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Mini Case: 26 - 19
variation, we need the expected stock price and the standard deviation of the stock
price (both of these are measured at the time the option expires). For the real option,
we need the expected value of the project’s cash flows at the date the real option
expires, and the standard deviation of the project’s value at the date the real option
expires.
High $111.91
Average $74.61
Low $37.30
Expected Value =.3($111.91)+.4($74.61)+.3($37.3)
CV = $74.61 / $28.90 = 0.39.
Here is a formula for the variance of a stock’s return, if you know the coefficient of
variation of the expected stock price at some point in the future. The CV should be
for the entire project, including all scenarios:
Now, we proceed to use the OPM:
V = $67.83[N(d1)] - $70e-(0.06)(1)[N(d2)].
d1 =
5.0
)1(
5.0
)142(.
)15)](0.142/206.0[()$67.83/$70ln(
= 0.2641.
d2 = d1 - (0.142)0.5(1)0.5 = 0.2641 - 0.3768
= -0.1127.
N(d1) = N(0.2641) = 0.6041.
g. Now suppose the cost of the project is $75 million and the project cannot be
delayed. But if Tropical Sweets implements the project, then Tropical Sweets
will have a growth option. It will have the opportunity to replicate the original
project at the end of its life. What is the total expected NPV of the two projects
if both are implemented?
NPV = NPV Of Original Project + NPV Of Replication Project
= -$0.39 + -$0.39/(1+0.10)3
= -$0.39 + -$0.30 = -$0.69.
Still looks like a loser, but you will only implement project 2 if demand is high. We
might have chosen to discount the cost of the replication project at the risk-free rate,
h. Tropical Sweets will replicate the original project only if demand is high. Using
decision tree analysis, estimate the value of the project with the growth option.
Answer: The future cash flows of the optimal decisions are shown below. The cash flow in
Low -$75 $15 $15 $15 $0 $0 $0
To find the NPV, we discount the risky cash flows at the 10 percent cost of capital,
and the non-risky cost to replicate (i.e., the $75 million) at the risk-free rate.
NPV high = -$75 + $45/1.10 + $45/1.102 + $45/1.103 + $45/1.104
Thus, the option to replicate adds enough value that the project now has a positive
NPV.
Mini Case: 26 - 22
i. Use a financial option model to estimate the value of the growth option.
Answer: X = Strike Price = Cost Of Implement Project = $75 million.
RRF = Risk-Free Rate = 6%.
T = Time To Maturity = 3 years.
P = Current Price Of Stock = Current Value Of The Project’s Future Cash Flows.
σ2 = Variance Of Stock Return = Variance Of Project’s Rate Of Return.
0 1 2 3 4 5 6
High $45 $45 $45
Average $30 $30 $30
Low $15 $15 $15
P = 0.3[$111.91/1.13] + 0.4[$74.61/1.13] + 0.3[$37.30/1.13] = $56.05.
Mini Case: 26 - 23
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
Direct approach for estimating σ2:
From our previous analysis, we know the current value of the project and the value
for each scenario at the time the option expires (year 3). Here is the time line:
Current Value Value At Expiration
Year 0 Year 3
High $56.02 $111.91
Average $56.02 $74.61
Expected Return = 0.3(0.259) + 0.4(0.10) + 0.3(-0.127)
= 8.0%.
2 = 0.3(0.259-0.08)2 + 0.4(0.10-0.08)2 + 0.3(-0.127-0.08)2
Mini Case: 26 - 24
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
The indirect approach:
First, find the coefficient of variation for the value of the project at the time the option
expires (year 3).
We previously calculated the value of the project at the time the option expires, and
we can use this to calculate the expected value and the standard deviation.
Value At Expiration
Year 3
High $111.91
+ .3($37.30-$74.61)2]1/2
= $28.90.
Coefficient of Variation = CV = Expected Value / value
CV = $74.61 / $28.90 = 0.39.
Now, we proceed to use the OPM:
V = $56.06[N(d1)] - $75e-(0.06)(3)[N(d2)].
