Mover Advantage"]
["                                                             Stochastic Value",null," "]
["Exercise 9.1 A"]
[null," "]
["Risk-free Rate of Interest (r)",0.04]
["Expected Drift of V (m)",0]
["Volatility of Value (s)",0.2]
["Leader's Market Share After Follower's Entry (a)",0.66666000000000003]
["Total Market Value (V)",1000000]
["Investment Cost (K)",1000000]
["Follower's Real Option Value ",{"$f":"IF(B9<B14,B17,B18)","v":27778.888900000005},"IF(B9<B14,B17,B18)"]
["Leader's Real Option Value ",{"$f":"IF(B9<B14,B19,B20)","v":-55557.777799999691},"IF(B9<B14,B19,B20)"]
[]
["Investment Trigger Follower (VF) ",{"$f":"(B22/(B22-1))*B10*(1/(1-B8))","v":5999880.0023999522},"(B22/(B22-1))*B10*(1/(1-B8))"]
["Investment Trigger Leader (VL) ",{"$f":"B25","v":1101025.4635044036}," "]
[]
["Follower's Real Option Value (Before Entry)",{"$f":"(((1-B8)*B14-B10)*(B9/B14)^B22)","v":27778.888900000005},"(((1-B8)*B14-B10)*(B9/B14)^B22)"]
["Follower's Real Option Value (After Entry)",{"$f":"((1-B8)*B9-B10)","v":-666660},"((1-B8)*B9-B10)"]
["Leader's Real Option Value (Before Entry of F.)",{"$f":"B9-(B9^B22)*(B14^(1-B22))+B8*B14*(B9/B14)^B22-B10","v":-55557.777799999691},"B9-(B9^B22)*(B14^(1-B22))+B8*B14*(B9/B14)^B22-B10"]
["Leader's Real Option Value (After Entry of F.)",{"$f":"B8*B9","v":666660},"B8*B9"]
[]
["b1",{"$f":"0.5-(B6/B7^2)+SQRT(((B6/B7^2)-0.5)^2+(2*B5/B7^2))","v":1.9999999999999998},"0.5-(B6/B7^2)+SQRT(((B6/B7^2)-0.5)^2+(2*B5/B7^2))"]
["IF B22=2","QUADRATIC SOLUTION"]
["d",{"$f":"(B14^(-B22))*((1-B8)*B14-B10)+(1-B8)*B14^(1-B22)","v":8.333666670000021E-8},"(B14^(-B22))*((1-B8)*B14-B10)+(1-B8)*B14^(1-B22)"]
["B15=",{"$f":"(1-SQRT(1-4*B24*B10))/(2*B24)","v":1101025.4635044036},"(1-SQRT(1-4*B24*B10))/(2*B24)"]
[]
["Assuming that the total market is $1,000,000 and that Julia's value will be 2/3rds of that amount after"]
["the follower enters, at the current V, the leader's value is negative. Note that the current NPV after the"]
["follower enters for both the leader and follower is now -$1,000,000, since the total market is $1,000,000"]
["and both have the same investment cost of $1,000,000. Note that if V=$1,101,025, the value of the "]
["follower and leader are equal, so it pays then to be the leader."]
["Mark should not enter until V is six times the current V, when he will have a value of his RO earnings of  "]
["$1,999,940."]

{"sheet":"Exercise 9.1 B","index":44,"n_rows":28,"n_cols":3,"rows_kept":28,"cut":false,"hidden":false,"merged":[]}
["Duopoly Competition with Permanent First-Mover Advantage"]
["                                                             Stochastic Value",null," "]
["Exercise 9.1 B"]
[null," "]
["Risk-free Rate of Interest (r)",0.04]
["Expected Drift of V (m)",0]
["Volatility of Value (s)",0.2]
["Leader's Market Share After Follower's Entry (a)",0.66666000000000003]
["Total Market Value (V)",1101025]
["Investment Cost (K)",1000000]
["Follower's Real Option Value ",{"$f":"IF(B9<B14,B17,B18)","v":33675.126148664654},"IF(B9<B14,B17,B18)"]
["Leader's Real Option Value ",{"$f":"IF(B9<B14,B19,B20)","v":33674.747702670866},"IF(B9<B14,B19,B20)"]
[]
["Investment Trigger Follower (VF) ",{"$f":"(B22/(B22-1))*B10*(1/(1-B8))","v":5999880.0023999522},"(B22/(B22-1))*B10*(1/(1-B8))"]
["Investment Trigger Leader (VL) ",{"$f":"B25","v":1101025.4635044036}," "]
[]
["Follower's Real Option Value (Before Entry)",{"$f":"(((1-B8)*B14-B10)*(B9/B14)^B22)","v":33675.126148664654},"(((1-B8)*B14-B10)*(B9/B14)^B22)"]
["Follower's Real Option Value (After Entry)",{"$f":"((1-B8)*B9-B10)","v":-632984.32649999997},"((1-B8)*B9-B10)"]
["Leader's Real Option Value (Before Entry of F.)",{"$f":"B9-(B9^B22)*(B14^(1-B22))+B8*B14*(B9/B14)^B22-B10","v":33674.747702670866},"B9-(B9^B22)*(B14^(1-B22))+B8*B14*(B9/B14)^B22-B10"]
["Leader's Real Option Value (After Entry of F.)",{"$f":"B8*B9","v":734009.32650000008},"B8*B9"]
[]
["b1",{"$f":"0.5-(B6/B7^2)+SQRT(((B6/B7^2)-0.5)^2+(2*B5/B7^2))","v":1.9999999999999998},"0.5-(B6/B7^2)+SQRT(((B6/B7^2)-0.5)^2+(2*B5/B7^2))"]
["IF B22=2","QUADRATIC SOLUTION"]
["d",{"$f":"(B14^(-B22))*((1-B8)*B14-B10)+(1-B8)*B14^(1-B22)","v":8.333666670000021E-8},"(B14^(-B22))*((1-B8)*B14-B10)+(1-B8)*B14^(1-B22)"]
["B15=",{"$f":"(1-SQRT(1-4*B24*B10))/(2*B24)","v":1101025.4635044036},"(1-SQRT(1-4*B24*B10))/(2*B24)"]
[]
["If V=$1,101,025, the leader and follower value functions would be equal (B17=B19), so at "]
["that point it pays to be the leader and Julia should invest."]

{"sheet":"Problem 9.2","index":45,"n_rows":35,"n_cols":3,"rows_kept":35,"cut":false,"hidden":false,"merged":[]}
["RIVALRY UNDER PRICE & QUANTITY UNCERTAINTY"]
["Problem 9.2"]
["r",0.04]
["u",0]
["w",0]
["s"," "]
["s2"," "]
["a"," "]
["a2"," "]
["r"," "]
[" "," "," "]
["b",2," "]
["P",0.1]
["Q",5]
["X",{"$f":"+B14*B13","v":0.5}]
["K",12.5]
["XF",{"$f":"B12*(B3-B5-B4)*B16/(B12-1)","v":1},"B12*(B3-B5-B4)*B16/(B12-1)"]
["Option",{"$f":"B16/(B12-1)*((B15/B17)^B12)","v":3.125},"B16/(B12-1)*((B15/B17)^B12)"]
["NPV",{"$f":"B15/(B3-B4-B5)-B16","v":0},"B15/(B3-B4-B5)-B16"]
["Follower ROV",{"$f":"IF(B15<B17,B18,B19)","v":3.125},"IF(B15<B17,B18,B19)"]
["m",1," "]
["m*",2," "]
["Leader before",{"$f":"(B15/B17)^B12*B16*B12/(B12-1)*(B21-B22)+B15*B22/(B3-B5-B4)-B16","v":6.25},"(B15/B17)^B12*B16*B12/(B12-1)*(B21-B22)+B15*B22/(B3-B5-B4)-B16"]
["Leader after",{"$f":"B15*B21/(B3-B5-B4)","v":12.5},"B15*B21/(B3-B5-B4)"]
["Leader ROV",{"$f":"IF(B15<B17,B23,B24)","v":6.25},"IF(B15<B17,B23,B24)"]
["XL",0.33333334475953785," "]
["Solver",{"$f":"((B26/B17)^B12)*B16*B12/(B12-1)*(B21-B22)+B26*B22/(B3-B4-B5)-B16-(B16/(B12-1))*((B26/B17)^B12)","v":2.8565510801215055E-7},"Set B27=0, Changing B26."]
[{"$f":"A29","v":"Quadratic"},{"$f":"((-B22/(B3-B4-B5))+SQRT(4*(B16^2)*(2*(B21-B22)-1)+(-B22/(B3-B4-B5))^2))/(2*B16*(2*(B21-B22)-1))","v":0.33333333333333331}]
["Quadratic","                                                                                                                                                 ((-B22/(B3-B4-B5))+SQRT(4*(B16^2)*(2*(B21-B22)-1)+(-B22/(B3-B4-B5))^2))/(2*B16*(2*(B21-B22)-1))"]
["Solver","((B26/B17)^B12)*B16*B12/(B12-1)*(B21-B22)+B26*B22/(B3-B4-B5)-B16-B16/(B12-1)*(B26/B17)^B12"]
["Julia should become the leader (invest) now since X>XL .  "]
["Mark should restrain himself until X reaches 1 (any combination of P & Q, such as   "]
["P=.10 and Q=10), but the follower's ROV is significant."]
[" "]
[null,null," "]

{"sheet":"Problem 9.3","index":46,"n_rows":39,"n_cols":3,"rows_kept":39,"cut":false,"hidden":false,"merged":[]}
["RIVALRY UNDER NET REVENUE & INVESTMENT COST UNCERTAINTY"]
["Problem 9.3"]
["Riskless rate",0.08]
["Value Drift",0.04]
["Cost Drift",0]
["Value Volatility"," "]
["Cost Volatility"," "]
["Correlation"," "]
["s2"," "]
["a2"," "]
["g2  "," "," "]
["b1      ",2," "]
["PV of CF (F)=V",{"$f":"B14/(B3-B4)","v":12.5},"B14/(B3-B4)"]
["Eq AnnualRevenue",0.5]
["K",12.5," "]
["Y Current",{"$f":"B14/B15","v":0.04},"B14/B15"]
["YF Trigger ",{"$f":"(B3-B4)*B12/(B12-1)","v":0.08},"(B3-B4)*B12/(B12-1)"]
["Follower Before",{"$f":"B15/(B12-1)*(B16/B17)^B12","v":3.125},"B15/(B12-1)*(B16/B17)^B12"]
["Follower After",{"$f":"B14/(B3-B4)-B15","v":0},"B14/(B3-B4)-B15"]
["Follower Value",{"$f":"IF(B16<B17,B18,B19)","v":3.125},"IF(B16<B17,B18,B19)"]
["m (L's Market A/F)",1," "]
["m*(Total Market)",2," "]
["Leader Before",{"$f":"B14*B22/(B3-B4)+(B16/B17)^B12*B12*B15/(B12-1)*(B21-B22)-B15","v":6.25},"B14*B22/(B3-B4)+(B16/B17)^B12*B12*B15/(B12-1)*(B21-B22)-B15"]
["Leader After",{"$f":"B14*B21/(B3-B4)","v":12.5},"B14*B21/(B3-B4)"]
["Leader   Value",{"$f":"IF(B16<B17,B23,B24)","v":6.25},"IF(B16<B17,B23,B24)"]
["Follower at YL",{"$f":"B15/(B12-1)*(B28/B17)^B12","v":1.3888891368399987},"B15/(B12-1)*(B28/B17)^B12"]
["Leader at YL",{"$f":"B15*B28*B22/(B3-B4)+(B28/B17)^B12*B12*B15/(B12-1)*(B21-B22)-B15","v":1.3888898806932612},"B15*B28*B22/(B3-B4)+(B28/B17)^B12*B12*B15/(B12-1)*(B21-B22)-B15"]
["YL Trigger",2.6666669046997216E-2,"SOLVER: SET B29=0, CHANGING B28."]
["YF-YL",{"$f":"B27-B26","v":7.4385326254144957E-7},"B27-B26"]
["Quadratic",{"$f":"((-B22/(B3-B4-B5))+SQRT(4*(B15^2)*(2*(B21-B22)-1)+(-B22/(B3-B4-B5))^2))/(2*B15*(2*(B21-B22)-1))/B15","v":2.6666666666666665E-2}]
["                                                                                                                                                ((-B22/(B3-B4-B5))+SQRT(4*(B16^2)*(2*(B21-B22)-1)+(-B22/(B3-B4-B5))^2))/(2*B16*(2*(B21-B22)-1))/b15"]
["YF Trigger *K",{"$f":"B17*B15","v":1}]
["USE:   INPUTS INTO BOLD BLUE CELLS"]
["SOLVER: SET B29=0, CHANGING B28."]
[" "]
["Notice that the follower's trigger multiplied by K equals 1 (B32), so the quadratic solution can"]
["be used.  This is an out-of-the money call option for the follower, since he will"]
["have V=12.5/2-K=-6.25, but the real option value is significant."]
["The leader should enter now since Y>Y(L), but the follower should delay."]

{"sheet":"Problem 9.4","index":47,"n_rows":31,"n_cols":3,"rows_kept":31,"cut":false,"hidden":false,"merged":[]}
["Duopoly Competition with Permanent First-Mover Advantage"]
["                                                             Stochastic Value",null," "]
["Problem 9.4"]
[null," "]
["Risk-free Rate of Interest (r)",0.05]
["Expected Drift of V (m)",0]
["Volatility of Value (s)",0.4]
["Leader's Market Share After Follower's Entry (a)",0.65]
["Total Market Value (V)",1250000]
["Investment Cost (K)",1000000]
["Follower's Real Option Value ",{"$f":"IF(B9<B14,B17,B18)","v":126502.87022759898},"IF(B9<B14,B17,B18)"]
["Leader's Real Option Value ",{"$f":"IF(B9<B14,B19,B20)","v":68415.965177400736},"IF(B9<B14,B19,B20)"]
[]
["Investment Trigger Follower (VF) ",{"$f":"(B22/(B22-1))*B10*(1/(1-B8))","v":9419037.0134559348},"(B22/(B22-1))*B10*(1/(1-B8))"]
["Investment Trigger Leader (VL) ",1340661.3507450651," "]
[]
["Follower's Real Option Value (Before Entry)",{"$f":"(((1-B8)*B14-B10)*(B9/B14)^B22)","v":126502.87022759898},"(((1-B8)*B14-B10)*(B9/B14)^B22)"]
["Follower's Real Option Value (After Entry)",{"$f":"((1-B8)*B9-B10)","v":-562500},"((1-B8)*B9-B10)"]
["Leader's Real Option Value (Before Entry of F.)",{"$f":"B9-(B9^B22)*(B14^(1-B22))+B8*B14*(B9/B14)^B22-B10","v":68415.965177400736},"B9-(B9^B22)*(B14^(1-B22))+B8*B14*(B9/B14)^B22-B10"]
["Leader's Real Option Value (After Entry of F.)",{"$f":"(B8*B9)","v":812500},"(B8*B9)"]
[]
["b1",{"$f":"0.5-(B6/B7^2)+SQRT(((B6/B7^2)-0.5)^2+(2*B5/B7^2))","v":1.4354143466934852},"0.5-(B6/B7^2)+SQRT(((B6/B7^2)-0.5)^2+(2*B5/B7^2))"]
["Leader's Value Function at Trigger",{"$f":"B15-(B15^B22)*(B14^(1-B22))+B8*B14*(B15/B14)^B22-B10","v":139878.19001222029},"B15-(B15^B22)*(B14^(1-B22))+B8*B14*(B15/B14)^B22-B10"]
["Follower's Value Function at Trigger",{"$f":"(((1-B8)*B14-B10)*(B15/B14)^B22)","v":139878.19001207242},"(((1-B8)*B14-B10)*(B15/B14)^B22)"]
["B22-B23, changing B14.",{"$f":"B23-B24","v":1.4787656255066395E-7},"B23-B24"]
[]
["Since beta does not equal 2, the simple solution cannot be used."]
["The leader's trigger is the result of equating the value functions of the leader and follower."]
["subsituting the trigger for V in cells B23 and B24, setting B25=0, by changing B15, using Solver."]
["Now Julia should delay becoming the leader since V<V(L), and "]
["Mark should restrain himself until V reaches over 7.5 times the current V, due to the high V volatility."]

