Problem Set II - Risk Return and Capital Budgeting Solutions

Problem Set II - Risk Return and Capital Budgeting...

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Problem Set II Solutions Capital Budgeting and Risk Return Problem 1 Discount rate = 10% A) NPV of investing in machine A can be calculated as sum of present value of the cash flows (cash outflow at t = 0 and annuity for next six years). NPV (Machine A) = -$1,000,000 + $gG±,±±± ±.² ³1 − ² ².² ´ µ = $88,815.17 NPV of investing in machine B can be calculated as sum of present value of the cash flows (cash outflow at t = 0 and annuity for next three years; and cash flow at t = 3 and another annuity for next three years). NPV (Machine B) = ¶−$400,000 + $g±±,±±± ±.² ³1 − ² ².² · µ¸ + ² ².² · ¶−$400,000 + $g±±,±±± ±.² ³1 − ² ².² · µ¸ = $170,526.22 As NPV of machine B is greater than NPV of machine A, company should buy machine B. B) NPV of machine A in this case remains same. NPV (Machine B) = ¶−$400,000 + $g±±,±±± ±.² ³1 − ² ².² · µ¸ + ² ².² · ¶−$550,000 + $g±±,±±± ±.² ³1 − ² ².² · µ¸ = $57,829 As in this case, NPV of machine A is greater than NPV of machine B, company should buy machine A. Problem 2 a) Even though the firm will only know if they get the contract a year from now, they have to commit to buy the equipment today. The chance of getting the contract is 70%. Hence the chance of future inflows is also 70%.The inflows start at year 2 for a period of 10 years. Years 0 1 2 3 e 10 11 |―――――――|――― ―――|―――――――|――― ―――|――― ―――|――― ―――| Investment -$1,000,000 Contract awarded (p=70%) $ 250,000 $ 250,000 e $ 250,000 $ 250,000 Contract lost (p=30%) $ 0 $ 0 e $ 0 $ 0 Int rate (yearly) |― ―| Present values Investment PV annuity won PV annuity lost 15%
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= $105,839.55 b) If you could delay the commitment to purchase the equipment by a year then you would only purchase the equipment if you win the contract. = $155,030 c) The value of flexibility = NPV (with option) – NPV (without option) = $155,030 – ($105,840) = $49,190 Problem 3 a) The returns of Cisco and GM are as follows: Economy Return on Cisco Stock Return on GM Stock Depression (70 + 2.50 – 100)/100 = -0.275 (45 + 3.50 – 50)/50 = -0.03 Moderate (100 + 5 – 100)/100 = 0.05 (50 + 4 – 50)/50 = 0.08 Boom (140 + 7 – 100)/100 = 0.47 (60 3 – 50)/50 = 0.26 Expected returns = i i r prob r E ) ( E(r) of Cisco = 0.25(-0.275) + 0.5(0.05) + 0.25(0.47) = 0.0738
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Problem Set II - Risk Return and Capital Budgeting...

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