978-1305632295 Chapter 26 Solution Manual Part 3

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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?

Answer: Suppose the cost of the project is $75 million instead of $70 million, and there is no

option to wait.

NPV = PV of future cash flows – cost

The project now looks like a loser. Using NPV analysis:

NPV = NPV Of Original Project + NPV Of Replication Project

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

year 3 for the high demand scenario is the cash flow from the original project and the

cost of the replication project.

0 1 2 3 4 5 6

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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.

Thus, the option to replicate adds enough value that the project now has a positive

NPV.

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%.

We explain how to calculate P and σ2 below.

Step 1: Find the value of all cash flows beyond the exercise date discounted back to

the exercise date. Here is the time line. The exercise date is year 1, so we discount

all future cash flows back to year 3.

012345 6

High: PV3 = $45/1.10 + $45/1.102 + $45/1.103 = $111.91

The current expected present value, P, is:

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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

The annual rate of return is:

This is lower than the variance found for the previous option because the dispersion

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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

Coefficient of Variation = CV = Expected Value / value

To find the variance of the project’s rate or return, we use the formula below:

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Now, we proceed to use the OPM:

V = $56.06[N(d1)] – $75e-(0.06)(3)[N(d2)].

d1 =

5.0

)3(

5.0

)047.0(

)3)](0.047/206.0[()$56.06/$75ln( 

= -0.1085.

d2 = d1 – (0.047)0.5(3)0.5 = -.1085 – 0.3755

= -0.4840.

N(d1) = N(-0.1080) = 0.4568.

N(d2) = N(-0.4835) = 0.3142.

Therefore,

Total Value = NPV Of Project 1 + Value Of Growth Option

j. What happens to the value of the growth option if the variance of the project’s

return is 0.142? What if it is 0.50? How might this explain the high valuations

of many dot.com companies?

Answer: If risk, defined by σ2, goes up, then value of growth option goes up (see the file Ch26

mini case.xls for calculations):

If the future profitability of dot.com companies is very volatile (i.e., there is the

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