{"sheet":"Problem 9.5","index":48,"n_rows":33,"n_cols":3,"rows_kept":33,"cut":false,"hidden":false,"merged":[]}
["RIVALRY UNDER PRICE & QUANTITY UNCERTAINTY"]
["Problem 9.5"," "]
["r",0.04]
["u",0]
["w",0]
["s",0.4]
["s2",{"$f":"+B6^2","v":0.16000000000000003}]
["a",0.3]
["a2",{"$f":"B8^2","v":0.09}]
["r",-0.2]
["z2",{"$f":"B7+B9+2*B6*B8*B10","v":0.20200000000000001},"B7+B9+2*B6*B8*B10"]
["b",{"$f":"0.5-(B4-B5)/(B11)+SQRT(((B4-B5)/(B11)-0.5)^2 + 2*B3/(B11))","v":1.3037658887763253},"0.5-(B4-B5)/(B11)+SQRT(((B4-B5)/(B11)-0.5)^2 + 2*B3/(B11))"]
["P",0.2]
["Q",5]
["X",{"$f":"B13*B14","v":1},"B13*B14"]
["K",20]
["XF",{"$f":"B12*(B3-B5-B4)*B16/(B12-1)","v":3.4336070953281772},"B12*(B3-B5-B4)*B16/(B12-1)"]
["Option",{"$f":"B16/(B12-1)*((B15/B17)^B12)","v":13.182495691160646},"B16/(B12-1)*((B15/B17)^B12)"]
["NPV",{"$f":"B15/(B3-B4-B5)-B16","v":5},"B15/(B3-B4-B5)-B16"]
["Follower ROV",{"$f":"IF(B15<B17,B18,B19)","v":13.182495691160646},"IF(B15<B17,B18,B19)"]
["m",2," "]
["m*",4," "]
["Leader before",{"$f":"(B15/B17)^B12*B16*B12/(B12-1)*(B21-B22)+B15*B22/(B3-B5-B4)-B16","v":45.626223577847725},"(B15/B17)^B12*B16*B12/(B12-1)*(B21-B22)+B15*B22/(B3-B5-B4)-B16"]
["Leader after",{"$f":"B15*B21/(B3-B5-B4)","v":50},"B15*B21/(B3-B5-B4)"]
["Leader ROV",{"$f":"IF(B15<B17,B23,B24)","v":45.626223577847725},"IF(B15<B17,B23,B24)"]
["XL",0.29819099952294875]
["Solver",{"$f":"(B26/B17)^B12*B16*B12/(B12-1)*(B21-B22)+B26*B22/(B3-B4-B5)-B16-B16/(B12-1)*(B26/B17)^B12","v":-3.9141398655573312E-7}]
["(B26/B17)^B12*B16*B12/(B12-1)*(B21-B22)+B26*B22/(B3-B4-B5)-B16-B16/(B12-1)*(B26/B17)^B12"]
["Set B27=0, Changing B26."]
[]
["Julia should invest now since X>XL , and also the NPV is positive."]
["Mark should restrain himself until X reaches 3.4 times the current level   "]
["although his option value is significant."]

{"sheet":"Problem 9.6","index":49,"n_rows":38,"n_cols":3,"rows_kept":38,"cut":false,"hidden":false,"merged":[]}
["RIVALRY UNDER NET REVENUE & INVESTMENT COST UNCERTAINTY"]
["Problem 9.6"," "]
["Riskless rate",0.04]
["Value Drift",0]
["Cost Drift",0.02]
["Value Volatility",0.6]
["Cost Volatility",0.1]
["Correlation",0.2]
["s2",{"$f":"+B6^2","v":0.36}]
["a2",{"$f":"+B7^2","v":1.0000000000000002E-2}]
["g2  ",{"$f":"B9+B10-2*B6*B7*B8","v":0.34599999999999997},"B9+B10-2*B6*B7*B8"]
["b1      ",{"$f":"0.5+(B4-B5)/B11+SQRT(((B4-B5)/B11-0.5)^2+2*B5/B11)","v":1.0954588417112547},"0.5+(B4-B5)/B11+SQRT(((B4-B5)/B11-0.5)^2+2*B5/B11)"]
["PV of CF (F)=V",{"$f":"B14/(B3-B4)","v":1000000},"B14/(B3-B4)"]
["Eq AnnualReturnF",40000," "]
["K",1000000," "]
["Y Current",{"$f":"B14/B15","v":0.04},"B14/B15"]
["YF Trigger ",{"$f":"(B3-B4)*B12/(B12-1)","v":0.45902875923209469},"(B3-B4)*B12/(B12-1)"]
["Follower Before",{"$f":"B15/(B12-1)*(B16/B17)^B12","v":723166.95487637375},"B15/(B12-1)*(B16/B17)^B12"]
["Follower After",{"$f":"B14/(B3-B4)-B15","v":0},"B14/(B3-B4)-B15"]
["Follower Value",{"$f":"IF(B16<B17,B18,B19)","v":723166.95487637375},"IF(B16<B17,B18,B19)"]
["m (L's Market A/F)",2," "]
["m*(Total Market)",3," "]
["Leader Before",{"$f":"B14*B22/(B3-B4)+(B16/B17)^B12*B12*B15/(B12-1)*(B21-B22)-B15","v":1207800.3652472724},"B14*B22/(B3-B4)+(B16/B17)^B12*B12*B15/(B12-1)*(B21-B22)-B15"]
["Leader After",{"$f":"B14*B21/(B3-B4)","v":2000000},"B14*B21/(B3-B4)"]
["Leader   Value",{"$f":"IF(B16<B17,B23,B24)","v":1207800.3652472724},"IF(B16<B17,B23,B24)"]
["Follower at YL",{"$f":"B15/(B12-1)*(B28/B17)^B12","v":448584.93449889362},"B15/(B12-1)*(B28/B17)^B12"]
["Leader at YL",{"$f":"B15*B28*B22/(B3-B4)+(B28/B17)^B12*B12*B15/(B12-1)*(B21-B22)-B15","v":448584.93449905119},"B15*B28*B22/(B3-B4)+(B28/B17)^B12*B12*B15/(B12-1)*(B21-B22)-B15"]
["YL Trigger",2.5866550230057711E-2,"SOLVER: SET B29=0, CHANGING B28."]
["YF-YL",{"$f":"B27-B26","v":1.5756813809275627E-7},"B27-B26"]
["USE:   INPUTS INTO BOLD BLUE CELLS"]
["SOLVER: SET B29=0, CHANGING B28."]
["NOTE: ASSUMES K FOR EACH FIRM IS THE SAME REGARDLESS OF MARKET SHARE."]
[]
["This wonderful RO class and models indicate that Julia should invest now to become the"]
["leader since Y>Y(L), since she will have a very good return until Mark is inspired."]
["Mark should restrain himself for a little while, until Y>.46, which may be soon.  If he is"]
["impatient, perhaps he might attempt to sell his option to enter, although the number of students"]
["in this wonderful RO class are, so far, limited."]

{"sheet":"Exercise 10.1","index":50,"n_rows":22,"n_cols":4,"rows_kept":22,"cut":false,"hidden":false,"merged":[]}
[null,"Real Debt Strategy Simple"]
["Exercise10.1"]
[" "]
[null,"ACCOUNTS","REAL"]
["ASSETS",{"$f":"B10","v":100},{"$f":"C10-C15*C19*(C19/C10)^-C20","v":87.5},"C10-C15*C19*(C19/C10)^-C20"]
["DEBT",100,{"$f":"B6+((1-C15)*C19-B6)*(C19/C10)^-C20","v":62.5},"B6+((1-C15)*C19-B6)*(C19/C10)^-C20"]
["EQ",{"$f":"B5-B6","v":0},{"$f":"C5-C6","v":25},"C5-C6"]
[]
["INPUT"," "]
["NOM V",100,{"$f":"B10","v":100}," "]
["Coupon",4,{"$f":"B11","v":4}," "]
["NOM Debt",{"$f":"B11/C17","v":100},{"$f":"B12","v":100}," "]
["d",null,0.04," "]
["s",null,0.2," "]
["a",null,0.5," "]
["t",null,0," "]
["r(f)",null,0.04," "]
["OUTPUT"]
["VB   ",null,{"$f":"((((1-C16)*C11)/C17))*-C20/(1-C20)","v":49.999999999999993},"(1-C16)*(C11/C17)*(-C20/(-C20+1))"]
["b2",null,{"$f":"(0.5-(C17-C13)/(C14^2)-SQRT((0.5-(C17-C13)/(C14^2))^2+2*C17/(C14^2)))","v":-0.99999999999999978}," "]
[null,null," "]
["b2","(0.5-(C17-C13)/(C14^2)-SQRT((0.5-(C17-C13)/(C14^2))^2+2*C17/(C14^2)))"]

{"sheet":"Exercise 10.2","index":51,"n_rows":22,"n_cols":4,"rows_kept":22,"cut":false,"hidden":false,"merged":[]}
[null,"Real Debt Strategy Simple"]
["Exercise10.2"]
[" "]
[null,"ACCOUNTS","REAL"]
["ASSETS",{"$f":"B10","v":100},{"$f":"C10-C15*C19*(C19/C10)^-C20","v":85.18518518518519},"C10-C15*C19*(C19/C10)^-C20"]
["DEBT",100,{"$f":"B6+((1-C15)*C19-B6)*(C19/C10)^-C20","v":70.370370370370381},"B6+((1-C15)*C19-B6)*(C19/C10)^-C20"]
["EQ",{"$f":"B5-B6","v":0},{"$f":"C5-C6","v":14.81481481481481},"C5-C6"]
[]
["INPUT"," "]
["NOM V",100,{"$f":"B10","v":100}," "]
["Coupon",8,{"$f":"B11","v":8}," "]
["NOM Debt",{"$f":"B11/C17","v":100},{"$f":"B12","v":100}," "]
["d",null,0.06," "]
["s",null,0.2," "]
["a",null,0.5," "]
["t",null,0," "]
["r(f)",null,0.08," "]
["OUTPUT"]
["VB   ",null,{"$f":"((((1-C16)*C11)/C17))*-C20/(1-C20)","v":66.666666666666657},"(1-C16)*(C11/C17)*(-C20/(-C20+1))"]
["b2",null,{"$f":"(0.5-(C17-C13)/(C14^2)-SQRT((0.5-(C17-C13)/(C14^2))^2+2*C17/(C14^2)))","v":-1.9999999999999998}," "]
[null,null," "]
["b2","(0.5-(C17-C13)/(C14^2)-SQRT((0.5-(C17-C13)/(C14^2))^2+2*C17/(C14^2)))"]

{"sheet":"Exercise 10.3","index":52,"n_rows":22,"n_cols":4,"rows_kept":22,"cut":false,"hidden":false,"merged":[]}
[null,"Real Debt Strategy Simple"]
["Exercise10.3"]
[" "]
[null,"ACCOUNTS","REAL"]
["ASSETS",{"$f":"B10","v":200},{"$f":"C10-C15*C19*(C19/C10)^-C20","v":193.75},"C10-C15*C19*(C19/C10)^-C20"]
["DEBT",100,{"$f":"B6+((1-C15)*C19-B6)*(C19/C10)^-C20","v":81.25},"B6+((1-C15)*C19-B6)*(C19/C10)^-C20"]
["EQ",{"$f":"B5-B6","v":100},{"$f":"C5-C6","v":112.5},"C5-C6"]
[]
["INPUT"," "]
["NOM V",200,{"$f":"B10","v":200}," "]
["Coupon",4,{"$f":"B11","v":4}," "]
["NOM Debt",{"$f":"B11/C17","v":100},{"$f":"B12","v":100}," "]
["d",null,0.04," "]
["s",null,0.2," "]
["a",null,0.5," "]
["t",null,0," "]
["r(f)",null,0.04," "]
["OUTPUT"]
["VB   ",null,{"$f":"((((1-C16)*C11)/C17))*-C20/(1-C20)","v":49.999999999999993},"(1-C16)*(C11/C17)*(-C20/(-C20+1))"]
["b2",null,{"$f":"(0.5-(C17-C13)/(C14^2)-SQRT((0.5-(C17-C13)/(C14^2))^2+2*C17/(C14^2)))","v":-0.99999999999999978}," "]
[null,null," "]
["b2","(0.5-(C17-C13)/(C14^2)-SQRT((0.5-(C17-C13)/(C14^2))^2+2*C17/(C14^2)))"]

{"sheet":"Problem 10.4","index":53,"n_rows":22,"n_cols":4,"rows_kept":22,"cut":false,"hidden":false,"merged":[]}
[null,"Real Debt Strategy Simple"]
["Problem10.4"]
[" "]
[null,"ACCOUNTS","REAL"]
["ASSETS",{"$f":"B10","v":100},{"$f":"C10+(C16*C11/C17)*(1-(C19/C10)^-C20)-C15*C19*(C19/C10)^-C20","v":115.45606441432012},"C10+(C16*C11/C17)*(1-(C19/C10)^-C20)-C15*C19*(C19/C10)^-C20"]
["DEBT",{"$f":"B11/C17","v":100},{"$f":"B6+((1-C15)*C19-B6)*(C19/C10)^-C20","v":62.203413920870183},"B6+((1-C15)*C19-B6)*(C19/C10)^-C20"]
["EQ",{"$f":"B5-B6","v":0},{"$f":"C5-C6","v":53.252650493449941},"C5-C6"]
[]
["INPUT"," "]
["NOM V",100,{"$f":"B10","v":100}," "]
["Coupon",4,{"$f":"B11","v":4}," "]
["NOM Debt",{"$f":"B11/C17","v":100},{"$f":"B12","v":100}," "]
["d",null,0.04," "]
["s",null,0.3," "]
["a",null,0.4," "]
["t",null,0.35," "]
["r(f)",null,0.04," "]
["OUTPUT"]
["VB   ",null,{"$f":"(1-C16)*(C11/C17)*(-C20/(-C20+1))","v":23.524423356287159},"(1-C16)*(C11/C17)*(-C20/(-C20+1))"]
["b2",null,{"$f":"(0.5-(C17-C13)/(C14^2)-SQRT((0.5-(C17-C13)/(C14^2))^2+2*C17/(C14^2)))","v":-0.56718737290547483}," "]
[null,null," "]
["b2","(0.5-(C17-C13)/(C14^2)-SQRT((0.5-(C17-C13)/(C14^2))^2+2*C17/(C14^2)))"]

