CP

the current price of the stock. Note that a stock’s current price is the present value of its

expected future cash flows. For Murphy’s real option, the underlying asset is the project

itself, and its current “price” is the present value of its expected future cash flows.

Therefore, as a proxy for the stock price we can use the present value of the project’s fu-

ture cash flows. And fifth, the variance of the project’s expected return can be used to

represent the variance of the stock’s return in the Black-Scholes model.

Figure 17-4 shows how one can estimate the present value of the project’s cash

inflows. We need to find the current value of the underlying asset, that is, the project.

642 CHAPTER 17 Option Pricing with Applications to Real Options

FIGURE 17-3 Decision Tree and Sensitivity Analysis for the Investment Timing Option

(Millions of Dollars)

PART1. DECISION TREE ANALYSIS: IMPLEMENT IN ONE YEAR ONLY I FOPTIMAL(DISCOUNT COST AT THE RISK-FREE RATE

AND OPERATING CASH FLOWS AT THE WACC)

Future Cash Flows

NPV of This Probability

2002 2003 2004 2005 2006 Scenarioc Probability NPV

$50 $33 $33 $33 $20.04 0.25 $5.01

High

Wait Average

0.50

$50 $25 $25 $25 $3.74 0.50 $1.87

Low

$0 $0 $0 $0 $0.00 0.25 $0.00

1.00

Expected value of NPVs 

Standard deviationa

Coefficient of variationb

PART2. SENSITIVITY ANALYSIS O FNPV TO CHANGES IN THE COST O FCAPITAL USED TO DISCOUNT COST AND CASH FLOWS

Cost of Capital Used to Discount the 2003 Cost

3.0% 4.0% 5.0% 6.0% 7.0% 8.0% 9.0%

8.0% $13.11 $13.46 $13.80 $14.14 $14.47 $14.79 $15.11

9.0% 11.78 12.13 12.47 12.81 13.14 13.47 13.78

10.0% 10.50 10.85 11.20 11.53 11.86 12.19 12.51

11.0% 9.27 9.62 9.97 10.30 10.64 10.96 11.28

12.0% 8.09 8.44 8.78 9.12 9.45 9.78 10.09

13.0% 6.95 7.30 7.64 7.98 8.31 8.64 8.95

14.0% 5.85 6.20 6.54 6.88 7.21 7.54 7.85

15.0% 4.79 5.14 5.48 5.82 6.15 6.48 6.79

16.0% 3.77 4.12 4.46 4.80 5.13 5.45 5.77

17.0% 2.78 3.13 3.47 3.81 4.14 4.46 4.78

18.0% 1.83 2.18 2.52 2.86 3.19 3.51 3.83

Notes:

aThe standard deviation is calculated as in Chapter 3.

bThe coefficient of variation is the standard deviation divided by the expected value.

cThe operating cash flows in years 2004–2006 are discounted at the WACC of 14 percent. The cost in 2003 is discounted at the risk-free rate

of 6 percent.

1.13

$7.75

$6.88

0.25

0.25

Cost of Capital Used to Discount

the 2004–2006 Operating

Cash Flows

Option Pricing with Applications to Real Options 637