CP

Before we conclude the discussion of decision trees, note that we used the same

cost of capital, 14 percent, to discount cash flows in the “proceed immediately”

scenario analysis in Part 1 and under the “delay one year” scenario in Part 2. However,

for three reasons this is not appropriate. First, since there is no possibility of losing

money if Murphy delays, the investment under that plan is clearly less risky than if

Murphy charges ahead today. Second, the 14 percent cost of capital might be appro-

priate for risky cash flows, yet the investment in the project in 2003 in Part 2 is known

640 CHAPTER 17 Option Pricing with Applications to Real Options

PART1. SCENARIO ANALYSIS: PROCEED WITH PROJECT TODAY

Future Cash Flows

NPV of This Probability

2002 2003 2004 2005

$33 $33 $33

High

$50 Average

0.50

$25 $25 $25

Low

$5 $5 $5

1.00

Expected value of NPVs 

Standard deviationa

Coefficient of variationb

PART2. DECISION TREE ANALYSIS: IMPLEMENT NEXT YEAR ONLY I FOPTIMAL

Future Cash Flows

NPV of this Probability

2002 2003 2004 2005 2006 Scenariod Probability NPV

$50 $33 $33 $33 $23.35 0.25 $5.84

High

Wait Average

0.50

$50 $25 $25 $25 $7.05 0.50 $3.53

Low

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

1.00

Expected value of NPVs 

Standard deviationa

Coefficient of variationb

Notes:a

bThe standard deviation is calculated as explained in Chapter 3.

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

dThe WACC is 14 percent.

The NPV in Part 2 is as of 2002. Therefore, each of the project cash flows is discounted back one more year than in Part 1.

0.92

$8.57

$9.36

22.32

$24.02

$1.08

$38.39 0.25 $9.60

$8.04 0.50 $4.02

$26.61 0.25 $6.65

Scenarioc Probability NPV

FIGURE 17-2 DCF and Decision Tree Analysis for the Investment Timing Option

(Millions of Dollars)

0.25

0.25

0.25

0.25

Option Pricing with Applications to Real Options 635