{"sheet":"Problem 10.5","index":54,"n_rows":25,"n_cols":5,"rows_kept":25,"cut":false,"hidden":false,"merged":[]}
[null,"Real Debt Strategy ",null," "]
[" ","Problem 10.5"]
["BASE CASE"]
[null,"ACCOUNTS","REAL 1","REAL 2"]
["ASSETS",{"$f":"B10","v":100},{"$f":"C10+(C16*C11/C17)*(1-(C19/C10)^-C20)-C15*C19*(C19/C10)^-C20","v":118.53969609437975},{"$f":"D10+(D16*D11/D17)*(1-(D19/D10)^-D20)-D15*D19*(D19/D10)^-D20","v":122.71507520194902},"V*"]
["DEBT",{"$f":"B11/C17","v":133.33333333333334},{"$f":"(C11/C17)+((1-C15)*C19-(C11/C17))*(C19/C10)^-C20","v":90.334942442418878},{"$f":"(D11/D17)+((1-D15)*D19-(D11/D17))*(D19/D10)^-D20","v":94.701734196691973},"D*"]
["EQ",{"$f":"B5-B6","v":-33.333333333333343},{"$f":"C5-C6","v":28.204753651960871},{"$f":"D5-D6","v":28.013341005257047},"E*"]
[null,null,"WE CHOOSE","YOU CHOOSE"]
["Retained Equity","MAX",{"$f":"C7","v":28.204753651960871},{"$f":"(1-D24)*D7","v":28.013341005257047}]
["NOM V",100,{"$f":"B10","v":100},100]
["Coupon",8,8,8]
["NOM Debt",{"$f":"B11/C17","v":133.33333333333334},133.33333333333334,133.33333333333334]
["d",null,0.06,{"$f":"C13","v":0.06}]
["s",null,0.2,{"$f":"C14","v":0.2}]
["a",null,0.5,{"$f":"C15","v":0.5}]
["t",null,0.35,{"$f":"C16","v":0.35}]
["r(f)",null,0.06,{"$f":"C17","v":0.06}]
["OUTPUT"]
["VB   ",null,{"$f":"(1-C16)*(C11/C17)*(-C20/(-C20+1))","v":49.030926021075707},{"$f":"$B$6/D23","v":44.44444444444445}]
["b2",null,{"$f":"(0.5-(C17-C13)/(C14^2)-SQRT((0.5-(C17-C13)/(C14^2))^2+2*C17/(C14^2)))","v":-1.3027756377319943},{"$f":"(0.5-(D17-D13)/(D14^2)-SQRT((0.5-(D17-D13)/(D14^2))^2+2*D17/(D14^2)))","v":-1.3027756377319943}]
["LTV",{"$f":"$B$6/B5","v":1.3333333333333335},{"$f":"$B$6/C19","v":2.7193721219138438},{"$f":"$B$6/D19","v":3}]
[]
[null," ","LTV MAX",3]
[null,null,"SHARED EQUITY",0]
["DEBT* + SH EQ"," ",{"$f":"C6","v":90.334942442418878},{"$f":"D6","v":94.701734196691973}]

{"sheet":"Problem 10.6","index":55,"n_rows":29,"n_cols":10,"rows_kept":29,"cut":false,"hidden":false,"merged":[]}
[null,null,null," ",null,"Real Debt Strategy i"]
["Problem 10.6"]
["BASE CASE",null,null,null," "]
[null,"ACCOUNTS","REAL 1","REAL 2","REAL 3","REAL 4","REAL 5","REAL 6","REAL 7"]
["ASSETS",{"$f":"B10","v":40},{"$f":"C10+(C16*C11/C17)*(1-(C19/C10)^-C20)-C15*C19*(C19/C10)^-C20","v":36.253880774474801},{"$f":"D10+(D16*D11/D17)*(1-(D19/D10)^-D20)-D15*D19*(D19/D10)^-D20","v":43.560841707710097},42.860126272246134,41.8615578499656,41.06040097752981,39.916022285668191,38.995674631318138,"V*"]
["DEBT",{"$f":"B11/C17","v":66.666666666666671},{"$f":"(C11/C17)+((1-C15)*C19-(C11/C17))*(C10^C20)*C19^-C20","v":34.668605538403241},{"$f":"(D11/D17)+((1-D15)*D19-(D11/D17))*(D10^D20)*D19^-D20","v":42.416793371007479},41.630896053093608,40.528300249586508,39.657731440960944,38.434740698121963,37.467828710203079,"D*"]
["EQ",{"$f":"B5-B6","v":-26.666666666666671},{"$f":"C10-(1-C16)*(C11/C17)+((1-C16)*(C11/C17)-C19)*((C19/C10)^-C20)","v":1.5852752360715421},{"$f":"D10-(1-D16)*(D11/D17)+((1-D16)*(D11/D17)-D19)*((D19/D10)^-D20)","v":1.1440483367026362},1.2292302191525302,1.3332576003790733,1.4026695365688706,1.4812815875462402,1.527845921115043,"E*"]
[null,null,"WE CHOOSE","YOU CHOOSE","NEGOTIATE","NEGOTIATE","NEGOTIATE","NEGOTIATE","NEGOTIATE"]
["Retained Equity",null,{"$f":"C7","v":1.5852752360715421},{"$f":"(1-D23)*D7","v":1.1440483367026362},1.2169379169610048,1.3065924483714917,1.3605894504718044,1.4220303240443906,1.4514536250592909]
["NOM V",40,{"$f":"B10","v":40},{"$f":"C10","v":40},{"$f":"D10","v":40},40,{"$f":"B10","v":40},40,40]
["Coupon",4,{"$f":"B11","v":4},{"$f":"C11","v":4},4,4,4,4,4]
["NOM Debt",{"$f":"B11/C17","v":66.666666666666671},66.666666666666671,{"$f":"C12","v":66.666666666666671},66.666666666666671,66.666666666666671,66.666666666666671,66.666666666666671,66.666666666666671]
["d",null,0.01,{"$f":"C13","v":0.01},0.01,0.01,0.01,0.01,0.01]
["s",null,0.2,{"$f":"C14","v":0.2},0.2,0.2,0.2,0.2,0.2]
["a",null,0.5,{"$f":"C15","v":0.5},0.5,0.5,0.5,0.5,0.5]
["t",null,0.3,0.3,0.3,0.3,0.3,0.3,0.3]
["r(f)",null,0.06,0.06,0.06,0.06,0.06,0.06,0.06]
["OUTPUT",null,null," "]
["VB   ",null,{"$f":"(1-C16)*(C11/C17)*(-C20/(-C20+1))","v":33.837196510349166},{"$f":"$B$6/D22","v":30.03003003003003},{"$f":"$B$6/E22","v":30.441400304414007},31.007751937984498,31.446540880503147,32.051282051282051,32.520325203252035]
["b2",null,{"$f":"(0.5-(C17-C13)/(C14^2)-SQRT((0.5-(C17-C13)/(C14^2))^2+2*C17/(C14^2)))","v":-2.6374586088176866},{"$f":"(0.5-(D17-D13)/(D14^2)-SQRT((0.5-(D17-D13)/(D14^2))^2+2*D17/(D14^2)))","v":-2.6374586088176866},-2.6374586088176866,-2.6374586088176866,-2.6374586088176866,-2.6374586088176866,-2.6374586088176866]
["LTV",{"$f":"$B$12/B5","v":1.6666666666666667},{"$f":"$B$12/C5","v":1.8388835965280865},{"$f":"$B$12/D5","v":1.5304265035555302},1.555447276174647,1.592551020332404,1.6236243455866353,1.6701730996528497,1.7095913148563777]
[null,null,"LTV MAX",2.2200000000000002,2.19,2.15,2.12,2.08,2.0499999999999998]
[null,null,"SHARED EQUITY",0,0.01,{"$f":"E23+0.01","v":0.02},{"$f":"F23+0.01","v":0.03},0.04,0.05]
["DEBT LOSS + SH EQ",{"$f":"$B$6-(1-C15)*B10","v":46.666666666666671},{"$f":"$B$6-C6","v":31.99806112826343},{"$f":"$B$6-D6+D23*D7","v":24.249873295659192},{"$f":"$B$6-E6+E23*E7","v":25.048062915764589},26.165031569087745,27.051015311802793,28.291177232046557,29.275230252519343]
["CHANGE DEBT LOSS",null,{"$f":"C24-$B$24","v":-14.668605538403241},-22.416793371007479,-21.618603750902082,-20.501635097578927,-19.615651354863878,-18.375489434620114,-17.391436414147329]
["LTV",null,null,"$B$12/D5"]
["VB   ",null,null,"$B$6/D22"]
["DEBT LOSS + SH EQ",null,"$B$6-C6","$B$6-D6+D23*D7"]
["CHANGE DEBT LOSS",null,"C24-$B$24"]

{"sheet":"Exercise 11.1","index":56,"n_rows":47,"n_cols":11,"rows_kept":47,"cut":false,"hidden":false,"merged":[]}
["EXERCISE 11.1","                           Renewal Template"]
["INPUT","Deterministic"]
["PI",80," "]
["CI",20]
["K",150]
["C*",{"$f":"B21","v":26.265502974809472}]
["sP",0]
["sC",0]
["r",0]
["r",0.14000000000000001,null,null,null,null,null,null,null," "]
["qP",-0.1]
["qC",0.03]
[]
["OUTPUT"]
["Q(b,h)",{"$f":"B11*B18+B12*B19-B10","v":-1.2140288774276087E-13}," "]
["SP",{"$f":"((B3/B20)^B18)-((B4/B21)^B19)-EXP(-B10*B22)","v":-5.605598901725628E-8}," "]
["SUM",{"$f":"SUM(ABS(B15:B16))","v":5.6056110420144023E-8},"SUM(ABS(B15:B16))"]
["b",-0.41187854027421994]
["h",3.2937381990818873]
["P*",32.25305816293119," ",null,"CALCULATOR"]
["C*",26.265502974809472,null,null,"T*C",{"$f":"(1/B12)*(LN(B21/B4))","v":9.0841376890279779},"(1/B12)*(LN(B21/B4))"]
["T*C",{"$f":"(1/B12)*(LN(B21/B4))","v":9.0841376890279779},null,null,"P(9)",{"$f":"$B$3*EXP(B11*B22)","v":32.253058171559488},"$B$3*EXP(B11*B22)"]
["T*P",{"$f":"(1/B11)*(LN(B20/B3))","v":9.084137691703166},null,null,"P*",{"$f":"EXP(F21*B11+LN(B3))","v":32.253058171559474},"EXP(F21*B11+LN(B3))"]
["SOLVER",{"$f":"ABS(B37)+ABS(B17)","v":2.9719717664633549E-7},"ABS(B37)+ABS(B17)"]
["P*-C*",{"$f":"B20-B21","v":5.9875551881217177}]
[{"$f":"B2","v":"Deterministic"}]
["Q(b,h)","B11*B18+B12*B19-B10",null,null,null," "]
["SP","((B3/B20)^B18)-((B4/B21)^B19)-EXP(-B10*B22)",null,null,null," "]
["SOLVER","SET B24=0,CHANGING B18:B21,B22=B23"]
[]
["T*C","(1/B12)*(LN(B6/B4))",null,null,null," "]
["T*P","(1/B11)*(LN(B20/B3))",null,null,null," "]
[]
["P* VALUE",{"$f":"B20*((1/B10)+(B11/B10)*(EXP(-B10*B23)/(B10-B11)))","v":203.46953198990232}]
["C* VALUE",{"$f":"B21*((1/B10)+(B12/B10)*(EXP(-B10*B23)/(B10-B12)))","v":201.95438071589186}]
["Renewal V-K",{"$f":"B3/(B10-B11)-B4/(B10-B12)-B5","v":1.5151515151515298}]
["NPV=0",{"$f":"B34-B35-B36","v":-2.4114106622619147E-7}]
[" "," "]
["P*","B20*((1/B10)+(B11/B10)*(EXP(-B10*B22)/(B10-B11)))"]
["C*","B6*((1/B10)+(B12/B10)*(EXP(-B10*B22)/(B10-B12)))"]
["Renewal V-K","B3/(B10-B11)-B4/(B10-B12)-B5"]
["NPV=0","B31-B32-B33",null,null," "," "]
[null,"CAR DETERIORATION OVER THE YEARS"]
["YEARS",1,2,3,4,5,6,7,8,9," "]
["CAR ENJOY",{"$f":"$B$3*EXP($B$11*B44)","v":72.386993442876758},{"$f":"$B$3*EXP($B$11*C44)","v":65.498460246238551},59.265457654537428,53.62560368285115,48.52245277701067,43.904930887522113,39.72682430331276,35.946317129377725,32.525572779247931," "]
["COST",{"$f":"$B$4*EXP($B$12*B44)","v":20.609090679070338},{"$f":"$B$4*EXP($B$12*C44)","v":21.236730930907193},21.883485674104207,22.549937031587515,23.236684854565659,23.944347262436203,24.673561199134863,25.424983006428093,26.199289014664945," "]
["P-C",{"$f":"B45-B46","v":51.777902763806424},44.261729315331358,37.381971980433221,31.075666651263635,25.285767922445011,19.96058362508591,15.053263104177898,10.521334122949632,6.3262837645829855," "]

