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{"sheet":"GUIDE_SOLUTIONS","index":0,"n_rows":40,"n_cols":3,"rows_kept":40,"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",{"$f":"C4","v":"Call Binomial, No Income"}]
[null,"PROBLEM 2.4","Black-Scholes Deferral Option"]
[null,"PROBLEM 2.5",{"$f":"C6","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","AMERICAN PERPETUAL"]
[null,"EXERCISE 4.1","Real American Perpetual Call Option"]
[null,"EXERCISE 4.2",{"$f":"C17","v":"Real American Perpetual Call Option"}]
[null,"EXERCISE 4.3",{"$f":"C18","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"]
["#4 Session","CHAPTER 14","INCENTIVE OPTIONS"]
[null,"EXERCISE 14.1","Active Floor"]
[null,"EXERCISE 14.2","Active Ceiling"]
[null,"EXERCISE 14.3","Active Collar"]
[null,"PROBLEM 14.4","Active Floor"]
[null,"PROBLEM 14.5","Active Collar"]
[null,"PROBLEM 14.6","Invest Collar"]
[null," "]
["REAL OPTION VALUE EXCEL 3 17 EARLY SOLUTIONS"]
[]
[" "," "," "]
["Session","CHAPTER 10","DEBT STRATEGIES "]
[null,"ODE PROOF","Option to Default"]
[null,"V DELTA","Equity & Debt & Bankruptcy"]
[null,"BASE CASE DEBT","Equity & Debt & Bankruptcy"]
[null,"STRATEGY a","Equity & Debt & Bankruptcy"]
[null,"FAIR STRATEGY","Equity & Debt & Bankruptcy: Renegotiation"]
[null,"SIMPLE STRATEGY","Personal Equity & Debt & Bankruptcy"]

{"sheet":"Debt ODE","index":1,"n_rows":20,"n_cols":4,"rows_kept":20,"cut":false,"hidden":false,"merged":[]}
[" ","ODE PROOF for DEBT CLAIM"]
[" "," "]
["INPUT"," "]
["V",40]
["C",4]
["D",{"$f":"B5/B12","v":66.666666666666671}]
["d",0]
["m=r-d",{"$f":"B12-B7","v":0.06}]
["s",0.2]
["a",0.5]
["t",0.35]
["r(f)",0.06]
["OUTPUT"]
["VB   ",{"$f":"(1-B11)*(B5/B12)*(-B16/(-B16+1))","v":32.5},"(1-B11)*(B5/B12)*(-B16/(-B16+1))",10.9]
["D* (V)",{"$f":"(B5/B12)+((1-B10)*B14-(B5/B12))*(B14/B4)^-B16","v":39.62432861328125},"(B5/B12)+((1-B10)*B14-(B5/B12))*(B14/B4)^-B16",10.6]
["b2",{"$f":"(0.5-(B12-B7)/(B9^2)-SQRT((0.5-(B12-B7)/(B9^2))^2+2*B12/(B9^2)))","v":-2.9999999999999991},"(0.5-(B12-B7)/(B9^2)-SQRT((0.5-(B12-B7)/(B9^2))^2+2*B12/(B9^2)))",10.5]
[]
["ODE ",{"$f":"0.5*(B9^2)*(B4^2)*B20+B12*B4*B19-B12*B15+B5","v":0},"0.5*(B9^2)*(B4^2)*B20+B12*B4*B19-B12*B15+B5",10.199999999999999]
["D'(V) ",{"$f":"B16*((1-B10)*B14-(B5/B12))*(1/B4)*(B14/B4)^-B16","v":2.0281753540039063},"B16*((1-B10)*B14-(B5/B12))*(1/B4)*(B14/B4)^-B16","A6"]
["D''(V)  ",{"$f":"((B16^2)-B16)*((1-B10)*B14-(B5/B12))*(1/(B4^2))*(B14/B4)^-B16","v":-0.20281753540039058},"((B16^2)-B16)*((1-B10)*B14-(B5/B12))*(1/(B4^2))*(B14/B4)^-B16","A7"]

