Finance Chapter 26 Homework The Annual Rate Return Is High Return

Mini Case: 26 – 15

MINI CASE

Assume that you have just been hired as a financial analyst by Tropical Sweets Inc., a mid-

sized California company that specializes in creating exotic candies from tropical fruits such

as mangoes, papayas, and dates. The firm’s CEO, George Yamaguchi, recently returned

from an industry corporate executive conference in San Francisco, and one of the sessions

he attended was on real options. Since no one at Tropical Sweets is familiar with the basics

of real options, Yamaguchi has asked you to prepare a brief report that the firm’s executives

could use to gain at least a cursory understanding of the topics.

To begin, you gathered some outside materials the subject and used these materials to

draft a list of pertinent questions that need to be answered. In fact, one possible approach

to the paper is to use a question-and-answer format. Now that the questions have been

drafted, you have to develop the answers.

a. What are some types of real options?

Answer: 1. Investment timing options

2. Growth options

a. Expansion of existing product line

b. What are five possible procedures for analyzing a real option?

Answer: 1. DCF analysis of expected cash flows, ignoring option.

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c. Tropical Sweets is considering a project that will cost $70 million and will generate

expected cash flows of $30 per year for three years. The cost of capital for this

type of project is 10 percent and the risk-free rate is 6 percent. After discussions

with the marketing department, you learn that there is a 30 percent chance of high

demand, with future cash flows of $45 million per year. There is a 40 percent

chance of average demand, with cash flows of $30 million per year. If demand is

low (a 30 percent chance), cash flows will be only $15 million per year. What is

the expected NPV?

Answer: Initial Cost = $70 Million

Expected Cash Flows = $30 Million Per Year For Three Years

Cost Of Capital = 10%

PV Of Expected CFs = $74.61 Million

Expected NPV = $74.61 – $70

= $4.61 Million

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d. Now suppose this project has an investment timing option, since it can be delayed

for a year. The cost will still be $70 million at the end of the year, and the cash

flows for the scenarios will still last three years. However, Tropical Sweets will

know the level of demand, and will implement the project only if it adds value to

the company. Perform a qualitative assessment of the investment timing option’s

value.

Answer: If we immediately proceed with the project, its expected NPV is $4.61 million.

However, the project is very risky. If demand is high, NPV will be $41.91 million.

If demand is average, NPV will be $4.61 million. If demand is low, NPV will be –

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e. Use decision tree analysis to calculate the NPV of the project with the investment

timing option.

Answer: The project will be implemented only if demand is average or high.

Here is the time line:

0 1 2 3 4

f. Use a financial option pricing model to estimate the value of the investment timing

option.

Answer: The option to wait resembles a financial call option— we get to “buy” the project for

$70 million in one year if value of project in one year is greater than $70 million.

This is like a call option with a strike price of $70 million and an expiration date of

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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 1.

0 1 2 3 4

High $45 $45 $45

Average $30 $30 $30

Low $15 $15 $15

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Following is an explanation of each approach.

Subjective estimate:

The typical stock has σ2 of about 12%. Most projects will be somewhat riskier than

Direct approach:

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 1). Here is the time line:

Current Value Value At Expiration

Year 0 Year 1

Expected Return = 0.3(0.65) + 0.4(0.10) + 0.3(-0.45)

= 10%.

2 = 0.3(0.65-0.10)2 + 0.4(0.10-0.10)2 + 0.3(-0.45-0.10)2

= 0.182

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The indirect approach:

Given a current stock price and an anticipated range of possible stock prices at some

point in the future, we can use our knowledge of the distribution of stock returns

(which is lognormal) to relate the variance of the stock’s rate of return to the range of

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 1

High $111.91

Average $74.61

Low $37.30

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Now, we proceed to use the OPM:

V = $67.83[N(d1)] – $70e-(0.06)(1)[N(d2)].

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

= $74.61 – $75 = -$0.39 million.

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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.

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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.

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

2 = 0.3(0.259-0.08)2 + 0.4(0.10-0.08)2 + 0.3(-0.127-0.08)2

= 0.023

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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).

Expected Value =.3($111.91)+.4($74.61)+.3($37.3)

= $74.61.

value = [.3($111.91-$74.61)2 + .4($74.61-$74.61)2

+ .3($37.30-$74.61)2]1/2

= $28.90.

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Now, we proceed to use the OPM:

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

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):

σ2 = 0.047, option value = $5.92