{"sheet":"Exercise 11.2","index":57,"n_rows":40,"n_cols":6,"rows_kept":40,"cut":false,"hidden":false,"merged":[]}
[null,null," Renewal Template"]
[" ","Stochastic P",null,"EXERCISE 11.2"]
["PI",80," "]
["CI",30]
["K",100]
["C*",30]
["sP",0.3]
["sC",0]
["r",0]
["r",0.14000000000000001]
["qP",-0.05]
["qC",0]
[]
["OUTPUT"," "]
["Q(b,h=0)",{"$f":"(0.5-B11/(B7^2))-SQRT((0.5-B11/(B7^2))^2+2*B10/(B7^2))-B19","v":0}]
["SP",{"$f":"(B20/(B19*(B10-B11)))*(B19-1+((B3/B20)^B19))-B3/(B10-B11)+B5","v":7.6143521710037021E-8}," "]
["SUM",{"$f":"SUM(ABS(B15:B16))","v":7.6143521710037021E-8}]
["OUTPUT"," "]
["b",-1]
["P*",41.012822635607236," "]
["h",0,null,null,null," "]
["P*-C*",{"$f":"B20-B6","v":11.012822635607236},null,null,null," "]
[{"$f":"B2","v":"Stochastic P"}]
["Q(b,h=0)","(0.5-B11/(B7^2))-SQRT((0.5-B11/(B7^2))^2+2*B10/(B7^2))-B19",null,null,null," "]
["SP","(B20/(B19*(B10-B11)))*(B19-1+((B3/B20)^B19))-B3/(B10-B11)+B5",null,null,null," "]
["SOLVER","SET B17=0, CHANGING B20."]
["QUADRATIC"," "]
["a",{"$f":"1/-((B10-B11)*B3)","v":-6.5789473684210523E-2}," "]
["b",{"$f":"(B19-1)/(-(B10-B11))","v":10.526315789473685}," "]
["c",{"$f":"-((B3/(B10-B11))-B5)","v":-321.05263157894734}," "]
["P*",{"$f":"(-B29+SQRT((B29^2)-4*B28*B30))/(2*B28)","v":41.012822620764119}," "]
[]
["a","1/-((B10-B11)*B3)"]
["b","(B19-1)/(-(B10-B11))"]
["c","-((B3/(B10-B11))-B5)"]
["P*","(-B29+SQRT((B29^2)-4*B28*B30))/(2*B28)"]
[]
["Actual Age",{"$f":"(1/B11)*LN((0.5*B3)/B3)","v":13.862943611198906},"Years"]
["Renewal Age",{"$f":"(1/B11)*LN(B31/B3)","v":13.362837400335394},"Years"]
["Renewal Age","(1/B11)*LN(B31/B3)"]

{"sheet":"Exercise 11.3","index":58,"n_rows":40,"n_cols":4,"rows_kept":40,"cut":false,"hidden":false,"merged":[]}
[null,null," Renewal Template"]
[" ","Stochastic P",null,"EXERCISE 11.3"]
["PI",80," "]
["CI",1]
["K",100]
["C*",1]
["sP",0.2]
["sC",0]
["r",0]
["r",0.08]
["qP",-0.04]
["qC",0]
[]
["OUTPUT"," "]
["Q(b,h=0)",{"$f":"(0.5-B11/(B7^2))-SQRT((0.5-B11/(B7^2))^2+2*B10/(B7^2))-B19","v":0}]
["SP",{"$f":"(B20/(B19*(B10-B11)))*(B19-1+((B3/B20)^B19))-B3/(B10-B11)+B5","v":-1.0231815394945443E-12}," "]
["SUM",{"$f":"SUM(ABS(B15:B16))","v":1.0231815394945443E-12}]
["OUTPUT"," "]
["b",-1]
["P*",49.0161332303405," "]
["h",0]
["P*-C*",{"$f":"B20-B6","v":48.0161332303405}]
[{"$f":"B2","v":"Stochastic P"}]
["Q(b,h=0)","(0.5-B11/(B7^2))-SQRT((0.5-B11/(B7^2))^2+2*B10/(B7^2))-B19"]
["SP","(B20/(B19*(B10-B11)))*(B19-1+((B3/B20)^B19))-B3/(B10-B11)+B5"]
["SOLVER","SET B17=0, CHANGING B20."]
["QUADRATIC"," "]
["a",{"$f":"1/-((B10-B11)*B3)","v":-0.10416666666666667}," "]
["b",{"$f":"(B19-1)/(-(B10-B11))","v":16.666666666666668}," "]
["c",{"$f":"-((B3/(B10-B11))-B5)","v":-566.66666666666674}," "]
["P*",{"$f":"(-B29+SQRT((B29^2)-4*B28*B30))/(2*B28)","v":49.016133230340657}," "]
[]
["a","1/-((B10-B11)*B3)"]
["b","(B19-1)/(-(B10-B11))"]
["c","-((B3/(B10-B11))-B5)"]
["P*","(-B29+SQRT((B29^2)-4*B28*B30))/(2*B28)"]
[]
["Actual Age",{"$f":"(1/B11)*LN(50/B3)","v":11.75009073114339},"Years"]
["Renewal Age",{"$f":"(1/B11)*LN(B31/B3)","v":12.246928528880519},"Years"]
["Renewal Age","(1/B11)*LN(B31/B3)"]

{"sheet":"Problem 11.4","index":59,"n_rows":37,"n_cols":7,"rows_kept":37,"cut":false,"hidden":false,"merged":[]}
["Renewal Template"]
["INPUT","Stochastic P & C",null,"PROBLEM 11.4"]
["PI",80,null,null," "]
["CI",20]
["K",150]
["C*",26.3]
["sP",0.4]
["sC",0.4]
["r",-1]
["r",0.14000000000000001]
["qP",-0.1]
["qC",0.03]
[]
["OUTPUT"," "]
["Q(b,h)",{"$f":"0.5*(B7^2)*B23*(B23-1)+0.5*(B8^2)*B24*(B24-1)+B9*B7*B8*B23*B24+B11*B23+B12*B24-B10","v":-4.5568687712105316E-11},null," "]
["SP",{"$f":"B25/(-B23*(B10-B11))-B6/(B24*(B10-B12))","v":-1.0000455290537502E-6},null," "]
["H(b,h)",{"$f":"B18*B19+B20","v":-3.3722611281206127E-7},null," "]
["PART 1",{"$f":"B6/(B24*(B10-B12))","v":284.3375692077322}]
["PART 2",{"$f":"1-B23-B24-((B3^B23)*(B4^B24)/(B6^(B23+B24)))*((-B23*(B10-B11)/(B24*(B10-B12)))^-B23)","v":5.3287055317634557E-3}]
["PART 3",{"$f":"-B3/(B10-B11)+B4/(B10-B12)+B5","v":-1.5151515151515298}]
["SUM",{"$f":"SUM(ABS(B15:B17))","v":1.3373172105535236E-6},null,"  "]
[" "]
["b",-0.36503677468255741]
["h",0.84086992006403938]
["P*",24.91048051670775,null,null," "]
["P*-C*",{"$f":"B25-B6","v":-1.3895194832922506}]
[" "]
["Q(b,h)","0.5*(B7^2)*B23*(B23-1)+0.5*(B8^2)*B24*(B24-1)+B9*B7*B8*B23*B24+B11*B23+B12*B24-B10",null,null,null,null," "]
["SP","B25/(-B23*(B10-B11))-B6/(B24*(B10-B12))",null,null,null,null," "]
["H(b,h)","B18*B19+B20",null,null,null,null," "]
["PART 1","B6/(B24*(B10-B12))"]
["PART 2","1-B23-B24-((B3^B23)*(B4^B24)/(B6^(B23+B24)))*((-B23*(B10-B11)/(B24*(B10-B12)))^-B23)"]
["PART 3","-B3/(B10-B11)+B4/(B10-B12)+B5"]
[" ",null," "]
["SOLVER","SET B21=0,CHANGING B23:B25."]
[" "," "]
["T*P",{"$f":"(1/B11)*(LN(B25/B3))","v":11.667380154731287}]

{"sheet":"Problem 11.5","index":60,"n_rows":28,"n_cols":6,"rows_kept":28,"cut":false,"hidden":false,"merged":[]}
[null,null," Renewal Template"]
[" ","Stochastic P",null,"PROBLEM 11.5"]
["PI",80," "]
["CI",30]
["K",100]
["C*",30]
["sP",0.11547]
["sC",0]
["r",0]
["r",0.14000000000000001]
["qP",-0.05]
["qC",0]
[]
["OUTPUT"," "]
["Q(b,h=0)",{"$f":"(0.5-B11/(B7^2))-SQRT((0.5-B11/(B7^2))^2+2*B10/(B7^2))-B19","v":-9.9999999991773336E-7}]
["SP",{"$f":"(B20/(B19*(B10-B11)))*(B19-1+((B3/B20)^B19))-B3/(B10-B11)+B5","v":-1.5670881850837759E-5}," "]
["SUM",{"$f":"SUM(ABS(B15:B16))","v":1.6670881850755492E-5}]
["OUTPUT"," "]
["b",-1.9999994476001508]
["P*",45.607619308070248," "]
["h",0,null,null,null," "]
["P*-C*",{"$f":"B20-B6","v":15.607619308070248},null,null,null," "]
[{"$f":"B2","v":"Stochastic P"}]
["Q(b,h=0)","(0.5-B11/(B7^2))-SQRT((0.5-B11/(B7^2))^2+2*B10/(B7^2))-B19",null,null,null," "]
["SP","(B20/(B19*(B10-B11)))*(B19-1+((B3/B20)^B19))-B3/(B10-B11)+B5",null,null,null," "]
["SOLVER","SET B17=0, CHANGING B19:B20"]
[]
["T*P",{"$f":"(1/B11)*(LN(B20/B3))","v":11.239036840445511}]

{"sheet":"Problem 11.6","index":61,"n_rows":30,"n_cols":5,"rows_kept":30,"cut":false,"hidden":false,"merged":[]}
["Renewal Template"]
["INPUT","Stochastic P & C",null,"PROBLEM 11.6"]
["PI",80,null,null," "]
["CI",20]
["K",100]
["C*",20]
["sP",0.3]
["sC",0]
["r",0]
["r",7.0000000000000007E-2]
["qP",-0.04]
["qC",0]
[]
["OUTPUT"," "]
["Q(b,h=0)",{"$f":"(0.5-B11/(B7^2))-SQRT((0.5-B11/(B7^2))^2+2*B10/(B7^2))-B19","v":0}]
["SP",{"$f":"(B20/(B19*(B10-B11)))*(B19-1+((B3/B20)^B19))-B3/(B10-B11)+B5","v":-2.2889253159519285E-7}]
["SUM",{"$f":"SUM(ABS(B15:B16))","v":2.2889253159519285E-7}]
["OUTPUT"," "]
["b",-0.62001420448096933]
["P*",47.977257955454661]
["h",0]
["P*-C*",{"$f":"B20-B6","v":27.977257955454661}]
[{"$f":"B2","v":"Stochastic P & C"}]
["Q(b,h=0)","(0.5-B11/(B7^2))-SQRT((0.5-B11/(B7^2))^2+2*B10/(B7^2))-B19"]
["SP","(B20/(B19*(B10-B11)))*(B19-1+((B3/B20)^B19))-B3/(B10-B11)+B5"]
["SOLVER","SET B17=0, CHANGING B19:B20."]
[]
["Actual Age",{"$f":"(1/B11)*LN(60/B3)","v":7.1920518112945224},"Years"]
["Renewal Age",{"$f":"(1/B11)*LN(B20/B3)","v":12.78248821589654},"Years"]
["Renewal Age","(1/B11)*LN(B20/B3)"]

{"sheet":"Exercise 12.1","index":62,"n_rows":47,"n_cols":7,"rows_kept":47,"cut":false,"hidden":false,"merged":[]}
["Continuous American Perpetual SINGLE SWITCH Option"]
["ONE WAY SWITCH FROM OUTPUT x TO y ",null," ","EXERCISE 12.1"]
["OUTPUT x","x",1," "]
["OUTPUT y","y",1," "]
["Convenience yield of x","δx",0.05]
["Convenience yield of y","δy",0.05]
["Volatility of x","σx",0.1]
["Volatility of y","σy",0.1]
["Correlation x with y","ρ",0]
["Risk-free interest rate","r",0.05]
["Operating cost for x","cx",0]
["Operating cost for y","cy",0]
["Switching cost from x to y","S12",0.2]
[" "," "," "]
["PV of revenues x","X",{"$f":"(C3/C5-C11/C10)","v":20}," "]
["PV of revenues y","Y",{"$f":"(C4/C6-C12/C10)","v":20}," "]
["Switching boundary x to y","x12",{"$f":"C3","v":1}]
[" "," "," "]
[null,"SOLUTION",null,"OPTION VALUE"]
["Asset value in operating mode '1'","V1(x,y)",{"$f":"C3/C5-C11/C10+C22*C3^C24*C4^C25","v":23.167114578904759},{"$f":"C20-C15","v":3.1671145789047586}]
["Asset value in operating mode '2'","V2(x,y)",{"$f":"C4/C6-C12/C10","v":20},{"$f":"C21-C16","v":0}]
[null,"A",3.1671145789047577]
["Switching boundary x to y","y12 (x)",1.5710542808123311]
["Solution quadrant","β11",-1.7823587246678378,"must be negative",null," "," "]
["Solution quadrant","β12",2.8001823093614622,"must be positive"]
[null,"EQUATIONS",null,"REVISED EQS"]
["Value matching 1","EQ 19",{"$f":"(C22*C23^C25+C17/C5-C11/C10-C23/C6+C12/C10+C13)","v":1.7864827950297979E-9},"(C22*C23^C25+C17/C5-C11/C10-C23/C6+C12/C10+C13)"]
["Smooth pasting 1A","EQ 20",{"$f":"(C24*C22*C23^C25+1/C5)","v":1.484538998397511E-7},"(C24*C22*C23^C25+1/C5)"]
["Smooth pasting 1B","EQ 21",{"$f":"(C25*C22*C23^(C25-1)-1/C6)","v":-1.1253588994009078E-7},"(C25*C22*C23^(C25-1)-1/C6)"]
["Solution quadrant 1","EQ 22",{"$f":"0.5*C7^2*C24*(C24-1)+0.5*C8^2*C25*(C25-1)-C10","v":2.183414560263941E-11},"0.5*C7^2*C24*(C24-1)+0.5*C8^2*C25*(C25-1)-C10"]
[null,"Sum",{"$f":"SUM(ABS(C27:C30))","v":2.6279810672047432E-7}," "]
[null,"SOLVER: SET C31=0, CHANGING C22:C25"]
[{"$f":"B27","v":"EQ 19"},"(C22*C17^C24*C23^C25+C17/C5-C11/C10-C23/C6+C12/C10+C13)"]
[{"$f":"B28","v":"EQ 20"},"(C24*C22*C17^(C24-1)*C23^C25+1/C5)"]
[{"$f":"B29","v":"EQ 21"},"(C25*C22*C17^C24*C23^(C25-1)-1/C6)"]
[{"$f":"B30","v":"EQ 22"},"0.5*C7^2*C24*(C24-1)+0.5*C8^2*C25*(C25-1)+C9*C7*C8*C24*C25+C24*(C10-C5)+C25*(C10-C6)-C10"]
["SPREAD",null,{"$f":"C23-C4","v":0.57105428081233112}]
["V1(x,y)  EQ 5","C3/C5-C11/C10+C22*C3^C24*C4^C25"]
["V2(x,y)  EQ 7","C4/C6-C12/C10"]
[]
[null,"CALCULATOR ANSWER"]
[null,"y12 (x)",{"$f":"-C25/C24","v":1.5710542836337882},{"$f":"(C23^C25)/(C23^(C25-1))","v":1.5710542808123311}]
[null,null,"-C25/C24","(C23^C25)/(C23^(C25-1))"]
[null,"A",{"$f":"(-1/C5)/(C24*C42^C25)","v":3.1671145864863437}]
[null,null,"(-1/C5)/(C24*C42^C25)"]
[null,"V1(x,y)",{"$f":"C3/C5-C11/C10+C22*C3^C24*C4^C25","v":23.167114578904759}]
[null,null,"C3/C5-C11/C10+C22*C3^C24*C4^C25"]