{"sheet":"V Delta","index":2,"n_rows":38,"n_cols":11,"rows_kept":38,"cut":false,"hidden":false,"merged":[]}
[null,null,null,"LELAND 1994"]
[" ",null,null," "]
["INPUT",null,null," "]
["V",30,{"$f":"B4+10","v":40},{"$f":"C4+10","v":50},60,70,80,90,100,110,120]
["C",4,4,4,{"$f":"D5","v":4},{"$f":"E5","v":4},4,4,4,4,4]
["D",{"$f":"B5/B12","v":66.666666666666671},66.666666666666671,{"$f":"D5/D12","v":66.666666666666671},{"$f":"E5/E12","v":66.666666666666671},{"$f":"F5/F12","v":66.666666666666671},66.666666666666671,66.666666666666671,66.666666666666671,66.666666666666671,66.666666666666671]
["d",0,0,0,0,0,0,0,0,0,0]
["m",{"$f":"B12-B7","v":0.06},{"$f":"C12-C7","v":0.06},0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06]
["s",0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2]
["a",0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5]
["t",0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35]
["r(f)",0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06]
["OUTPUT"]
["VB   EQ14",{"$f":"(1-B11)*B5/(B12+0.5*B9^2)","v":32.5},32.5,{"$f":"(1-D11)*D5/(D12+0.5*D9^2)","v":32.5},{"$f":"(1-E11)*E5/(E12+0.5*E9^2)","v":32.5},{"$f":"(1-F11)*F5/(F12+0.5*F9^2)","v":32.5},32.5,32.5,32.5,32.5,32.5]
["D* EQ7",{"$f":"(B5/B12)+((1-B10)*B14-(B5/B12))*(B14^B22)*B4^-B22","v":2.5663097993827222},{"$f":"(C5/C12)+((1-C10)*C14-(C5/C12))*(C14^C22)*C4^-C22","v":39.624328613281222},{"$f":"(D5/D12)+((1-D10)*D14-(D5/D12))*(D14^D22)*D4^-D22","v":52.820989583333301},{"$f":"(E5/E12)+((1-E10)*E14-(E5/E12))*(E14^E22)*E4^-E22","v":58.654122058256149},61.620865980320701,63.286374409993485,64.292579375285783,64.935957031249998,65.366358901515156,65.665098590615358]
["D* EQ15",{"$f":"(B5/B12)*(1-((B5/B4)^B22)*B20)","v":2.566309799382712},39.624328613281243,{"$f":"(D5/D12)*(1-((D5/D4)^D22)*D20)","v":52.820989583333343},{"$f":"(E5/E12)*(1-((E5/E4)^E22)*E20)","v":58.654122058256178},61.620865980320708,63.286374409993492,64.292579375285783,64.935957031249998,65.366358901515156,65.665098590615358]
["v(V) EQ16",{"$f":"B4+(B11*B5/B12)*(1-((B5/B4)^B22)*B19)","v":3.0066068672839528},42.101745605468743,{"$f":"D4+(D11*D5/D12)*(1-((D5/D4)^D22)*D19)","v":62.462760416666669},{"$f":"E4+(E11*E5/E12)*(1-((E5/E4)^E22)*E19)","v":77.042492525077165},89.371754282069972,100.67938486735025,111.46938050125743,121.97451171874999,132.31243054251189,142.54697823230131]
["E(V) EQ17",{"$f":"B4-(1-B11)*(B5/B12)*(1-((B5/B4)^B22)*B21)","v":0.44029706790123413},2.4774169921875,{"$f":"D4-(1-D11)*(D5/D12)*(1-((D5/D4)^D22)*D21)","v":9.6417708333333323},{"$f":"E4-(1-E11)*(E5/E12)*(1-((E5/E4)^E22)*E21)","v":18.388370466820987},27.750888301749271,37.393010457356766,47.17680112597165,57.038554687499996,66.946071640996735,76.881879641685956]
["h",{"$f":"(1+B22+B10*(1-B11)*B22/B11)*B21","v":909.92518833705128},909.92518833705128,{"$f":"(1+D22+D10*(1-D11)*D22/D11)*D21","v":909.92518833705128},{"$f":"(1+E22+E10*(1-E11)*E22/E11)*E21","v":909.92518833705128},909.92518833705128,909.92518833705128,909.92518833705128,909.92518833705128,909.92518833705128,909.92518833705128]
["k",{"$f":"(1+B22-(1-B10)*(1-B11)*B22)*B21","v":405.63507080078023},405.63507080078023,{"$f":"(1+D22-(1-D10)*(1-D11)*D22)*D21","v":405.63507080078023},{"$f":"(1+E22-(1-E10)*(1-E11)*E22)*E21","v":405.63507080078023},405.63507080078023,405.63507080078023,405.63507080078023,405.63507080078023,405.63507080078023,405.63507080078023]
["m",{"$f":"(((1-B11)*B22/(B12*(1+B22)))^B22)*((1+B22)^-1)","v":134.09423828124969},134.09423828124969,{"$f":"(((1-D11)*D22/(D12*(1+D22)))^D22)*((1+D22)^-1)","v":134.09423828124969},{"$f":"(((1-E11)*E22/(E12*(1+E22)))^E22)*((1+E22)^-1)","v":134.09423828124969},134.09423828124969,134.09423828124969,134.09423828124969,134.09423828124969,134.09423828124969,134.09423828124969]
["b1",{"$f":"((B12-B7-0.5*(B9^2))+SQRT((B12-B7-0.5*(B9^2))^2+2*(B9^2)*B12))/(B9^2)","v":2.9999999999999991},2.9999999999999991,{"$f":"((D12-D7-0.5*(D9^2))+SQRT((D12-D7-0.5*(D9^2))^2+2*(D9^2)*D12))/(D9^2)","v":2.9999999999999991},{"$f":"((E12-E7-0.5*(E9^2))+SQRT((E12-E7-0.5*(E9^2))^2+2*(E9^2)*E12))/(E9^2)","v":2.9999999999999991},2.9999999999999991,2.9999999999999991,2.9999999999999991,2.9999999999999991,2.9999999999999991,2.9999999999999991]
[]
["ASSETS",{"$f":"B17","v":3.0066068672839528},42.101745605468743,{"$f":"D17","v":62.462760416666669},{"$f":"E17","v":77.042492525077165},89.371754282069972,100.67938486735025,111.46938050125743,121.97451171874999,132.31243054251189,142.54697823230131]
["NOM D",{"$f":"B6","v":66.666666666666671},66.666666666666671,{"$f":"D6","v":66.666666666666671},{"$f":"E6","v":66.666666666666671},66.666666666666671,66.666666666666671,66.666666666666671,66.666666666666671,66.666666666666671,66.666666666666671]
["PUT",{"$f":"B25-B16","v":64.100356867283963},27.042338053385429,{"$f":"D25-D16","v":13.845677083333328},{"$f":"E25-E16","v":8.0125446084104937},5.045800686345963,3.3802922566731795,2.3740872913808886,1.7307096354166731,1.3003077651515156,1.0015680760513135]
["EQUITY",{"$f":"B18","v":0.44029706790123413},2.4774169921875,{"$f":"D18","v":9.6417708333333323},{"$f":"E18","v":18.388370466820987},27.750888301749271,37.393010457356766,47.17680112597165,57.038554687499996,66.946071640996735,76.881879641685956]
["L & E",{"$f":"B25-B26+B27","v":3.0066068672839421},42.101745605468743,{"$f":"D25-D26+D27","v":62.462760416666676},{"$f":"E25-E26+E27","v":77.042492525077165},89.371754282069986,100.67938486735025,111.46938050125743,121.97451171874999,132.31243054251189,142.54697823230131]
[]
["VB   EQ14","(1-C11)*C5/(C12+0.5*C9^2)"]
[{"$f":"A15","v":"D* EQ7"},"(C5/C12)+((1-C10)*C14-(C5/C12))*(C14^C22)*C4^-C22"]
["D* EQ15","(C5/C12)*(1-((C5/C4)^C22)*C20)"]
["v(V) EQ16","C4+(C11*C5/C12)*(1-((C5/C4)^C22)*C19)"]
["E(V) EQ17","C4-(1-C11)*(C5/C12)*(1-((C5/C4)^C22)*C21)"]
["h","(1+C22+C10*(1-C11)*C22/C11)*C21"]
["k","(1+C22-(1-C10)*(1-C11)*C22)*C21"]
["m","(((1-C11)*C22/(C12*(1+C22)))^C22)*((1+C22)^-1)"]
["b1","((C12-C7-0.5*(C9^2))+SQRT((C12-C7-0.5*(C9^2))^2+2*(C9^2)*C12))/(C9^2)"]

