BD_SM_c22 - Chapter 22 Real Options 22-1. Decision Tree 176...

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Chapter 22 Real Options 22-1. Decision Tree
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176 Berk/DeMarzo Corporate Finance 22-2. Decision Tree
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Chapter 22 Real Options 177 22-3. Decision Tree 22-4. By delaying, you delay the benefits of taking on the project and your competitors might take advantage of this delay. However, by delaying, uncertainty can be resolved, so you can become better informed and make better decisions. Year 0 1 2
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178 Berk/DeMarzo Corporate Finance 22-5. a. S* = S – PV(Div) = 40(1. – 15) = 40(0.85) PV(K) = 35 / (1.04) = 33.6538 T = 1 σ = 0.25 1 2 12 ln(S * / PV(K) T d0 . 1 6 5 9 2 K . 0 8 4 1 C S* N(d ) PV(K)N(d ) $3.54 σ =+ = σ =− = So the value of waiting is $3.54 million. The value of investing today is $40 – $35 = $5 million. So, they should enter the business now. b. S* = S – PV(Div) = 36(1. – 15) = 36(0.85) PV(K) = 35 / (1.04) = 33.6538 T = 1 σ = 0.25 1 2 ln(S * / PV(K) T . 2 5 5 5 2 K . 5 0 5 5 C $1.90 σ = σ = So the value of waiting is $1.90 million. The value of investing today is $36 – $35 = $1 million. So, they should not enter the business now. c. $1.90 $35
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Chapter 22 Real Options 179 22-6. Decision Tree If you book now, your expected benefit from skiing in 4 months is: 6,000(0.60) 0(0.40) $3,600 += The NPV of booking today is therefore: 4 12 3, 600 NPV 2,500 $1,008.82 1.08 =− = If you wait to book the expected benefit in 4 months is: () ( ) 2,000 0.60 0 0.4 0 $1,200 The PV of this today is 4 12 $1,200 $1,169.61 1.08 = So you should wait.
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180 Berk/DeMarzo Corporate Finance 22-7. a. Decision Tree 1 2 12 0 1 2 3 5 6 7 17 20% 10(1.1) 2 10(1.1) 3 10(1.1) 5 10(1.1) 5 10(1.1) 5 10(1.1) 5 80% x (1 – 0.2) x (1 – 0.2) 2 x (1-0.2) 12 –100 10(1.05) 2 10(1.05) 3 10(1.05) 5 10(1.05) 5 10(1.05) 5 10(1.05) 5 x (1 – 0.2) x (1 – 0.2) 2 x (1 – 0.2) 12 If the high growth rate state occurs, then the NPV is: () ( ) 5 12 high 5 10 1.1 1 0.02 10 . 9 8 NPV 4 10 1 100 0.1 0.2 1.1 1.1 $1,247,147 ⎛⎞ ⎜⎟ =+ + ⎝⎠ = Note : Since the first 4 cash flows grow out of the same rate as the discount rate, their present value is just the sum of the cash flows. If the low growth rate state occurs, then the NPV is: ( ) 5 41 2 low 5 10 1.05 10 1.05 1 0.02 1 1.05 1 0.98 NPV 1 1 100 1.1 0.1 0.05 1.1 0.1 0.02 1.1 1.1 32.42 48.54 100 19.04 million =− + −+ =+− = So the expected value is: NPV = 1.25(0.20) + –19.04(0.80) = –14.98 b. Decision Tree If the high growth rate state occurs, then the NPV at time 1 is: 5 12 high 4 10 1.1 1 0.02 . 9 8 NPV 3 10 1.1 1 100 0.1 0.02 1.1 1.1 0.372 million −− + = Note : Since the first 3 cash flows grow at the same rate as the discount rate, their present value is just the sum of the cash flows, so the value at time 1 is just the PV compounded.
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Chapter 22 Real Options 181 If the low growth rate state occurs, then the NPV at time 1 is: () ( ) 5 31 2 low 4 10 1.05 10 1.05 1 0.02 1 1.05 1 0.98 NPV 1 1 100 1.1 0.1 0.05 1.1 0.1 0.02 1.1 1.1 24.87 53.39 100 21.74 million ⎛⎞ ⎜⎟ =− + −+ ⎝⎠ =+− = So investment will only occur in the high growth state. The value today of this is: 0 0.372 NPV 0.2 $67.6 million 1.1 == c. Since the NPV of investing today is negative, you should wait and only invest if the high state occurs. 22-8. Notice that if the firm makes the investment, the current dividend will be 10(1 – 0.1) = $9 million. It will have two possible growth rates in one period. If the return on investment turns out to be 14%, then the growth rate will be g = retention ratio × return on new investment = 0.1 × 0.14 = 1.4%. If the return on new
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BD_SM_c22 - Chapter 22 Real Options 22-1. Decision Tree 176...

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