{"sheet":"Exercise 12.1A","index":63,"n_rows":47,"n_cols":4,"rows_kept":47,"cut":false,"hidden":false,"merged":[]}
["Continuous American Perpetual SINGLE SWITCH Option"]
["ONE WAY SWITCH FROM OUTPUT x TO y",null," ","EXERCISE 12.1A"]
["OUTPUT x","x",70," "]
["OUTPUT y","y",100," "]
["Convenience yield of x","δx",0.04]
["Convenience yield of y","δy",0.04]
["Volatility of x","σx",0.2]
["Volatility of y","σy",0.2]
["Correlation x with y","ρ",-1]
["Risk-free interest rate","r",0.05]
["Operating cost for x","cx",0]
["Operating cost for y","cy",0]
["Switching cost from x to y","S12",100]
["Switching cost from y to x","S21"," "]
["PV of revenues x","X",{"$f":"(C3/C5-C11/C10)","v":1750}," "]
["PV of revenues y","Y",{"$f":"(C4/C6-C12/C10)","v":2500}," "]
["Switching boundary x to y","x12",{"$f":"C3","v":70}]
[" "," "," "]
[null,"SOLUTION",null,"OPTION VALUE"]
["Asset value in operating mode '1'","V1(x,y)",{"$f":"C3/C5-C11/C10+C22*C3^C24*C4^C25","v":2997.1069698888623},{"$f":"C20-C15","v":1247.1069698888623}]
["Asset value in operating mode '2'","V2(x,y)",{"$f":"C4/C6-C12/C10","v":2500},{"$f":"C21-C16","v":0}]
[null,"A",9.9936888714969001]
["Switching boundary x to y","y12 (x)",269.91965279737508]
["Solution quadrant","β11",-0.35728932244395595,"must be negative"]
["Solution quadrant","β12",1.3777058551761352,"must be positive"]
[null,"EQUATIONS"]
["Value matching 1","EQ 19",{"$f":"(C22*C17^C24*C23^C25+C17/C5-C11/C10-C23/C6+C12/C10+C13)","v":-6.6032953327521682E-8}]
["Smooth pasting 1A","EQ 20",{"$f":"(C24*C22*C17^(C24-1)*C23^C25+1/C5)","v":-1.7340084923489485E-10}]
["Smooth pasting 1B","EQ 21",{"$f":"(C25*C22*C17^C24*C23^(C25-1)-1/C6)","v":1.8571810755929619E-10}]
["Solution quadrant 1","EQ 22",{"$f":"0.5*C7^2*C24*(C24-1)+0.5*C8^2*C25*(C25-1)+C9*C7*C8*C24*C25+C24*(C10-C5)+C25*(C10-C6)-C10","v":-2.235711615838909E-14}]
[null,"Sum",{"$f":"SUM(ABS(C27:C30))","v":6.6392094641432031E-8}," "]
[null,"SOLVER: SET C31=0, CHANGING C22:C25"]
[{"$f":"B27","v":"EQ 19"},"(C22*C17^C24*C23^C25+C17/C5-C11/C10-C23/C6+C12/C10+C13)"]
[{"$f":"B28","v":"EQ 20"},"(C24*C22*C17^(C24-1)*C23^C25+1/C5)"]
[{"$f":"B29","v":"EQ 21"},"(C25*C22*C17^C24*C23^(C25-1)-1/C6)"]
[{"$f":"B30","v":"EQ 22"},"0.5*C7^2*C24*(C24-1)+0.5*C8^2*C25*(C25-1)+C9*C7*C8*C24*C25+C24*(C10-C5)+C25*(C10-C6)-C10"]
["SPREAD",null,{"$f":"C23-C4","v":169.91965279737508}]
["V1(x,y)  EQ 5","C3/C5-C11/C10+C22*C3^C24*C4^C25"]
["V2(x,y)  EQ 7","C4/C6-C12/C10"]
[]
[null,"CALCULATOR ANSWER"]
[null,"y12 (x)",{"$f":"-C25*C17/C24","v":269.91965279750798}]
[null,null,"-C25*C17/C24"]
[null,"A",{"$f":"(-1/C5)/(C24*(C17^(C24-1))*(C42^C25))","v":9.9936888714208028}]
[null,"(-1/C25)/(C24*(C17^(C24-1))*C23^C25)"]
[null,"V1(x,y)",{"$f":"C44*C3^C24*C4^C25","v":1247.106969879366}]
[null,"C44*C3^C24*C4^C25"]

{"sheet":"Exercise 12.2","index":64,"n_rows":34,"n_cols":6,"rows_kept":34,"cut":false,"hidden":false,"merged":[]}
["SINGLE American Perpetual IN-OUT SWITCH Option"]
["Exercise 12.2","INPUT",null,null," "]
["PRICE","x",10," "]
["COST","y",9," "]
["Convenience yield of x","δx",0.04]
["Convenience yield of y","δy",0.04]
["Volatility of x","σx",0.4]
["Volatility of y","σy",0.4]
["Correlation x with y","ρ",0.5]
["Risk-free interest rate","r",0.05]
["Switching cost from x to y","S12",10]
["Switching boundary OP to SHUT","x12",{"$f":"C3","v":10}]
[null,"SOLUTION",null,"OPTION","OPERATING"]
["Asset value in operating mode ","V1(x,y)",{"$f":"(C15*C3^C17*C4^C18+C3/C5-C4/C6)","v":121.20774602925491},{"$f":"(C15*C3^C17*C4^C18)","v":96.20774602925492},{"$f":"C3/C5-C4/C6","v":25}," "]
[null,"A",10.756021233920901]
["Switching boundary OP to SHUT","y12 (x)",38.669161597444685,{"$f":"-C18*C12/C17","v":38.669161302708375}]
["Solution quadrant","β11",-0.35374236680289733,"must be negative"]
["Solution quadrant","β12",1.367892064150307,"must be positive"]
[null,"EQUATIONS"]
["Value matching 1","EQ 35",{"$f":"(C15*C12^C17*C16^C18+C12/C5-C16/C6+C11)","v":-4.6961872612882871E-7}," "]
["Smooth pasting 1A","EQ 36",{"$f":"(C17*C15*(C12^(C17-1))*C16^C18+1/C5)","v":-3.1092173102820198E-7}," "]
["Smooth pasting 1B","EQ 37",{"$f":"(C18*C15*C12^C17*(C16^(C18-1))-1/C6)","v":1.2037175878276685E-7}," "]
["Solution quadrant 1","EQ 38",{"$f":"0.5*C7^2*C17*(C17-1)+0.5*C8^2*C18*(C18-1)+C9*C7*C8*C17*C18+C17*(C10-C5)+C18*(C10-C6)-C10","v":-1.9656852534577496E-11}]
[null,"Sum",{"$f":"SUM(ABS(C20:C23))","v":9.0093187279233211E-7},"Solver"]
[null,"SOLVER: SET C24=0, CHANGING C15:C18"]
["SPREAD",null,{"$f":"C16-C4","v":29.669161597444685}]
["V1(x,y)","(C15*C3^C17*C4^C18+C3/C5-C4/C6)"]
[{"$f":"B20","v":"EQ 35"},"(C15*C12^C17*C16^C18+C12/C5-C16/C6+C11)"]
[{"$f":"B21","v":"EQ 36"},"(C17*C15*(C12^(C17-1))*C16^C18+1/C5)"]
[{"$f":"B22","v":"EQ 37"},"(C18*C15*C12^C17*(C16^(C18-1))-1/C6)"]
[{"$f":"B23","v":"EQ 38"},"0.5*C7^2*C17*(C17-1)+0.5*C8^2*C18*(C18-1)+C9*C7*C8*C17*C18+C17*(C10-C5)+C18*(C10-C6)-C10"]
["V1(x,y)","(C15*C3^C17*C4^C18+C3/C5-C4/C6)"]
[null,"y12 (x)","-C18*C12/C17"]
[null,"A",{"$f":"(-1/C5)/(C17*(C12^(C17-1))*C16^C18)","v":10.756021100149674},"(-1/C5)/(C17*(C12^(C17-1))*C16^C18)"]

{"sheet":"Exercise 12.3","index":65,"n_rows":41,"n_cols":4,"rows_kept":41,"cut":false,"hidden":false,"merged":[]}
["Continuous American Perpetual SINGLE SWITCH Option"]
["ONE WAY SWITCH FROM INPUT x TO y ",null," ","Exercise 12.3"]
["INPUT x","x",1," "]
["INPUT y","y",1," "]
["Convenience yield of x","δx",0.04]
["Convenience yield of y","δy",0.04]
["Volatility of x","σx",0.2]
["Volatility of y","σy",0.2]
["Correlation x with y","ρ",0.5]
["Risk-free interest rate","r",0.05]
["Output price for x","px",3]
["Output price for y","py",3]
["Switching cost from x to y","S12",1]
[" "," "," "]
["PV of revenues using x","X",{"$f":"(-C3/C5+C11/C10)","v":35}," "]
["PV of revenues using y","Y",{"$f":"(-C4/C6+C12/C10)","v":35}," "]
["Switching boundary x to y","x12",{"$f":"C3","v":1}]
[" "," "," "]
[null,"SOLUTION",null,"OPTION VALUE"]
["Asset value in operating mode '1'","V1(x,y)",{"$f":"-C3/C5+C11/C10+C22*C3^C24*C4^C25","v":41.066435190951765},{"$f":"C20-C15","v":6.0664351909517649}]
["Asset value in operating mode '2'","V2(x,y)",{"$f":"-C4/C6+C12/C10","v":35}," "]
[null,"A",6.0664351909517675," "]
["Switching boundary x to y","y12 (x)",0.46286271680021174]
["Solution quadrant","β11",2.0115168096068259,"must be positive"]
["Solution quadrant","β12",-0.93105613550377053,"must be negative"]
[null,"EQUATIONS"]
["Value matching 1","EQ 52",{"$f":"C22*C17^C24*C23^C25-C17/C5+C11/C10+C23/C6-C12/C10+C13","v":1.9731388078980672E-8}]
["Smooth pasting 1A","EQ 53",{"$f":"C24*C22*C17^(C24-1)*C23^C25-1/C5","v":8.5656100878850339E-8}]
["Smooth pasting 1B","EQ 54",{"$f":"C25*C22*C17^C24*C23^(C25-1)+1/C6","v":-8.8874518411330428E-8}]
["Solution quadrant 1","EQ 55",{"$f":"0.5*C7^2*C24*(C24-1)+0.5*C8^2*C25*(C25-1)+C9*C7*C8*C24*C25+C24*(C10-C5)+C25*(C10-C6)-C10","v":-3.0297854503036348E-11}]
[null,"Sum",{"$f":"SUM(ABS(C27:C30))","v":1.9429230522366447E-7}," "]
[null,"SOLVER: SET C31=0, CHANGING C22:C25"]
[{"$f":"B27","v":"EQ 52"},"C22*C17^C24*C23^C25-C17/C5+C11/C10+C23/C6-C12/C10+C13"]
[{"$f":"B28","v":"EQ 53"},"C24*C22*C17^(C24-1)*C23^C25-1/C5"]
[{"$f":"B29","v":"EQ 54"},"C25*C22*C17^C24*C23^(C25-1)+1/C6"]
[{"$f":"B30","v":"EQ 55"},"0.5*C7^2*C24*(C24-1)+0.5*C8^2*C25*(C25-1)+C9*C7*C8*C24*C25+C24*(C10-C5)+C25*(C10-C6)-C10"]
["SPREAD",null,{"$f":"-C23+C4","v":0.53713728319978826}]
["V1(x,y)  ","-C3/C5+C11/C10+C22*C3^C24*C4^C25"]
["V2(x,y)  ","-C4/C6+C12/C10"]
[null,"y12 (x)",{"$f":"-C25/C24","v":0.46286271685979902},"-C25/C24"]
[null,"V1(x,y)",{"$f":"-C3/C5+C11/C10+6.07*C3^C24*C4^C25","v":41.07},"-C3/C5+C11/C10+6.07*C3^C24*C4^C25"]

{"sheet":"Problem 12.4","index":66,"n_rows":39,"n_cols":4,"rows_kept":39,"cut":false,"hidden":false,"merged":[]}
["Continuous American Perpetual SINGLE SWITCH Option"]
["ONE WAY SWITCH FROM OUTPUT x TO y ",null,"PROBLEM 12.4"]
["OUTPUT x","x",7000," "]
["OUTPUT y","y",10000," "]
["Convenience yield of x","δx",0.04]
["Convenience yield of y","δy",0.04]
["Volatility of x","σx",0.2]
["Volatility of y","σy",0.2]
["Correlation x with y","ρ",0]
["Risk-free interest rate","r",0.05]
["Operating cost for x","cx",0]
["Operating cost for y","cy",0]
["Switching cost from x to y","S12",3000]
[" "," "," "]
["PV of revenues x","X",{"$f":"(C3/C5-C11/C10)","v":175000},"LHS EQ5"]
["PV of revenues y","Y",{"$f":"(C4/C6-C12/C10)","v":250000},"LHS EQ 7"]
["Switching boundary x to y","x12",{"$f":"C3","v":7000}]
[" "," "," "]
[null,"SOLUTION",null,"OPTION VALUE"]
["Asset value in operating mode '1'","V1(x,y)",{"$f":"C3/C5-C11/C10+C22*C3^C24*C4^C25","v":279883.72162091616},{"$f":"C20-C15","v":104883.72162091616}]
["Asset value in operating mode '2'","V2(x,y)",{"$f":"C4/C6-C12/C10","v":250000},{"$f":"C21-C16","v":0}]
[null,"A",7.6565004238263192]
["Switching boundary x to y","y12 (x)",18565.267400536639]
["Solution quadrant","β11",-0.61160650555624085,"must be negative"]
["Solution quadrant","β12",1.6220911885086871,"must be positive"]
[null,"EQUATIONS",null," "]
["Value matching 1","EQ 19",{"$f":"(C22*C17^C24*C23^C25+C17/C5-C11/C10-C23/C6+C12/C10+C13)","v":1.3440148904919624E-7}," "]
["Smooth pasting 1A","EQ 20",{"$f":"(C24*C22*C17^(C24-1)*C23^C25+1/C5)","v":-8.0397910551255336E-12}," "]
["Smooth pasting 1B","EQ 21",{"$f":"(C25*C22*C17^C24*C23^(C25-1)-1/C6)","v":1.1162626378791174E-11}," "]
["Solution quadrant 1","EQ 22",{"$f":"0.5*C7^2*C24*(C24-1)+0.5*C8^2*C25*(C25-1)+C9*C7*C8*C24*C25+C24*(C10-C5)+C25*(C10-C6)-C10","v":3.6082248300317588E-16}," "]
[null,"Sum",{"$f":"SUM(ABS(C27:C30))","v":1.3442069182745264E-7}," "]
[null,"SOLVER: SET C31=0, CHANGING C22:C25"]
[{"$f":"B27","v":"EQ 19"},"(C22*C17^C24*C23^C25+C17/C5-C11/C10-C23/C6+C12/C10+C13)"]
[{"$f":"B28","v":"EQ 20"},"(C24*C22*C17^(C24-1)*C23^C25+1/C5)"]
[{"$f":"B29","v":"EQ 21"},"(C25*C22*C17^C24*C23^(C25-1)-1/C6)"]
[{"$f":"B30","v":"EQ 22"},"0.5*C7^2*C24*(C24-1)+0.5*C8^2*C25*(C25-1)+C9*C7*C8*C24*C25+C24*(C10-C5)+C25*(C10-C6)-C10"]
["SPREAD",null,{"$f":"C23-C4","v":8565.2674005366389}]
["V1(x,y)  EQ 5","C3/C5-C11/C10+C22*C3^C24*C4^C25"]
["V2(x,y)  EQ 7","C4/C6-C12/C10"]