{"sheet":"BASE CASE DEBT","index":3,"n_rows":26,"n_cols":5,"rows_kept":26,"cut":false,"hidden":false,"merged":[]}
[null,"Real Debt Strategy"]
["Figure 10.1"]
["BASE CASE"]
[null,"ACCOUNTS","REAL"]
["ASSETS",{"$f":"B10","v":40},{"$f":"C10+(C16*C11/C17)*(1-(C19/C10)^-C20)-C15*C19*(C19/C10)^-C20","v":42.10174560546875},null,10.7]
["DEBT",{"$f":"B11/C17","v":66.666666666666671},{"$f":"(C11/C17)+((1-C15)*C19-(C11/C17))*(C19/C10)^-C20","v":39.62432861328125},null,10.6]
["EQ",{"$f":"B5-B6","v":-26.666666666666671},{"$f":"C10-(1-C16)*(C11/C17)+((1-C16)*(C11/C17)-C19)*((C19/C10)^-C20)","v":2.4774169921875},null,10.8]
[]
["INPUT","BASE"]
["NOM V",40,{"$f":"B10","v":40}]
["Coupon",4,{"$f":"B11","v":4}]
["NOM Debt",{"$f":"B11/C17","v":66.666666666666671},66.666666666666671]
["d",null,0]
["s",null,0.2]
["a",null,0.5]
["t",null,0.35]
["r(f)",null,0.06]
["OUTPUT"]
["VB   ",null,{"$f":"(1-C16)*(C11/C17)*(-C20/(-C20+1))","v":32.5},null,10.9]
["b2",null,{"$f":"(0.5-(C17-C13)/(C14^2)-SQRT((0.5-(C17-C13)/(C14^2))^2+2*C17/(C14^2)))","v":-2.9999999999999991},null,10.5]
[]
["V*","C10+(C16*C11/C17)*(1-(C19/C10)^-C20)-C15*C19*(C19/C10)^-C20"]
["D*","(C11/C17)+((1-C15)*C19-(C11/C17))*(C19/C10)^-C20"]
["E*","C10-(1-C16)*(C11/C17)+((1-C16)*(C11/C17)-C19)*((C19/C10)^-C20)"]
["VB   ","(1-C16)*(C11/C17)*(-C20/(-C20+1))"]
["b2","(0.5-(C17-C13)/(C14^2)-SQRT((0.5-(C17-C13)/(C14^2))^2+2*C17/(C14^2)))"]

{"sheet":"Strategy a","index":4,"n_rows":26,"n_cols":5,"rows_kept":26,"cut":false,"hidden":false,"merged":[]}
[null,"Real Debt Strategy"]
["Figure 10.2"]
["BASE CASE"]
[null,"ACCOUNTS","REAL"]
["ASSETS",{"$f":"B10","v":35},{"$f":"C10+(C16*C11/C17)*(1-(C19/C10)^-C20)-C15*C19*(C19/C10)^-C20","v":26.640700923226426},null,10.7]
["DEBT",{"$f":"B11/C17","v":66.666666666666671},{"$f":"(C11/C17)+((1-C15)*C19-(C11/C17))*(C19/C10)^-C20","v":26.300261175898925},null,10.6]
["EQ",{"$f":"B5-B6","v":-31.666666666666671},{"$f":"C10-(1-C16)*(C11/C17)+((1-C16)*(C11/C17)-C19)*((C19/C10)^-C20)","v":0.34043974732750293},null,10.8]
[]
["INPUT","BASE"]
["NOM V",35,{"$f":"B10","v":35}]
["Coupon",4,{"$f":"B11","v":4}]
["NOM Debt",{"$f":"B11/C17","v":66.666666666666671},66.666666666666671]
["d",null,0]
["s",null,0.2]
["a",null,0.5]
["t",null,0.35]
["r(f)",null,0.06]
["OUTPUT"]
["VB   ",null,{"$f":"(1-C16)*(C11/C17)*(-C20/(-C20+1))","v":32.5},null,10.9]
["b2",null,{"$f":"(0.5-(C17-C13)/(C14^2)-SQRT((0.5-(C17-C13)/(C14^2))^2+2*C17/(C14^2)))","v":-2.9999999999999991},null,10.5]
[]
["V*","C10+(C16*C11/C17)*(1-(C19/C10)^-C20)-C15*C19*(C19/C10)^-C20"]
["D*","(C11/C17)+((1-C15)*C19-(C11/C17))*(C19/C10)^-C20"]
["E*","C10-(1-C16)*(C11/C17)+((1-C16)*(C11/C17)-C19)*((C19/C10)^-C20)"]
["VB   ","(1-C16)*(C11/C17)*(-C20/(-C20+1))"]
["b2","(0.5-(C17-C13)/(C14^2)-SQRT((0.5-(C17-C13)/(C14^2))^2+2*C17/(C14^2)))"]

