CP

Note, though, that judgmental estimates were made at many points in the

analysis, and it is useful to see how sensitive the final outcome is to certain of the

key inputs. Thus, in Part 2 of Figure 17-6 we show the sensitivity of the option’s

value to different estimates of the variance. It is comforting to see that for all rea-

sonable estimates of variance, the option to delay remains more valuable than im-

mediate implementation.

Approach 5. Financial Engineering

Sometimes an analyst might not be satisfied with the results of a decision tree analysis

and cannot find a standard financial option that corresponds to the real option. In such

a situation the only alternative is to develop a unique model for the specific real option

being analyzed, which is called financial engineering. When financial engineering is

applied on Wall Street, where it was developed, the result is a newly designed financial

646 CHAPTER 17 Option Pricing with Applications to Real Options

FIGURE 17-6 Estimating the Value of the Investment Timing Option

Using a Standard Financial Option (Millions of Dollars)

PART1. FIND THE VALUE OF A CALL OPTION USING THE BLACK-SCHOLES MODEL

Real Option

rRF Risk-free interest rate  6%

t  Time in years until the option expires  1

X  Cost to implement the project  $50.00

P  Current value of the project  $44.80a

^2  Variance of the project’s rate of return  20.0%b

d 1  {ln(P/X) [rRF(^2 /2)]t}/(t1/2)  0.112

d 2  d 1 (t1/2) 0.33

N(d 1 ) 0.54

N(d 2 ) 0.37

V  P[N(d 1 )] XerRFt[N(d 2 )] 

PART2. SENSITIVITY ANALYSIS O FOPTION VALUE TO CHANGES IN VARIANCE

Variance Option Value

12.0% $5.24

14.0 5.74

16.0 6.20

18.0 6.63

20.0

22.0 7.42

24.0 7.79

26.0 8.15

28.0 8.49

30.0 8.81

32.0 9.13

Notes:

aThe current value of the project is taken from Figure 17-4.

bThe variance of the project’s rate of return is taken from Part 3 of Figure 17-5.

7.04

$7.04

Option Pricing with Applications to Real Options 641