{"sheet":"Problem 12.4A","index":67,"n_rows":58,"n_cols":4,"rows_kept":58,"cut":false,"hidden":false,"merged":[]}
["                         Multiple American Perpetual Output Switch Option"]
["Problem 12.4A"," "," "]
["OUTPUT x","x",10," "]
["OUTPUT y","y",8," "]
["Convenience yield of x","δx",0.05]
["Convenience yield of y","δy",0.05]
["Volatility of x","σx",0.1]
["Volatility of y","σy",0.1]
["Correlation x with y","ρ",0]
["Risk-free interest rate","r",0.05]
["Operating cost for x","cx",1]
["Operating cost for y","cy",1]
[" "," "," "]
[" "," "," "]
["Switching cost from x to y","S12",1]
["Switching cost from y to x","S21",1]
["PV of revenues x","X",{"$f":"(C3/C5-C11/C10)","v":180}," "]
["PV of revenues y","Y",{"$f":"(C4/C6-C12/C10)","v":140}," "]
["Switching boundary x to y","x12",{"$f":"C3","v":10}]
["Switching boundary y to x","x21",{"$f":"C3","v":10}]
[null,"SOLUTION",null,"OPTION VALUE"]
["Asset value in operating mode '1'","V1(x,y)",{"$f":"C3/C5-C11/C10+C24*C3^C28*C4^C29","v":202.12918377940375},{"$f":"C22-C17","v":22.129183779403746}]
["Asset value in operating mode '2'","V2(x,y)",{"$f":"C4/C6-C12/C10+C25*C3^C30*C4^C31","v":201.51725974334079},{"$f":"C23-C18","v":61.517259743340787}]
[null,"A",3.8212650331997025]
[null,"B",3.8113127211172713]
["Switching boundary x to y","y12 (x)",11.532881897795276]
["Switching boundary y to x","y21 (x)",8.6070859099723833]
["Solution quadrant","β11",-1.7737467259466804,"must be negative"]
["Solution quadrant","β12",2.8086956978193145,"must be positive"]
["Solution quadrant","β21",2.8092588150762139,"must be positive"]
["Solution quadrant","β22",-1.7731748117945609,"must be negative"]
[null,"EQUATIONS"]
["Value matching 1","EQ9",{"$f":"(C24*C19^C28*C26^C29+C19/C5-C11/C10-C25*C19^C30*C26^C31-C26/C6+C12/C10+C15)","v":2.8530365625556442E-8}]
["Value matching 2","EQ10",{"$f":"(C24*C20^C28*C27^C29+C20/C5-C11/C10-C25*C20^C30*C27^C31-C27/C6+C12/C10-C16)","v":4.9126981593872188E-8}]
["Smooth pasting 1A","EQ11",{"$f":"(C28*C24*C19^(C28-1)*C26^C29+1/C5-C30*C25*C19^(C30-1)*C26^C31)","v":1.6436434435718184E-9}]
["Smooth pasting 1B","EQ12",{"$f":"(C29*C24*C19^C28*C26^(C29-1)-C31*C25*C19^C30*C26^(C31-1)-1/C6)","v":1.6880790099094156E-9}]
["Smooth pasting 2A","EQ13",{"$f":"(C28*C24*C20^(C28-1)*C27^C29+1/C5-C30*C25*C20^(C30-1)*C27^C31)","v":1.4972169282145842E-8}]
["Smooth pasting 2B","EQ14",{"$f":"(C29*C24*C20^C28*C27^(C29-1)-C31*C25*C20^C30*C27^(C31-1)-1/C6)","v":-1.5599738389937556E-8}]
["Solution quadrant 1","EQ6",{"$f":"0.5*C7^2*C28*(C28-1)+0.5*C8^2*C29*(C29-1)+C9*C7*C8*C28*C29+C28*(C10-C5)+C29*(C10-C6)-C10","v":-5.586697771065019E-12}]
["Solution quadrant 2","EQ8",{"$f":"0.5*C7^2*C30*(C30-1)+0.5*C8^2*C31*(C31-1)+C9*C7*C8*C30*C31+C30*(C10-C5)+C31*(C10-C6)-C10","v":-7.7812756238415659E-14}]
[null,"Sum",{"$f":"SUM(ABS(C33)+ABS(C34)+ABS(C35)+ABS(C36)+ABS(C37)+ABS(C38)+ABS(C39)+ABS(C40))","v":1.1156664185552057E-7}," "]
[null,"SOLVER: SET C41=0, CHANGING C24:C31"]
[" ","D",{"$f":"C29*C30-C28*C31","v":4.7451901310138238},"C29*C30-C28*C31"]
[null,"Wedge x",{"$f":"1-(C29-C31)/C43","v":3.4417929922874402E-2},"1-(C29-C31)/C43"]
[null,"Wedge y",{"$f":"1-(C30-C28)/C43","v":3.4178733731008326E-2},"1-(C30-C28)/C43"]
[null,"EQ 15",{"$f":"(C26/C6)*C45-(C19/C5)*C44-C15","v":6.1433329534565928E-9},"(C26/C6)*C45-(C19/C5)*C44-C15"]
[null,"EQ 16",{"$f":"(C20/C5)*C44-(C27/C6)*C45-C16","v":3.4237688240068564E-8},"(C20/C5)*C44-(C27/C6)*C45-C16"]
["EQ9","(C24*C19^C28*C26^C29+C19/C5-C11/C10-C25*C19^C30*C26^C31-C26/C6+C12/C10+C15)"]
["EQ10","(C24*C20^C28*C27^C29+C20/C5-C11/C10-C25*C20^C30*C27^C31-C27/C6+C12/C10-C16)"]
["EQ11","(C28*C24*C19^(C28-1)*C26^C29+1/C5-C30*C25*C19^(C30-1)*C26^C31)"]
["EQ12","(C29*C24*C19^C28*C26^(C29-1)-C31*C25*C19^C30*C26^(C31-1)-1/C6)"]
["EQ13","(C28*C24*C20^(C28-1)*C27^C29+1/C5-C30*C25*C20^(C30-1)*C27^C31)"]
["EQ14","(C29*C24*C20^C28*C27^(C29-1)-C31*C25*C20^C30*C27^(C31-1)-1/C6)"]
["EQ6","0.5*C7^2*C28*(C28-1)+0.5*C8^2*C29*(C29-1)+C9*C7*C8*C28*C29+C28*(C10-C5)+C29*(C10-C6)-C10"]
["EQ8","0.5*C7^2*C30*(C30-1)+0.5*C8^2*C31*(C31-1)+C9*C7*C8*C30*C31+C30*(C10-C5)+C31*(C10-C6)-C10"]
["SPREAD",null,{"$f":"C26-C27","v":2.9257959878228927}]
["V1(x,y)  EQ 5","C3/C5-C11/C10+C24*C3^C28*C4^C29"]
["V2(x,y)  EQ 7","C4/C6-C12/C10+C25*C3^C30*C4^C31"]

{"sheet":"Problem 12.5","index":68,"n_rows":47,"n_cols":6,"rows_kept":47,"cut":false,"hidden":false,"merged":[]}
["Continuous Multiple American Perpetual IN-OUT Exchange Option "]
["Problem 12.5","INPUT",null,null," "," "]
["PRICE","x",10," "]
["COST","y",9," "]
["Convenience yield of x","δx",0.04]
["Convenience yield of y","δy",0.04]
["Volatility of x","σx",0.4]
["Volatility of y","σy",0.4]
["Correlation x with y","ρ",0.5]
["Risk-free interest rate","r",0.05]
[" "," "," "]
[" "," "," "]
[" "," "," "]
[" "," "," "]
["Switching cost from x to y","S12",10]
["Switching cost from y to x","S21",10]
[" "," "," "," "]
[" "," "," "," "]
["Switching boundary OP to SHUT","x12",{"$f":"C3","v":10}]
["Switching boundary SHUT to OP","x21",{"$f":"C3","v":10}]
[null,"SOLUTION",null,"OPTION","OPERATING"]
["Asset value in operating mode ","V1(x,y)",{"$f":"(C24*C3^C28*C4^C29+C3/C5-C4/C6)","v":142.57124171919679},{"$f":"(C24*C19^C28*C4^C29)","v":117.57124171919678},{"$f":"C3/C5-C4/C6","v":25}," "]
["Asset value in shut down mode","V2(x,y)",{"$f":"(C25*C3^C30*C4^C31)","v":140.67574104512872},{"$f":"C23","v":140.67574104512872},null," "]
[null,"A",11.750591913949066]
[null,"B",11.449561282076536]
["Switching boundary OP to SHUT","y12 (x)",17.674678208015855]
["Switching boundary SHUT to OP","y21 (x)",4.6422272765799217]
["Solution quadrant","β11",-0.30966851121789318,"must be negative"]
["Solution quadrant","β12",1.3727221951680819,"must be positive"]
["Solution quadrant","β21",1.3735532605223886,"must be positive"]
["Solution quadrant","β22",-0.29774705283378394,"must be negative"]
[null,"EQUATIONS"]
["Value matching 1","EQ 29",{"$f":"(C24*C19^C28*C26^C29+C19/C5-C26/C6-C25*C19^C30*C26^C31+C15)","v":-1.0257647886646737E-7},"(C24*C19^C28*C26^C29+C19/C5-C26/C6-C25*C19^C30*C26^C31+C15)"]
["Value matching 2","EQ 30",{"$f":"(C25*C20^C30*C27^C31-C24*C20^C28*C27^C29-C20/C5+C27/C6+C16)","v":3.0240656201385718E-8},"(C25*C20^C30*C27^C31-C24*C20^C28*C27^C29-C20/C5+C27/C6+C16)"]
["Smooth pasting 1A","EQ 31",{"$f":"(C28*C24*(C19^(C28-1))*C26^C29+1/C5-C30*C25*(C19^(C30-1))*C26^C31)","v":7.1755401620521297E-9},"(C28*C24*(C19^(C28-1))*C26^C29+1/C5-C30*C25*(C19^(C30-1))*C26^C31)"]
["Smooth pasting 1B","EQ 32",{"$f":"(C29*C24*C19^C28*(C26^(C29-1))-1/C6-C31*C25*C19^C30*(C26^(C31-1)))","v":-3.7035221556180886E-9},"(C29*C24*C19^C28*(C26^(C29-1))-1/C6-C31*C25*C19^C30*(C26^(C31-1)))"]
["Smooth pasting 2A","EQ 33",{"$f":"(C30*C25*(C20^(C30-1))*C27^C31-C28*C24*(C20^(C28-1))*C27^C29-1/C5)","v":-3.2137528194198239E-9},"(C30*C25*(C20^(C30-1))*C27^C31-C28*C24*(C20^(C28-1))*C27^C29-1/C5)"]
["Smooth pasting 2B","EQ 34",{"$f":"(C31*C25*C20^C30*(C27^(C31-1))-C29*C24*C20^C28*(C27^(C29-1))+1/C6)","v":-1.0234728620162059E-8},"(C31*C25*C20^C30*(C27^(C31-1))-C29*C24*C20^C28*(C27^(C29-1))+1/C6)"]
["Solution quadrant 1","EQ 26",{"$f":"0.5*C7^2*C28*(C28-1)+0.5*C8^2*C29*(C29-1)+C9*C7*C8*C28*C29+C28*(C10-C5)+C29*(C10-C6)-C10","v":-2.3112761704524587E-13}]
["Solution quadrant 2","EQ 28",{"$f":"0.5*C7^2*C30*(C30-1)+0.5*C8^2*C31*(C31-1)+C9*C7*C8*C30*C31+C30*(C10-C5)+C31*(C10-C6)-C10","v":3.6671360392759311E-13}]
[null,"Sum",{"$f":"SUM(ABS(C33)+ABS(C34)+ABS(C35)+ABS(C36)+ABS(C37)+ABS(C38)+ABS(C39)+ABS(C40))","v":1.5714527666632616E-7},"Solver"]
[null,"SOLVER: SET C41=0, CHANGING C24:C31"]
[null,"SPREAD",{"$f":"C26-C27","v":13.032450931435934}]
["EQ 26","0.5*C7^2*C28*(C28-1)+0.5*C8^2*C29*(C29-1)+C9*C7*C8*C28*C29+C28*(C10-C5)+C29*(C10-C6)-C10"]
["EQ 28","0.5*C7^2*C30*(C30-1)+0.5*C8^2*C31*(C31-1)+C9*C7*C8*C30*C31+C30*(C10-C5)+C31*(C10-C6)-C10"]
["V1(x,y)","(C24*C3^C28*C4^C29+C3/C5-C4/C6)"]
["V2(x,y)","(C25*C3^C30*C4^C31)"]