{"sheet":"Fair Strategy","index":5,"n_rows":29,"n_cols":10,"rows_kept":29,"cut":false,"hidden":false,"merged":[]}
[null,null,null," ",null,"Real Debt Strategy i"]
["Figure 10.10"]
["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":42.10174560546875},{"$f":"D10+(D16*D11/D17)*(1-(D19/D10)^-D20)-D15*D19*(D19/D10)^-D20","v":47.106492014213629},46.339798559085096,45.241653866803432,44.356089318255748,43.084499487181645,42.0564253463792,"V*"]
["DEBT",{"$f":"B11/C17","v":66.666666666666671},{"$f":"(C11/C17)+((1-C15)*C19-(C11/C17))*(C10^C20)*C19^-C20","v":39.624328613281222},{"$f":"(D11/D17)+((1-D15)*D19-(D11/D17))*(D10^D20)*D19^-D20","v":44.810623543028541},43.990730015676121,42.833316471238049,41.913739690478522,40.613606832041555,39.579022001550548,"D*"]
["EQ",{"$f":"B5-B6","v":-26.666666666666671},{"$f":"C10-(1-C16)*(C11/C17)+((1-C16)*(C11/C17)-C19)*((C19/C10)^-C20)","v":2.4774169921875},{"$f":"D10-(1-D16)*(D11/D17)+((1-D16)*(D11/D17)-D19)*((D19/D10)^-D20)","v":2.2958684711850905},2.3490685434089658,2.4083373955653746,2.442349627777233,2.4708926551401147,2.4774033448286747,"E*"]
[null,null,"WE CHOOSE","YOU CHOOSE","NEGOTIATE","NEGOTIATE","NEGOTIATE","NEGOTIATE","NEGOTIATE"]
["Retained Equity",null,{"$f":"C7","v":2.4774169921875},{"$f":"(1-D23)*D7","v":2.2958684711850905},2.325577857974876,2.3601706476540669,2.3690791389439161,2.3720569489345098,2.353533177587241]
["NOM V",40,{"$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,{"$f":"C12","v":66.666666666666671},66.666666666666671,66.666666666666671,66.666666666666671,66.666666666666671,66.666666666666671]
["d",null,0,{"$f":"C13","v":0},0,0,0,0,0]
["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,0.35,0.35,0.35,0.35,0.35,0.35,0.35]
["r(f)",null,0.06,0.06,0.06,0.06,0.06,0.06,0.06]
["OUTPUT",null,null," "]
["VB   ",null,{"$f":"(1-C16)*(C11/C17)*(-C20/(-C20+1))","v":32.5},{"$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":-2.9999999999999991},{"$f":"(0.5-(D17-D13)/(D14^2)-SQRT((0.5-(D17-D13)/(D14^2))^2+2*D17/(D14^2)))","v":-2.9999999999999991},-2.9999999999999991,-2.9999999999999991,-2.9999999999999991,-2.9999999999999991,-2.9999999999999991]
["LTV",{"$f":"$B$12/B5","v":1.6666666666666667},{"$f":"$B$12/C5","v":1.5834656190124121},{"$f":"$B$12/D5","v":1.4152330987956199},1.438648175858253,1.4735682931252008,1.5029879254758489,1.5473468987727503,1.5851719711695911]
[null,null,"LTV MAX",2.2200000000000002,2.19,2.15,2.12,2.08,2.0499999999999998]
[null,null,"SHARED EQUITY",0,0.01,{"$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$6-C6","v":27.04233805338545},{"$f":"$B$6-D6+D23*D7","v":21.856043123638131},{"$f":"$B$6-E6+E23*E7","v":22.699427336424641},23.881516943339928,24.826197465021465,26.151895540830722,27.211514832357558]
["CHANGE DEBT LOSS",null,{"$f":"C24-$B$24","v":-19.624328613281222},-24.810623543028541,-23.96723933024203,-22.785149723326743,-21.840469201645206,-20.514771125835949,-19.455151834309113]
["LTV",null,null,"$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":"Simple Strategy","index":6,"n_rows":26,"n_cols":5,"rows_kept":26,"cut":false,"hidden":false,"merged":[]}
[null,"Real Debt Strategy"]
[null,"Figure 10.11"]
["BASE CASE"]
[null,"ACCOUNTS","REAL"]
["ASSETS",{"$f":"B10","v":100},{"$f":"C10+(C16*C11/C17)*(1-(C19/C10)^-C20)-C15*C19*(C19/C10)^-C20","v":92.96875},null,10.7]
["DEBT",{"$f":"B11/C17","v":75},{"$f":"(C11/C17)+((1-C15)*C19-(C11/C17))*(C19/C10)^-C20","v":53.90625},null,10.6]
["EQ",{"$f":"B5-B6","v":25},{"$f":"C10-(1-C16)*(C11/C17)+((1-C16)*(C11/C17)-C19)*((C19/C10)^-C20)","v":39.0625},null,10.8]
[]
["INPUT","BASE"]
["NOM V",100,{"$f":"B10","v":100}]
["Coupon",3,{"$f":"B11","v":3}]
["NOM Debt",{"$f":"B11/C17","v":75},75]
["d",null,0.04]
["s",null,0.2]
["a",null,0.5]
["t",null,0]
["r(f)",null,0.04]
["OUTPUT"]
["VB   ",null,{"$f":"(1-C16)*(C11/C17)*(-C20/(-C20+1))","v":37.499999999999993},null,10.9]
["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,10.5]
[]
["V*","C10+(C16*C11/C17)*(1-(C19/C10)^-C20)-C15*C19*(C19/C10)^-C20"]
["D*","(C11/C17)+((1-C15)*C19-(C11/C17))*(C19/C10)^-C20"]
["E*","C10-(1-C16)*(C11/C17)+((1-C16)*(C11/C17)-C19)*((C19/C10)^-C20)"]
["VB   ","(1-C16)*(C11/C17)*(-C20/(-C20+1))"]
["b2","(0.5-(C17-C13)/(C14^2)-SQRT((0.5-(C17-C13)/(C14^2))^2+2*C17/(C14^2)))"]

{"sheet":"Exercise 2.1","index":7,"n_rows":29,"n_cols":5,"rows_kept":29,"cut":false,"hidden":false,"merged":[]}
["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"]
[]
["PV",{"$f":"EXP(-B4*B5)","v":0.95122942450071402},null,null,"EXP(-B4*B5)"]

{"sheet":"Exercise 2.2","index":8,"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":9,"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":10,"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",{"$f":"B5*B15*EXP(-B8*B9)-B6*B16*EXP(-B7*B9)","v":91.145664723121712},"B5*B15*EXP(-B8*B9)-B6*B16*EXP(-B7*B9)"]
[]
["d1",{"$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":0.676954750886957},"NORMSDIST(B13)"]
["N(d2)",{"$f":"NORMSDIST(B14)","v":0.50478179812514568},"NORMSDIST(B14)"]
[]
["SF",100000]
["TOTAL REAL CALL OPTION VALUE",{"$f":"B11*B18","v":9114566.472312171}]
["INTRINSIC REAL CALL VALUE",{"$f":"(B5-B6)*B18","v":5000000}]

{"sheet":"Problem 2.5","index":11,"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",{"$f":"B5*B15*EXP(-B8*B9)-B6*B16*EXP(-B7*B9)","v":327.75501946852518},"B5*B15*EXP(-B8*B9)-B6*B16*EXP(-B7*B9)"]
[]
["d1",{"$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":0.63346001742384173},"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":12,"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":68736.540599974745},"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)",{"$f":"NORMSDIST(B16)","v":0.36389726390554022},"NORMSDIST(B16)"]
["N(d2)",{"$f":"NORMSDIST(B17)","v":0.29182508012097036},"NORMSDIST(B17)"]
[]
["Margrabe Exchange Real Option is worth",null,{"$f":"B14","v":68736.540599974745}]
["ASSUMES: volatilities and correlation are constant, this a European option,"]
["Several assumptions required."," "]
[" "," "]
["Investment in facility for retail tenants worth ",null,{"$f":"B4-C28","v":50000}]
["Option to switch tenants in one year worth",null,{"$f":"B14","v":68736.540599974745}]
["So value of modular facility worth",null,{"$f":"C25+C26","v":118736.54059997475}]
["Investment cost ",null,1700000]

{"sheet":"Exercise 3.1","index":13,"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":14,"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":15,"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":16,"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":17,"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":18,"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":19,"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":138.88888888888883},"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":0.55555555555555536},"IF(B3<B12,B13*B14*(B3^(B14-1)),1)"]
["V*",{"$f":"(B14/(B14-1))*B4","v":900.00000000000023},"(B14/(B14-1))*B4"]
["A",{"$f":"(B12-B4)/(B12^B14)","v":5.5555555555555664E-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":13888888.888888882}]
["V* TOTAL",{"$f":"B12*B15","v":90000000.00000003}]

