FIGURE 17-5 Estimating the Input for Variance in the Option Analysis
of the Investment Timing Option (Millions of Dollars)
PART1. FIND THE VALUE AND RISK OF FUTURE CASH FLOWS AT THE TIME THE OPTION EXPIRES
Future Cash Flows PV in 2003
for This Probability
2002 2003 2004 2005 2006 Scenarioc Probability PV 2003
$33 $33 $33 $76.61 0.25 $19.15
High
Wait Average
0.50
$25 $25 $25 $58.04 0.50 $29.02
Low
$5 $5 $5 $11.61 0.25 $2.90
1.00
Expected value of PV 2003
Standard deviation of PV 2003 a
Coefficient of variation of PV 2003 b
PART2. DIRECT METHOD: USE THE SCENARIOS TO DIRECTLY ESTIMATE THE VARIANCE O FTHE PROJECT’S RETURN
Probability
Price 2002 d PV 2003 e Return 2003 f
High
$44.80 Average
0.50
Low
1.00
Expected return
Standard deviation of returna
Variance of returng
PART3. INDIRECT METHOD: USE THE SCENARIOS TO INDIRECTLY ESTIMATE THE VARIANCE O FTHE PROJECT’S RETURN
Expected “price” at the time the option expiresh $51.08
Standard deviation of expected “price” at the time the option expiresi $24.02
Coefficient of variation (CV) 0.47
Time (in years) until the option expires (t) 1
Variance of the project’s expected return ln(CV^2 1)/t 20.0%
Notes:
aThe standard deviation is calculated as explained in Chapter 3.
bThe coefficient of variation is the standard deviation divided by the expected value.
cThe WACC is 14 percent. The 2004–2006 cash flows are discounted back to 2003.
dThe 2002 price is the expected PV from Figure 17-4.
eThe 2003 PVs are from Part 1.
fThe returns for each scenario are calculated as (PV 2003 Price 2002 )/Price 2002.
gThe variance of return is the standard deviation squared.
hThe expected “price” at the time the option expires is taken from Part 1.
iThe standard deviation of expected “price” at the time the option expires is taken from Part 1.
28.7%
53.6%
14.0%
$11.61 74.1% 0.25 18.5%
$58.04 29.5% 0.50 14.8%
$76.61 71.0% 0.25 17.8%
ProbabilityReturn 2003
0.47
$24.02
$51.08
0.25
0.25
0.25
0.25
640 Option Pricing with Applications to Real Options