{"sheet":"Problem 12.6","index":69,"n_rows":53,"n_cols":7,"rows_kept":53,"cut":false,"hidden":false,"merged":[]}
["                         Multiple American Perpetual Input Switching Option"]
["Problem 12.6"," "," "]
["INPUT x","x",1," "]
["INPUT y","y",1," "]
["Convenience yield of x","δx",0.04]
["Convenience yield of y","δy",0.04]
["Volatility of x","σx",0.2]
["Volatility of y","σy",0.2]
["Correlation x with y","ρ",0.5]
["Risk-free interest rate","r",0.05]
["Output price for x","px",3]
["Output price for y","py",3]
[" "," "," "]
[" "," "," "]
["Switching cost from x to y","S12",0.5]
["Switching cost from y to x","S21",0.5]
["PV of revenues using x","X",{"$f":"(-C3/C5+C11/C10)","v":35}," "]
["PV of revenues using y","Y",{"$f":"(-C4/C6+C12/C10)","v":35}," "]
["Switching boundary x to y","x12",{"$f":"C3","v":1}]
["Switching boundary y to x","x21",1]
[null,"SOLUTION",null,"OPTION VALUE"]
["Asset value in operating mode '1'","V1(x,y)",{"$f":"-C3/C5+C11/C10+C24*C3^C28*C4^C29","v":42.691763448752361},{"$f":"C22-C17","v":7.6917634487523614}]
["Asset value in operating mode '2'","V2(x,y)",{"$f":"-C4/C6+C12/C10+C25*C3^C30*C4^C31","v":42.687994293305998},{"$f":"C23-C18","v":7.6879942933059979}]
[null,"A",7.6917634487523596]
[null,"B",7.6879942933059979]
["Switching boundary x to y","y12 (x)",0.70927643330695334]
["Switching boundary y to x","y21 (x)",1.3545989456187268]
["Solution quadrant","β11",2.0102777797852318,"must be positive",null," "," "]
["Solution quadrant","β12",-0.93995469994225744,"must be negative",null," "," "]
["Solution quadrant","β21",-0.94539927506188204,"must be negative",null," "," "]
["Solution quadrant","β22",2.0094845231460576,"must be positive",null," "," "]
[null,"EQUATIONS"]
["Value matching 1","EQ47",{"$f":"(C24*C19^C28*C26^C29-C19/C5+C11/C10-C25*C19^C30*C26^C31+C26/C6-C12/C10+C15)","v":-1.3740724114086333E-8}]
["Value matching 2","EQ48",{"$f":"(C24*C20^C28*C27^C29-C20/C5+C11/C10-C25*C20^C30*C27^C31+C27/C6-C12/C10-C16)","v":1.2165671137154277E-8}]
["Smooth pasting 1A","EQ49",{"$f":"(C28*C24*C19^(C28-1)*C26^C29-1/C5-C30*C25*C19^(C30-1)*C26^C31)","v":-1.3872460957742305E-7}]
["Smooth pasting 1B","EQ50",{"$f":"(C29*C24*C19^C28*C26^(C29-1)-C31*C25*C19^C30*C26^(C31-1)+1/C6)","v":1.4856354724201992E-7}]
["Smooth pasting 2A","EQ51",{"$f":"(C28*C24*C20^(C28-1)*C27^C29-1/C5-C30*C25*C20^(C30-1)*C27^C31)","v":-1.6892607312968266E-7}]
["Smooth pasting 2B","EQ52",{"$f":"(C29*C24*C20^C28*C27^(C29-1)-C31*C25*C20^C30*C27^(C31-1)+1/C6)","v":1.5437609235391392E-7}]
["Solution quadrant 1","EQ44",{"$f":"0.5*C7^2*C28*(C28-1)+0.5*C8^2*C29*(C29-1)+C9*C7*C8*C28*C29+C28*(C10-C5)+C29*(C10-C6)-C10","v":5.2433564434739566E-11}]
["Solution quadrant 2","EQ46",{"$f":"0.5*C7^2*C30*(C30-1)+0.5*C8^2*C31*(C31-1)+C9*C7*C8*C30*C31+C30*(C10-C5)+C31*(C10-C6)-C10","v":5.1572579540248853E-11}]
[null,"Sum",{"$f":"SUM(ABS(C33)+ABS(C34)+ABS(C35)+ABS(C36)+ABS(C37)+ABS(C38)+ABS(C39)+ABS(C40))","v":6.3660072369825516E-7}," "]
[null,"SOLVER: SET C41=0, CHANGING C24:C31"]
["EQ47","(C24*C19^C28*C26^C29-C19/C5+C11/C10-C25*C19^C30*C26^C31+C26/C6-C12/C10+C15)"]
["EQ48","(C24*C20^C28*C27^C29-C20/C5+C11/C10-C25*C20^C30*C27^C31+C27/C6-C12/C10-C16)"]
["EQ49","(C28*C24*C19^(C28-1)*C26^C29-1/C5-C30*C25*C19^(C30-1)*C26^C31)"]
["EQ50","(C29*C24*C19^C28*C26^(C29-1)-C31*C25*C19^C30*C26^(C31-1)+1/C6)"]
["EQ51","(C28*C24*C20^(C28-1)*C27^C29-1/C5-C30*C25*C20^(C30-1)*C27^C31)"]
["EQ52","(C29*C24*C20^C28*C27^(C29-1)-C31*C25*C20^C30*C27^(C31-1)+1/C6)"]
["EQ44","0.5*C7^2*C28*(C28-1)+0.5*C8^2*C29*(C29-1)+C9*C7*C8*C28*C29+C28*(C10-C5)+C29*(C10-C6)-C10"]
["EQ46","0.5*C7^2*C30*(C30-1)+0.5*C8^2*C31*(C31-1)+C9*C7*C8*C30*C31+C30*(C10-C5)+C31*(C10-C6)-C10"]
["SPREAD",null,{"$f":"-C26+C27","v":0.64532251231177351}]
["V1(x,y)  ","-C3/C5+C11/C10+C24*C3^C28*C4^C29"]
["V2(x,y)  ","-C4/C6+C12/C10+C25*C3^C30*C4^C31"]

{"sheet":"Exercise 13.1","index":70,"n_rows":47,"n_cols":4,"rows_kept":47,"cut":false,"hidden":false,"merged":[]}
["Continuous American Perpetual SINGLE SWITCH Option"]
["ONE WAY SWITCH FROM OUTPUT x TO y",null,"Exercise 13.1"," "]
["OUTPUT x Discount Class","x",50," "]
["OUTPUT y Upper Class","y",100," "]
["Convenience yield of x","δx",0.04]
["Convenience yield of y","δy",0.04]
["Volatility of x","σx",0.2]
["Volatility of y","σy",0.2]
["Correlation x with y","ρ",0.5]
["Risk-free interest rate","r",0.05]
["Operating cost for x","cx",10]
["Operating cost for y","cy",70]
["Switching cost from x to y","S12",300]
[" "," "," "]
["PV of revenues x","X",{"$f":"(C3/C5-C11/C10)","v":1050}," "]
["PV of revenues y","Y",{"$f":"(C4/C6-C12/C10)","v":1100}," "]
["Switching boundary x to y","x12",{"$f":"C3","v":50}]
[" "," "," "]
[null,"SOLUTION",null,"OPTION VALUE"]
["Asset value in operating mode '1'","V1(x,y)",{"$f":"C3/C5-C11/C10+C22*C3^C24*C4^C25","v":1622.2171148982545},{"$f":"C20-C15","v":572.21711489825452}]
["Asset value in operating mode '2'","V2(x,y)",{"$f":"C4/C6-C12/C10","v":1100},{"$f":"C21-C16","v":0}]
[null,"A",0.34738298712117754]
["Switching boundary x to y","y12 (x)",220.99342076826159]
["Solution quadrant","β11",-0.45047715129446736,"must be negative"]
["Solution quadrant","β12",1.9910497328491659,"must be positive"]
[null,"EQUATIONS"]
["Value matching 1","EQ 15",{"$f":"(C22*C17^C24*C23^C25+C17/C5-C11/C10-C23/C6+C12/C10+C13)","v":8.2795850175898522E-9}]
["Smooth pasting 1A","EQ 16",{"$f":"(C24*C22*C17^(C24-1)*C23^C25+1/C5)","v":-1.31922917034899E-10}]
["Smooth pasting 1B","EQ 17",{"$f":"(C25*C22*C17^C24*C23^(C25-1)-1/C6)","v":1.1991829751423211E-10}]
["Solution quadrant 1","EQ 18",{"$f":"0.5*C7^2*C24*(C24-1)+0.5*C8^2*C25*(C25-1)+C9*C7*C8*C24*C25+C24*(C10-C5)+C25*(C10-C6)-C10","v":5.2319260035460502E-15}]
[null,"Sum",{"$f":"SUM(ABS(C27:C30))","v":8.5314314640649869E-9}," "]
[null,"SOLVER: SET C31=0, CHANGING C22:C25"]
[{"$f":"B27","v":"EQ 15"},"(C22*C17^C24*C23^C25+C17/C5-C11/C10-C23/C6+C12/C10+C13)"]
[{"$f":"B28","v":"EQ 16"},"(C24*C22*C17^(C24-1)*C23^C25+1/C5)"]
[{"$f":"B29","v":"EQ 17"},"(C25*C22*C17^C24*C23^(C25-1)-1/C6)"]
[{"$f":"B30","v":"EQ 18"},"0.5*C7^2*C24*(C24-1)+0.5*C8^2*C25*(C25-1)+C9*C7*C8*C24*C25+C24*(C10-C5)+C25*(C10-C6)-C10"]
["SPREAD",null,{"$f":"C23-C4","v":120.99342076826159}]
["V1(x,y)  EQ 5","C3/C5-C11/C10+C22*C3^C24*C4^C25"]
["V2(x,y)  EQ 7","C4/C6-C12/C10"]
[]
[null,"CALCULATOR ANSWER"]
[null,"y12 (x)",{"$f":"-C25*C17/C24","v":220.99342076815554}]
[null,null,"-C25*C17/C24"]
[null,"A",{"$f":"(-1/C5)/(C24*(C17^(C24-1))*(C42^C25))","v":0.34738298711967702}]
[null,"(-1/C25)/(C24*(C17^(C24-1))*C23^C25)"]
[null,"V1(x,y)",{"$f":"C44*C3^C24*C4^C25","v":572.21711489578286}]
[null,null,"C44*C3^C24*C4^C25"]

{"sheet":"Exercise 13.2","index":71,"n_rows":31,"n_cols":3,"rows_kept":31,"cut":false,"hidden":false,"merged":[]}
["EXERCISE 13.2","Q1","Q2"]
["Booking Limit",{"$f":"MAX(MIN(NORMINV(B3,B4,B5),B6),0)","v":65.93196819821874},{"$f":"MAX(MIN(NORMINV(C3,C4,C5),C6),0)","v":71.536364964772872}]
["PROB",{"$f":"B7","v":0.625},{"$f":"C7","v":0.66666666666666663}]
["MEAN",50,{"$f":"B4","v":50}]
["STDEV",50,50]
["C",100,100]
["pd/pf",{"$f":"B8/B9","v":0.625},0.66666666666666663]
["pd",500,{"$f":"B8","v":500}]
["pf",800,750]
[]
[{"$f":"A2","v":"Booking Limit"},"MAX(MIN(NORMINV(B3,B4,B5),B6),0)"]
["Approximate",{"$f":"200*B7-60","v":65},{"$f":"200*C7-60","v":73.333333333333314}]
["B13=","200*B7-60"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[" "," "]
[" "," "]

{"sheet":"Exercise 13.3","index":72,"n_rows":36,"n_cols":9,"rows_kept":36,"cut":false,"hidden":false,"merged":[]}
["                                    OPTIMAL OVERBOOKING with Stochastic No Shows"]
["PRICE",300,{"$f":"B2","v":300},{"$f":"C2","v":300},300,300,300,300,300]
["DENIED Compensation",700,{"$f":"B3","v":700},700,700,700,700,700,700]
["CAPACITY",200,{"$f":"B4","v":200},200,200,200,200,200,200]
["Expected NoShows",5,{"$f":"B5+5","v":10},{"$f":"C5+5","v":15},20,25,30,35,40]
["Stdev NoShows",10,10,10,10,10,10,10,10]
["OB     NORMINV",{"$f":"MAX(NORMINV((B2/(B2+B3)),B5,B6),0)","v":0},{"$f":"MAX(NORMINV((C2/(C2+C3)),C5,C6),0)","v":4.7559948729195911},9.7559948729195902,14.75599487291959,19.75599487291959,24.75599487291959,29.75599487291959,34.755994872919594]
["BOOKINGS ALLOWED",{"$f":"B4+B7","v":200},{"$f":"C4+C7","v":204.75599487291959},209.75599487291959,214.75599487291959,219.75599487291959,224.75599487291959,229.75599487291959,234.75599487291959]
["NORMINV","MAX(NORMINV((B2/(B2+B3)),B5,B6),0)"]
["OB Approximate",null,{"$f":"-5.24+C5","v":4.76},{"$f":"-5.24+D5","v":9.76},14.76,19.759999999999998,24.759999999999998,29.759999999999998,34.76]
["Exercise 13.3","C10=","-5.24+C5"]
[]
["SUMMARY OUTPUT"]
[]
["Regression Statistics"]
["Multiple R",1]
["R Square",1]
["Adjusted R Square",-1.4]
["Standard Error",1.2429551525515691E-15]
["Observations",1]
[]
["ANOVA"]
[null,"df","SS","MS"," "," "]
["Regression",7,700.00000000000011,100.00000000000001," "," "]
["Residual",5,7.7246875562724725E-30,1.5449375112544945E-30]
["Total",12,700.00000000000011]
[]
[null,"Coefficients","Standard Error","t Stat"," "," "," "," "," "]
["Intercept",null,null,null,null,null,null," "," "]
["X Variable 1",null,null,null,null,null,null," "," "]
["X Variable 2",null,null,null,null,null,null," "," "]
["X Variable 3",null,null,null,null,null,null," "," "]
["X Variable 4",null,null,null,null,null,null," "," "]
["X Variable 5",null,null,null,null,null,null," "," "]
["X Variable 6",-5.2440051270804169,1.2649560668031734E-15,-4145602574430264," "," "," "," "," "]
["X Variable 7",1.0000000000000002,4.6979288920825746E-17,2.128597564951018E+16," "," "," "," "," "]