{"sheet":"Exercise 4.2","index":20,"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":21,"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",{"$f":"IF(B3<B12,(B12-B4)*(B3/B12)^B14,B10)","v":0.17794117647058838},"IF(B3<B12,(B12-B4)*(B3/B12)^B14,B10)"]
["F(V)",{"$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*",{"$f":"(B14/(B14-1))*B4","v":3.4000000000000008},"(B14/(B14-1))*B4"]
["A",{"$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":1.0000000000000004}]
["F(V*)",{"$f":"IF(B3<B12,B13*(B12^B14),B10)","v":1.7000000000000008}]
["V*-K",{"$f":"B12-B4","v":1.7000000000000008}]
[]
["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":22,"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)",{"$f":"IF(B3<B12,B13*(B3^B14),B10)","v":138.88888888888883},"IF(B3<B12,B13*(B3^B14),B10)"]
["V-K",{"$f":"B3-B4","v":50},"B3-B4"]
["F'(V)",{"$f":"IF(B3<B12,B13*B14*(B3^(B14-1)),1)","v":0.55555555555555536},"IF(B3<B12,B13*B14*(B3^(B14-1)),1)"]
["V*",{"$f":"(B14/(B14-1))*B4","v":900.00000000000023},"(B14/(B14-1))*B4"]
["A",{"$f":"(B12-B4)/(B12^B14)","v":5.5555555555555664E-4},"(B12-B4)/(B12^B14)"]
["b1",{"$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":1.1111111111111113E-3},"IF(B3<B12,B13*B14*(B14-1)*(B3^(B14-2)),0)"]
["F'(V*)",{"$f":"B13*B14*(B12^(B14-1))","v":1.0000000000000002},"B13*B14*(B12^(B14-1))"]
["F(V*)",{"$f":"IF(B3<B12,B13*(B12^B14),B10)","v":450.00000000000023},"IF(B3<B12,B13*(B12^B14),B10)"]
["V*-K",{"$f":"B12-B4","v":450.00000000000023},"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":23,"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":24,"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 14.1","index":25,"n_rows":36,"n_cols":4,"rows_kept":36,"cut":false,"hidden":false,"merged":[]}
["EXERCISE 14.1 ACTIVE FLOOR ONLY"]
["INPUT",null,null,"EQ"]
["R",2]
[" "," "]
["s",0.2]
["r",0.04]
["d",0.04]
["RL",4]
[" "," "]
["OUTPUT"]
["VCf",{"$f":"IF(B3<B8,B8/B6+B16,B3/B7+B18)","v":108.33333333333334},"IF(B3<B8,B8/B6+B16,B3/B7+B18)",11]
["VCf PV",{"$f":"IF(B3<B8,B8/B6,B3/B7)","v":100},"IF(B3<B8,B8/B6,B3/B7)",11]
["R/d",{"$f":"B3/B7","v":50},"B3/B7"," "]
["b1",{"$f":"0.5-(B6-B7)/(B5^2)+SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))","v":1.9999999999999998},"0.5-(B6-B7)/(B5^2)+SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))",4]
["b2",{"$f":"0.5-(B6-B7)/(B5^2)-SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))","v":-0.99999999999999978},"0.5-(B6-B7)/(B5^2)-SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))",4]
["ACf11*R^b1",{"$f":"B21*(B3^B14)","v":8.3333333333333357},"B21*(B3^B14)"," "]
[" "," "," "," "]
["ACf22*R^b2",{"$f":"B23*(B3^B15)","v":66.666666666666657},"B23*(B3^B15)"," "]
[" ","  "," "," "]
[" "," "," "," "]
["ACf11",{"$f":"(-B8/(B8^B14))*(B25/B27)","v":2.0833333333333344},"(-B8/(B8^B14))*(B25/B27)",12]
[" "," "," "," "]
["ACf22",{"$f":"(-B8/(B8^B15))*(B26/B27)","v":133.33333333333331},"(-B8/(B8^B15))*(B26/B27)",12]
[" "," "," "," "]
["[      ]",{"$f":"(B6*B15-B6-B7*B15)","v":-3.9999999999999994E-2},"(B6*B15-B6-B7*B15)"," "]
["(     )",{"$f":"(B6*B14-B6-B7*B14)","v":-0.04},"(B6*B14-B6-B7*B14)"," "]
["{      }",{"$f":"(B14-B15)*B6*B7","v":4.7999999999999996E-3},"(B14-B15)*B6*B7"," "]
[" "," "," "]
["ODE",{"$f":"0.5*(B5^2)*(B3^2)*B31+(B6-B7)*B3*B30-B6*B11+MIN(MAX(B8,B3))","v":0},"0.5*(B5^2)*(B3^2)*B31+(B6-B7)*B3*B30-B6*B11+MIN(MAX(B8,B3))"," "]
["VC D",{"$f":"IF(B3<B8,1/B6+B14*B21*(B3^(B14-1)),1/B7+B15*B23*(B3^(B15-1)))","v":33.333333333333336},"IF(B3<B8,1/B6+B14*B21*(B3^(B14-1)),1/B7+B15*B23*(B3^(B15-1)))"]
["VC G",{"$f":"IF(B3<B8,(B14-1)*B14*B21*(B3^(B14-2)),(B15-1)*B15*B23*(B3^(B15-2)))","v":4.1666666666666661},"IF(B3<B8,(B14-1)*B14*B21*(B3^(B14-2)),(B15-1)*B15*B23*(B3^(B15-2)))"]
["VC D",null,"Decomposition"]
["IF(B3<B8)",{"$f":"B14*B21*(B3^(B14-1))","v":8.3333333333333339},"B14*B21*(B3^(B14-1))"]
["IF(B8<B3",{"$f":"1/B7+B15*B23*(B3^(B15-1))","v":-8.3333333333333286},"1/B7+B15*B23*(B3^(B15-1))"]
["IF(B3<B8",{"$f":"1/B7","v":25},"1/B7"]
["IF(B8<B3",{"$f":"B15*B23*(B3^(B15-1))","v":-33.333333333333329},"B15*B23*(B3^(B15-1))"]