{"sheet":"Problem 13.4","index":73,"n_rows":56,"n_cols":5,"rows_kept":56,"cut":false,"hidden":false,"merged":[]}
["                         Multiple American Perpetual Output Switch Option"]
["Problem 13.4"," "," "]
["OUTPUT x Discount Class","x",50," "]
["OUTPUT y Upper Class","y",100," "]
["Convenience yield of x","δx",0.04]
["Convenience yield of y","δy",0.04]
["Volatility of x","σx",0.2]
["Volatility of y","σy",0.2]
["Correlation x with y","ρ",0.5]
["Risk-free interest rate","r",0.05]
["Operating cost for x","cx",30]
["Operating cost for y","cy",30]
[" "," "," "]
[" "," "," "]
["Switching cost from x to y","S12",300]
["Switching cost from y to x","S21",100]
["PV of revenues x","X",{"$f":"(C3/C5-C11/C10)","v":650}," "]
["PV of revenues y","Y",{"$f":"(C4/C6-C12/C10)","v":1900}," "]
["Switching boundary x to y","x12",{"$f":"C3","v":50}]
["Switching boundary y to x","x21",{"$f":"C3","v":50}]
[null,"SOLUTION",null,"OPTION","OPERATING"]
["Asset value in operating mode '1'","V1(x,y)",{"$f":"C3/C5-C11/C10+C24*C3^C28*C4^C29","v":1791.1443013826179},{"$f":"C24*C3^C28*C4^C29","v":1141.1443013826179},{"$f":"C3/C5-C11/C10","v":650}]
["Asset value in operating mode '2'","V2(x,y)",{"$f":"C4/C6-C12/C10+C25*C3^C30*C4^C31","v":2090.8353233392259},{"$f":"C25*C3^C30*C4^C31","v":190.83532333922568},{"$f":"C4/C6-C12/C10","v":1900}]
[null,"A",1.8339234632949521]
[null,"B",3.054396645637703]
["Switching boundary x to y","y12 (x)",101.72174661549593]
["Switching boundary y to x","y21 (x)",25.053581346043398]
["Solution quadrant","β11",-0.73619204823005047,"must be negative"]
["Solution quadrant","β12",2.0223637831385859,"must be positive"]
["Solution quadrant","β21",2.0213555941939818,"must be positive"]
["Solution quadrant","β22",-0.8192445958272403,"must be negative"]
[null,"EQUATIONS"]
["Value matching 1","EQ9",{"$f":"(C24*C19^C28*C26^C29+C19/C5-C11/C10-C25*C19^C30*C26^C31-C26/C6+C12/C10+C15)","v":1.2706618690572213E-7}]
["Value matching 2","EQ10",{"$f":"(C24*C20^C28*C27^C29+C20/C5-C11/C10-C25*C20^C30*C27^C31-C27/C6+C12/C10-C16)","v":2.4307382773258723E-8}]
["Smooth pasting 1A","EQ11",{"$f":"(C28*C24*C19^(C28-1)*C26^C29+1/C5-C30*C25*C19^(C30-1)*C26^C31)","v":3.1421034663026148E-9}]
["Smooth pasting 1B","EQ12",{"$f":"(C29*C24*C19^C28*C26^(C29-1)-C31*C25*C19^C30*C26^(C31-1)-1/C6)","v":-2.9634499298936134E-9}]
["Smooth pasting 2A","EQ13",{"$f":"(C28*C24*C20^(C28-1)*C27^C29+1/C5-C30*C25*C20^(C30-1)*C27^C31)","v":7.2830630415410269E-13}]
["Smooth pasting 2B","EQ14",{"$f":"(C29*C24*C20^C28*C27^(C29-1)-C31*C25*C20^C30*C27^(C31-1)-1/C6)","v":9.1186436179668817E-10}]
["Solution quadrant 1","EQ6",{"$f":"0.5*C7^2*C28*(C28-1)+0.5*C8^2*C29*(C29-1)+C9*C7*C8*C28*C29+C28*(C10-C5)+C29*(C10-C6)-C10","v":-3.1322167082237229E-14}]
["Solution quadrant 2","EQ8",{"$f":"0.5*C7^2*C30*(C30-1)+0.5*C8^2*C31*(C31-1)+C9*C7*C8*C30*C31+C30*(C10-C5)+C31*(C10-C6)-C10","v":-1.0137723993608461E-14}]
[null,"Sum",{"$f":"SUM(ABS(C33)+ABS(C34)+ABS(C35)+ABS(C36)+ABS(C37)+ABS(C38)+ABS(C39)+ABS(C40))","v":1.58391757203169E-7}," "]
[null,"SOLVER: SET C41=0, CHANGING C24:C31"]
[null,"M x to y",{"$f":"C6*(C15+C3/C5)","v":62},"C6*(C15+C3/C5)"]
[null,"M y to x",{"$f":"C6*(-C16+C3/C5)","v":46},"C6*(-C16+C3/C5)"]
[null,"M Spread",{"$f":"C43-C44","v":16},"C48-C49"]
["EQ9","(C24*C19^C28*C26^C29+C19/C5-C11/C10-C25*C19^C30*C26^C31-C26/C6+C12/C10+C15)"]
["EQ10","(C24*C20^C28*C27^C29+C20/C5-C11/C10-C25*C20^C30*C27^C31-C27/C6+C12/C10-C16)"]
["EQ11","(C28*C24*C19^(C28-1)*C26^C29+1/C5-C30*C25*C19^(C30-1)*C26^C31)"]
["EQ12","(C29*C24*C19^C28*C26^(C29-1)-C31*C25*C19^C30*C26^(C31-1)-1/C6)"]
["EQ13","(C28*C24*C20^(C28-1)*C27^C29+1/C5-C30*C25*C20^(C30-1)*C27^C31)"]
["EQ14","(C29*C24*C20^C28*C27^(C29-1)-C31*C25*C20^C30*C27^(C31-1)-1/C6)"]
["EQ6","0.5*C7^2*C28*(C28-1)+0.5*C8^2*C29*(C29-1)+C9*C7*C8*C28*C29+C28*(C10-C5)+C29*(C10-C6)-C10"]
["EQ8","0.5*C7^2*C30*(C30-1)+0.5*C8^2*C31*(C31-1)+C9*C7*C8*C30*C31+C30*(C10-C5)+C31*(C10-C6)-C10"]
["SPREAD",null,{"$f":"C26-C27","v":76.66816526945253},"C26-C27"]
["V1(x,y)  EQ 5","C3/C5-C11/C10+C24*C3^C28*C4^C29"]
["V2(x,y)  EQ 7","C4/C6-C12/C10+C25*C3^C30*C4^C31"]

{"sheet":"Problem 13.5","index":74,"n_rows":14,"n_cols":11,"rows_kept":14,"cut":false,"hidden":false,"merged":[]}
["PROBLEM 13.5"," "," "," "]
["Booking Limit",{"$f":"MAX(MIN(NORMINV(B3,B4,B5),B6),0)","v":63.971029888186195},{"$f":"MAX(MIN(NORMINV(C3,C4,C5),C6),0)","v":49.249999999999986},36.995831597116087,26.470428631678615,17.221804939698885,8.9529149009419626,1.4581336470394675,0,0,0]
["PROB",{"$f":"B7","v":0.55555555555555558},{"$f":"C7","v":0.5},0.45454545454545453,0.41666666666666669,0.38461538461538464,0.35714285714285715,0.33333333333333331,0.3125,0.29411764705882354,0.27777777777777779]
["MEAN",50,{"$f":"B4-$B$11*(C9-B9)","v":49.25},{"$f":"C4-$B$11*(D9-C9)","v":48.5},47.75,47,46.25,45.5,44.75,44,43.25]
["STDEV",100,{"$f":"B5+0.5*$B$11*(C9-B9)","v":100.375},{"$f":"C5+0.5*$B$11*(D9-C9)","v":100.75},101.125,101.5,101.875,102.25,102.625,103,103.375]
["C",100,100,100,100,100,100,100,100,100,100]
["pd/pf",{"$f":"B8/B9","v":0.55555555555555558},0.5,0.45454545454545453,0.41666666666666669,0.38461538461538464,0.35714285714285715,0.33333333333333331,0.3125,0.29411764705882354,0.27777777777777779]
["pd",500,{"$f":"B8","v":500},{"$f":"C8","v":500},{"$f":"D8","v":500},500,500,500,500,500,500]
["pf",900,{"$f":"B9+100","v":1000},{"$f":"C9+100","v":1100},1200,1300,1400,1500,1600,1700,1800]
["TOTAL REVENUE",{"$f":"B8*B2+B9*B4","v":76985.514944093098},{"$f":"C8*C2+C9*C4","v":73875},71847.915798558039,70535.214315839316,69710.902469849447,69226.457450470974,68979.066823519737,71600,74800,77850]
["Bus Class Beta",7.4999999999999997E-3]
["MEAN",null,"B4-$B$11*(C9-B9)"]
["STDEV"," ","B5+0.5*$B$11*(C9-B9)"]
[{"$f":"A2","v":"Booking Limit"},"MAX(MIN(NORMINV(B3,B4,B5),B6),0)"]

{"sheet":"Problem 13.6","index":75,"n_rows":9,"n_cols":9,"rows_kept":9,"cut":false,"hidden":false,"merged":[]}
["                                    OPTIMAL OVERBOOKING with Stochastic No Shows"]
["PRICE",500,{"$f":"B2","v":500},{"$f":"C2","v":500},500,500,500,500,500]
["DENIED Compensation",500,{"$f":"B3+100","v":600},{"$f":"C3+100","v":700},800,900,1000,1100,1200]
["CAPACITY",100,{"$f":"B4","v":100},100,100,100,100,100,100]
["Expected NoShows",50,50,50,50,50,50,50,50]
["Stdev NoShows",100,100,100,100,100,100,100,100]
["NORMINV",{"$f":"MAX(NORMINV((B2/(B2+B3)),B5,B6),0)","v":49.999999999999986},{"$f":"MAX(NORMINV((C2/(C2+C3)),C5,C6),0)","v":38.58147056785716},28.957160575207531,20.661876787880672,13.389364319943034,6.9272700704542487,1.12235888853305,0]
["BOOKINGS ALLOWED",{"$f":"B4+B7","v":150},{"$f":"C4+C7","v":138.58147056785717},128.95716057520752,120.66187678788067,113.38936431994304,106.92727007045426,101.12235888853306,100]
["NORMINV","MAX(NORMINV((B2/(B2+B3)),B5,B6),0)",null,null,null,null,null,"Problem 13.6"]

{"sheet":"Exercise 14.1","index":76,"n_rows":19,"n_cols":4,"rows_kept":19,"cut":false,"hidden":false,"merged":[]}
["Exercise 14.1"]
["INPUT","Stochastic R"]
["P",10,"Per MWhr"]
["Q",10,"MWhrs/per annum"]
["R",{"$f":"B3*B4","v":100},"B3*B4"]
["K",4000,"Per Capacity of 10 MWhrs/per annum"]
["s",0.1,"Given"]
["r",7.0000000000000007E-2,"Given"]
["q",0.04,"Given"]
["t",1,"Subsidy"]
["r-q",{"$f":"B8-B9","v":3.0000000000000006E-2},"B8-B9"]
["l",0,"Probability"]
["OUTPUT"," "," "]
["ROV1",{"$f":"IF(B5<B18,B17*(B5^B16),B15)","v":2777.7777777777783},"IF(B5<B18,B17*(B5^B16),B15)"," "]
["V-K",{"$f":"((1+B10)*B5/B11)-B6","v":2666.6666666666652},"((1+B10)*B5/B11)-B6"," "]
["b1",{"$f":"(1/B7^2)*(-(B11-0.5*(B7^2))+SQRT((B11-0.5*(B7^2))^2+(2*B8)*(B7^2)))","v":1.9999999999999998}," "," "]
["B1",{"$f":"((1+B10)*(B18^(1-B16)))/(B16*B11)","v":0.27777777777777807},"((1+B10)*(B18^(1-B16)))/(B16*B11)"," "]
["R*",{"$f":"B6*B11*(B16/(B16-1))/(1+B10)","v":120.00000000000003},"B6*B11*(B16/(B16-1))/(1+B10)"," "]
["b1","(1/B7^2)*(-(B11-0.5*(B7^2))+SQRT((B11-0.5*(B7^2))^2+(2*B8)*(B7^2)))"]

{"sheet":"Problem 14.4","index":77,"n_rows":19,"n_cols":4,"rows_kept":19,"cut":false,"hidden":false,"merged":[]}
["Problem 14.4"]
["INPUT","Stochastic R"]
["P",22.25,"Per MWhr"]
["Q",10,"MWhrs/per annum"]
["R",{"$f":"B3*B4","v":222.5},"B3*B4"]
["K",4000,"Per Capacity of 10 MWhrs/per annum"]
["s",0.2,"Given"]
["r",0.08,"Given"]
["q",0.04,"Given"]
["t",0.1,"Subsidy"]
["r-q",{"$f":"B8-B9","v":0.04},"B8-B9"]
["l",0,"Probability"]
["OUTPUT"," "," "]
["ROV1",{"$f":"IF(B5<B18,B17*(B5^B16),B15)","v":2801.2218268617939},"IF(B5<B18,B17*(B5^B16),B15)"," "]
["V-K",{"$f":"((1+B10)*B5/B11)-B6","v":2118.7500000000009},"((1+B10)*B5/B11)-B6"," "]
["b1",{"$f":"(1/B7^2)*(-(B11-0.5*(B7^2))+SQRT((B11-0.5*(B7^2))^2+(2*B8)*(B7^2)))","v":1.5615528128088303}," "," "]
["B1",{"$f":"((1+B10)*(B18^(1-B16)))/(B16*B11)","v":0.60515651567115447},"((1+B10)*(B18^(1-B16)))/(B16*B11)"," "]
["R*",{"$f":"B6*B11*(B16/(B16-1))/(1+B10)","v":404.47656820427852},"B6*B11*(B16/(B16-1))/(1+B10)"," "]
["b1","(1/B7^2)*(-(B11-0.5*(B7^2))+SQRT((B11-0.5*(B7^2))^2+(2*B8)*(B7^2)))"]

{"sheet":"ClassExercise ONE","index":78,"n_rows":23,"n_cols":3,"rows_kept":23,"cut":false,"hidden":false,"merged":[]}
["                                                       Perpetual American Option"]
["Class Exercise ONE"]
["Office",30]
["COST",44]
["s",0.2]
["r",0.04]
["d",0.04]
["ROV",{"$f":"IF(B3<B12,(B12-B4)*(B3/B12)^B14,B10)","v":5.1136363636363651},"IF(B3<B12,(B12-B4)*(B3/B12)^B14,B10)"]
["F(V)",{"$f":"IF(B3<B12,B13*(B3^B14),B10)","v":5.1136363636363651},"IF(B3<B12,B13*(B3^B14),B10)"]
["V-K",{"$f":"B3-B4","v":-14},"B3-B4"]
["F'(V)",{"$f":"IF(B3<B12,B13*B14*(B3^(B14-1)),1)","v":0.34090909090909094},"IF(B3<B12,B13*B14*(B3^(B14-1)),1)"]
["V*",{"$f":"(B14/(B14-1))*B4","v":88},"(B14/(B14-1))*B4"]
["A",{"$f":"(B12-B4)/(B12^B14)","v":5.681818181818188E-3},"(B12-B4)/(B12^B14)"]
["b1",{"$f":"0.5-(B6-B7)/(B5^2)+SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))","v":1.9999999999999998}]
["b1=","0.5-(B6-B7)/(B5^2)+SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))"]
["ODE",{"$f":"0.5*(B5^2)*(B3^2)*B17+(B6-B7)*B3*B11-B6*B9","v":0}]
["F''(V)",{"$f":"IF(B3<B12,B13*B14*(B14-1)*(B3^(B14-2)),0)","v":1.1363636363636366E-2}]
["F'(V*)",{"$f":"B13*B14*(B12^(B14-1))","v":1.0000000000000004}]
["F(V*)",{"$f":"IF(B3<B12,B13*(B12^B14),B10)","v":44}]
["V*-K",{"$f":"B12-B4","v":44}]
["SMETER",20000]
["ROV",{"$f":"IF(B3<B12,B21*(B12-B4)*(B3/B12)^B14,B10)","v":102272.72727272729},"IF(B3<B12,(B12-B4)*(B3/B12)^B14,B10)"]
["V*",{"$f":"(B14/(B14-1))*B4*B21","v":1760000},"(B14/(B14-1))*B4"]