{"sheet":"Exercise 14.2","index":26,"n_rows":37,"n_cols":4,"rows_kept":37,"cut":false,"hidden":false,"merged":[]}
["ACTIVE PPP WITH CEILING ONLY  EXERCISE 14.2"]
["INPUT",null,null,"EQ"]
["R",4]
[" "," "]
["s",0.2]
["r",0.04]
["d",0.04]
[" "," "]
["RH",15]
["OUTPUT"]
["VCc",{"$f":"IF(B3<B9,B3/B7+B17,B9/B6+B19)","v":91.111111111111114},"IF(B3<B9,B3/B7+B17,B9/B6+B19)",13]
[" "," "," "," "]
["R/d",{"$f":"B3/B7","v":100},"B3/B7"," "]
["b1",{"$f":"0.5-(B6-B7)/(B5^2)+SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))","v":1.9999999999999998},"0.5-(B6-B7)/(B5^2)+SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))",4]
["b2",{"$f":"0.5-(B6-B7)/(B5^2)-SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))","v":-0.99999999999999978},"0.5-(B6-B7)/(B5^2)-SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))",4]
[" "," "," "," "]
["ACc21*R^b1",{"$f":"B22*(B3^B14)","v":-8.8888888888888893},"B22*(B3^B14)"," "]
[" "," "," "," "]
["ACc32*R^b2",{"$f":"B24*(B3^B15)","v":-468.74999999999994},"B24*(B3^B15)"," "]
[" "," "," "," "]
[" "," "," "," "]
["ACc21",{"$f":"(B9/(B9^B14))*(B25/B27)","v":-0.55555555555555591},"(B9/(B9^B14))*(B25/B27)",14]
[" "," "," "," "]
["ACc32",{"$f":"(B9/(B9^B15))*(B26/B27)","v":-1874.9999999999993},"(B9/(B9^B15))*(B26/B27)",14]
["[      ]",{"$f":"(B6*B15-B6-B7*B15)","v":-3.9999999999999994E-2},"(B6*B15-B6-B7*B15)"," "]
["(     )",{"$f":"(B6*B14-B6-B7*B14)","v":-0.04},"(B6*B14-B6-B7*B14)"," "]
["{      }",{"$f":"(B14-B15)*B6*B7","v":4.7999999999999996E-3},"(B14-B15)*B6*B7"," "]
[" "," "," "]
["ODE",{"$f":"0.5*(B5^2)*(B3^2)*B31+(B6-B7)*B3*B30-B6*B11+MAX(MIN(B3,B9))","v":0},"0.5*(B5^2)*(B3^2)*B31+(B6-B7)*B3*B30-B6*B11+MAX(MIN(B3,B9))"," "]
["VC D",{"$f":"IF(B3<B9,1/B7+B14*B22*(B3^(B14-1)),1/B6+B15*B24*(B3^(B15-1)))","v":20.555555555555554},"IF(B3<B9,1/B7+B14*B22*(B3^(B14-1)),1/B6+B15*B24*(B3^(B15-1)))"]
["VC G",{"$f":"IF(B3<B9,(B14-1)*B14*B22*(B3^(B14-2)),(B15-1)*B15*B24*(B3^(B15-2)))","v":-1.1111111111111112},"IF(B3<B9,(B14-1)*B14*B22*(B3^(B14-2)),(B15-1)*B15*B24*(B3^(B15-2)))"]
["VC D"]
["IF(B3<B9)",{"$f":"1/B7+B14*B22*(B3^(B14-1))","v":20.555555555555554},"1/B7+B14*B22*(B3^(B14-1))"]
[null,null,"Decomposition"]
["IF(B3<B9)",{"$f":"1/B7","v":25},"1/B7"]
["IF(B3<B9)",{"$f":"B14*B22*(B3^(B14-1))","v":-4.4444444444444455},"B14*B22*(B3^(B14-1))"]
["IF(B9<B3",{"$f":"B15*B24*(B3^(B15-1))","v":117.18749999999999},"B15*B24*(B3^(B15-1))"]

{"sheet":"Exercise 14.3","index":27,"n_rows":33,"n_cols":4,"rows_kept":33,"cut":false,"hidden":false,"merged":[]}
["ACTIVE PPP WITH COLLAR EXERCISE 14.3"]
["INPUT",null,null,"EQ"]
["R",4]
["K",100]
["s",0.2]
["r",0.04]
["d",0.04]
["RL",4]
["RH",1000]
["OUTPUT"]
[" "," "," "," "]
[" "," "," "," "]
[" "," "," "," "]
["b1",{"$f":"0.5-(B6-B7)/(B5^2)+SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))","v":1.9999999999999998},"0.5-(B6-B7)/(B5^2)+SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))",4]
[" "," "," "," "]
["VC",{"$f":"IF(B3<B8,B8/B6+B22*(B3^B14),IF(B3>B9,B9/B6+B25*(B3^B18),B3/B7+B23*(B3^B14)+B24*(B3^B18)))","v":133.19999999999999},null,5]
["VC PV",{"$f":"IF(B3<B8,B8/B6,IF(B3>B9,B9/B6,B3/B7))","v":100},"IF(B3<$B$8,$B$8/B6,IF(B3>$B$9,$B$9/B6,B3/B7))"," "]
["b2",{"$f":"0.5-(B6-B7)/(B5^2)-SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))","v":-0.99999999999999978},"0.5-(B6-B7)/(B5^2)-SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))",4]
["AC21*R^b1",{"$f":"B23*(B3^B14)","v":-0.13333333333333353},"B23*(B3^B14)"," "]
["AC22*R^b2",{"$f":"B24*(B3^B18)","v":33.333333333333336},"B24*(B3^B18)"]
["VC",{"$f":"B17+B19+B20","v":133.19999999999999},"B17+B19+B20"," "]
["AC11",{"$f":"(B9/(B9^B14)-B8/(B8^B14))*(B26/B28)","v":2.0750000000000011},"($B$9/($B$9^B14)-$B$8/($B$8^B14))*(B26/B28)",10]
["AC21",{"$f":"(B9/(B9^B14))*(B26/B28)","v":-8.3333333333333506E-3},"($B$9/($B$9^B14))*(B26/B28)",10]
["AC22",{"$f":"(-B8/(B8^B18))*(B27/B28)","v":133.33333333333331},"(-$B$8/($B$8^B18))*(B27/B28)",10]
["AC32",{"$f":"(B9/(B9^B18)-B8/(B8^B18))*(B27/B28)","v":-8333199.9999999842},"($B$9/($B$9^B18)-$B$8/($B$8^B18))*(B27/B28)",10]
["[      ]",{"$f":"(B6*B18-B6-B7*B18)","v":-3.9999999999999994E-2},"(B6*B18-B6-B7*B18)",10]
["(     )",{"$f":"(B6*B14-B6-B7*B14)","v":-0.04},"(B6*B14-B6-B7*B14)",10]
["{      }",{"$f":"(B14-B18)*B6*B7","v":4.7999999999999996E-3},"(B14-B18)*B6*B7",10]
[]
["ODE",{"$f":"0.5*(B5^2)*(B3^2)*B32+(B6-B7)*B3*B31-B6*B16+B3","v":0},"0.5*(B5^2)*(B3^2)*B32+(B6-B7)*B3*B31-B6*B16+B3",2]
["VC D",{"$f":"1/B7+B14*B23*(B3^(B14-1))+B18*B24*(B3^(B18-1))","v":16.600000000000001},"1/B7+B14*B23*(B3^(B14-1))+B18*B24*(B3^(B18-1))"]
["VC G",{"$f":"B14*(B14-1)*B23*(B3^(B14-2))+B18*(B18-1)*B24*(B3^(B18-2))","v":4.1499999999999977},"B14*(B14-1)*B23*(B3^(B14-2))+B18*(B18-1)*B24*(B3^(B18-2))"]
["VC","IF(B3<$B$8,$B$8/B6+B22*(B3^B14),IF(B3>$B$9,$B$9/B6+B25*(B3^B18),B3/B7+B23*(B3^B14)+B24*(B3^B18)))"]

{"sheet":"Problem 14.4","index":28,"n_rows":37,"n_cols":4,"rows_kept":37,"cut":false,"hidden":false,"merged":[]}
["ACTIVE PPP WITH FLOOR ONLY PROBLEM 14.4"]
["INPUT",null,null,"EQ"]
["R",10]
[" "," "]
["s",0.25]
["r",0.04]
["d",0.04]
["RL",6]
[" "," "]
["OUTPUT"]
["VCf",{"$f":"IF(B3<B8,B8/B6+B16,B3/B7+B18)","v":291.61291836994315},"IF(B3<B8,B8/B6+B16,B3/B7+B18)",11]
["VCf PV",{"$f":"IF(B3<B8,B8/B6,B3/B7)","v":250},"IF(B3<B8,B8/B6,B3/B7)",11]
["R/d",{"$f":"B3/B7","v":250},"B3/B7"," "]
["b1",{"$f":"0.5-(B6-B7)/(B5^2)+SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))","v":1.7369316876852983},"0.5-(B6-B7)/(B5^2)+SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))",4]
["b2",{"$f":"0.5-(B6-B7)/(B5^2)-SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))","v":-0.73693168768529826},"0.5-(B6-B7)/(B5^2)-SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))",4]
["ACf11*R^b1",{"$f":"B21*(B3^B14)","v":147.24876842134665},"B21*(B3^B14)"," "]
[" "," "," "," "]
["ACf22*R^b2",{"$f":"B23*(B3^B15)","v":41.612918369943138},"B23*(B3^B15)"," "]
[" ","  "," "," "]
[" "," "," "," "]
["ACf11",{"$f":"(-B8/(B8^B14))*(B25/B27)","v":2.6984848451186187},"(-B8/(B8^B14))*(B25/B27)",12]
[" "," "," "," "]
["ACf22",{"$f":"(-B8/(B8^B15))*(B26/B27)","v":227.07005345893685},"(-B8/(B8^B15))*(B26/B27)",12]
[" "," "," "," "]
["[      ]",{"$f":"(B6*B15-B6-B7*B15)","v":-3.9999999999999994E-2},"(B6*B15-B6-B7*B15)"," "]
["(     )",{"$f":"(B6*B14-B6-B7*B14)","v":-0.04},"(B6*B14-B6-B7*B14)"," "]
["{      }",{"$f":"(B14-B15)*B6*B7","v":3.9581814005929545E-3},"(B14-B15)*B6*B7"," "]
[" "," "," "]
["ODE",{"$f":"0.5*(B5^2)*(B3^2)*B31+(B6-B7)*B3*B30-B6*B11+MIN(MAX(B8,B3))","v":0},"0.5*(B5^2)*(B3^2)*B31+(B6-B7)*B3*B30-B6*B11+MIN(MAX(B8,B3))"," "]
["VC D",{"$f":"IF(B3<B8,1/B6+B14*B21*(B3^(B14-1)),1/B7+B15*B23*(B3^(B15-1)))","v":21.933412183612727},"IF(B3<B8,1/B6+B14*B21*(B3^(B14-1)),1/B7+B15*B23*(B3^(B15-1)))"]
["VC G",{"$f":"IF(B3<B8,(B14-1)*B14*B21*(B3^(B14-2)),(B15-1)*B15*B23*(B3^(B15-2)))","v":0.53264535513527211},"IF(B3<B8,(B14-1)*B14*B21*(B3^(B14-2)),(B15-1)*B15*B23*(B3^(B15-2)))"]
["VC D"]
["IF(B3<B8)",{"$f":"B14*B21*(B3^(B14-1))","v":25.576105184367119},"B14*B21*(B3^(B14-1))"]
["IF(B8<B3",{"$f":"1/B7+B15*B23*(B3^(B15-1))","v":21.933412183612727},"1/B7+B15*B23*(B3^(B15-1))"]
[null,null,"Decomposition"]
["IF(B8<B3",{"$f":"1/B7","v":25},"1/B7"]
["IF(B8<B3",{"$f":"B15*B23*(B3^(B15-1))","v":-3.066587816387274},"B15*B23*(B3^(B15-1))"]

{"sheet":"Problem 14.5","index":29,"n_rows":33,"n_cols":4,"rows_kept":33,"cut":false,"hidden":false,"merged":[]}
["ACTIVE PPP WITH COLLAR PROBLEM 14.5"]
["INPUT",null,null,"EQ"]
["R",10]
[" "," "]
["s",0.25]
["r",0.04]
["d",0.04]
["RL",2]
["RH",12]
["OUTPUT"]
[" "," "," "," "]
[" "," "," "," "]
[" "," "," "," "]
["b1",{"$f":"0.5-(B6-B7)/(B5^2)+SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))","v":1.7369316876852983},"0.5-(B6-B7)/(B5^2)+SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))",4]
[" "," "," "," "]
["VC",{"$f":"IF(B3<B8,B8/B6+B22*(B3^B14),IF(B3>B9,B9/B6+B25*(B3^B18),B3/B7+B23*(B3^B14)+B24*(B3^B18)))","v":167.82173176360831},null,5]
["VC PV",{"$f":"IF(B3<B8,B8/B6,IF(B3>B9,B9/B6,B3/B7))","v":250},"IF(B3<$B$8,$B$8/B6,IF(B3>$B$9,$B$9/B6,B3/B7))"," "]
["b2",{"$f":"0.5-(B6-B7)/(B5^2)-SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))","v":-0.73693168768529826},"0.5-(B6-B7)/(B5^2)-SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))",4]
["AC21*R^b1",{"$f":"B23*(B3^B14)","v":-88.35133747758951},"B23*(B3^B14)"," "]
["AC22*R^b2",{"$f":"B24*(B3^B18)","v":6.1730692411978305},"B24*(B3^B18)"]
["VC",{"$f":"B17+B19+B20","v":167.82173176360831},"B17+B19+B20"," "]
["AC11",{"$f":"(B9/(B9^B14)-B8/(B8^B14))*(B26/B28)","v":4.4444041708038444},"($B$9/($B$9^B14)-$B$8/($B$8^B14))*(B26/B28)",10]
["AC21",{"$f":"(B9/(B9^B14))*(B26/B28)","v":-1.6191289596869252},"($B$9/($B$9^B14))*(B26/B28)",10]
["AC22",{"$f":"(-B8/(B8^B18))*(B27/B28)","v":33.684711803750034},"(-$B$8/($B$8^B18))*(B27/B28)",10]
["AC32",{"$f":"(B9/(B9^B18)-B8/(B8^B18))*(B27/B28)","v":-723.19767779626795},"($B$9/($B$9^B18)-$B$8/($B$8^B18))*(B27/B28)",10]
["[      ]",{"$f":"(B6*B18-B6-B7*B18)","v":-3.9999999999999994E-2},"(B6*B18-B6-B7*B18)",10]
["(     )",{"$f":"(B6*B14-B6-B7*B14)","v":-0.04},"(B6*B14-B6-B7*B14)",10]
["{      }",{"$f":"(B14-B18)*B6*B7","v":3.9581814005929545E-3},"(B14-B18)*B6*B7",10]
[]
["ODE",{"$f":"0.5*(B5^2)*(B3^2)*B32+(B6-B7)*B3*B31-B6*B16+B3","v":0},"0.5*(B5^2)*(B3^2)*B32+(B6-B7)*B3*B31-B6*B16+B3",2]
["VC D",{"$f":"1/B7+B14*B23*(B3^(B14-1))+B18*B24*(B3^(B18-1))","v":9.1990631951683035},"1/B7+B14*B23*(B3^(B14-1))+B18*B24*(B3^(B18-1))"]
["VC G",{"$f":"B14*(B14-1)*B23*(B3^(B14-2))+B18*(B18-1)*B24*(B3^(B18-2))","v":-1.0518818334258131},"B14*(B14-1)*B23*(B3^(B14-2))+B18*(B18-1)*B24*(B3^(B18-2))"]
["VC","IF(B3<$B$8,$B$8/B6+B22*(B3^B14),IF(B3>$B$9,$B$9/B6+B25*(B3^B18),B3/B7+B23*(B3^B14)+B24*(B3^B18)))"]

{"sheet":"Problem 14.6","index":30,"n_rows":32,"n_cols":4,"rows_kept":32,"cut":false,"hidden":false,"merged":[]}
["INVESTMENT OPPORTUNITY FOR A PPP WITH A COLLAR OPTION PROBLEM 14.6"]
["INPUT",null,null,"EQ"]
["R",4]
["K",100]
["s",0.25]
["r",0.04]
["d",0.04]
["RL",4]
["RH",10]
["OUTPUT"]
["ROV CALL",{"$f":"IF(B3<B13,((B4/(B14-1))*(B3/B13)^B14),B12)","v":30.606712889071549},"IF(B3<B13,((B4/(B14-1))*(B3/B13)^B14),B12)",16]
["R/d-K",{"$f":"MAX(B3/B7-B4,0)","v":0},"MAX(B3/B7-B4,0)"," "]
["R^",{"$f":"(B14/(B14-1))*B4*B7","v":9.4279115240165563},"(B14/(B14-1))*B4*B7",15]
["b1",{"$f":"0.5-(B6-B7)/(B5^2)+SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))","v":1.7369316876852983},"0.5-(B6-B7)/(B5^2)+SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))",4]
["A0",{"$f":"(B4*(B13^-B14))/(B14-1)","v":2.7547336414741652},"(B4*(B13^-B14))/(B14-1)",17]
[" "," ",null," "]
["ROV COLLAR",{"$f":"IF(B3<B20,B21*(B3^B14),B3/B7-B4+B23*(B3^B14)+B24*(B3^B18))","v":19.84619029836195},"IF(B3<B20,B21*(B3^B14),B3/B7-B4+B23*(B3^B14)+B24*(B3^B18))",22]
["b2",{"$f":"0.5-(B6-B7)/(B5^2)-SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))","v":-0.73693168768529826},"0.5-(B6-B7)/(B5^2)-SQRT(((B6-B7)/(B5^2)-0.5)^2 + 2*B6/(B5^2))",4]
["FIND R^",{"$f":"B20/B7-(B14/(B14-1))*B4+((B14-B18)/(B14-1))*B24*(B20^B18)","v":0},"B20/B7-(B14/(B14-1))*B4+((B14-B18)/(B14-1))*B24*(B20^B18)",20]
["R^",3.999999828338026,"SOLVER Set B19=0, changing B20"]
["AC0",{"$f":"(1/(B14-B18))*((1-B18)*(B20/B7)+B18*B4)*(B20^-B14)+B23","v":1.7862410860042586},"(1/(B14-B18))*((1-B18)*(B20/B7)+B18*B4)*(B20^-B14)+B23",21]
[" "," "," "," "]
["AC21",{"$f":"($B$9/($B$9^B14))*(B26/B28)","v":-1.8519642970491914},"($B$9/($B$9^B14))*(B26/B28)",10]
["AC22",{"$f":"(-$B$8/($B$8^B18))*(B27/B28)","v":112.27973382945815},"(-$B$8/($B$8^B18))*(B27/B28)",10]
[" "," "," "," "]
["[      ]",{"$f":"(B6*B18-B6-B7*B18)","v":-3.9999999999999994E-2},"(B6*B18-B6-B7*B18)",10]
["(     )",{"$f":"(B6*B14-B6-B7*B14)","v":-0.04},"(B6*B14-B6-B7*B14)",10]
["{      }",{"$f":"(B14-B18)*B6*B7","v":3.9581814005929545E-3},"(B14-B18)*B6*B7",10]
[null,null," "]
["AC21*R^b1",{"$f":"B23*(B3^B14)","v":-20.57641387436021},"B23*(B3^B14)","RL<R<RH"]
["AC22*R^b2",{"$f":"B24*(B3^B18)","v":40.42260417272216},"B24*(B3^B18)"]
["ROV COLLAR",{"$f":"B12+B30+B31","v":19.84619029836195},"B12+B30+B31"]