Chapter 4: Real Options and Project Analysis
1. Imagine that the price of copper rises to the point that the copper value of a penny is worth
more than $.01. As a result, pennies disappear from circulation. Your firm uses copper in its
production process, and you can melt pennies down and retrieve their copper content at zero
cost. At present, you have a six-month supply of copper reserves and you have also managed to
collect 1 million pennies. Should you melt the pennies down and add the copper to your
stockpile? Why or why not?
Answer: The ownership of a penny is an option. If the penny is melted, the owner gets the
valuable copper to sell at current market prices. However, if the owner keeps the penny, he
retains the option to use it as legal tender. If the price of copper makes the penny’s copper
content worth less than $.01, it is more valuable as legal tender. If the penny was melted and
prices dropped, the owner may not mint a new penny. The penny is generally more valuable as
an option. Hence, it should not be melted. (It is also illegal to deface or alter legal tender.)
2. Will a gold mine ever be shut permanently? Why or why not?
Answer: A gold mine is an option to mine the gold if the market prices make it profitable to do
so. Closing a mine permanently kills the value of the option to re-open the mine if market
conditions change favorably. The only time that a mine would be closed forever is when the cost
of maintaining the mine (including opportunity costs) is higher than the marginal option value. If
the value of the option truly drops to zero, it will be optimal to close the mine.
Some economists have stated that too many companies aren’t calculating the cost of not
investing in new technology, world-class manufacturing facilities, or market position overseas. What
are some of these costs? How do these costs relate to the notion of growth options discussed in
the chapter?
Answer: Executives in this situation need to consider the option values associated with new
technological investment. New technologies, while often costly, difficult to administer and hard to
defend in the short term, make it easier for a company to adapt to a changing technological
environment and a more competitive marketplace. With technology in place, the firm will find it
easier to enter and capture niche markets as they emerge. The relevant base case may not be the
status quo, but rather, an anticipated decline in sales following competitors’ adaptations to the new
This ease of adaptation has a value to the firm; it may make all future investments more profitable.
Firms may underestimate NPV when they fail to take the option-like characteristics of the new
technology into account, and mistakenly assume that the status quo will be maintained in the
absence of adaptation.
In December 1989, General Electric spent $150 million to buy a controlling interest in
Tungsram, the Hungarian state-owned light bulb maker. Even in its best year, Tungsram earned less
than a 4% return on equity (based on the price GE paid). What might account for GE’s decision to
spend so much money to acquire such a dilapidated, inefficient manufacturer?
Answer: Eastern Europe has the potential to be both a large market for Western goods and a
low-cost manufacturing platform for export to Western Europe. But there are major uncertainties as
to whether Eastern Europe will ever realize its market potential. As to manufacturing there,
questions exist as to whether a workforce with 45 years experience in “they pretend to pay us and
we pretend to work” can produce at the level and quality necessary to be competitive with their
Chapter 4: Real Options and Project Analysis
Western counterparts. By investing in Hungary, GE is buying an option to participate in the growth
of the Eastern European market. It also is learning what it takes to install modern Western
management methods in a former communist country and to use Hungary as a low-cost backdoor to
Western Europe. The latter is especially critical to GE as part of its strategy to expand its weak
global presence.
GE’s presence is particularly dim in the European lighting market, where it is just sixth in sales,
even though historically it has dominated the U.S. market. Then came a highly successful raid on
GE’s U.S. fortress by Philips, which is the world’s largest light bulb producer. GE decided to fight
back by storming Philip’s European base. But GE was unable to acquire a controlling interest in any
Western European firm and building a new plant would have cost at least $300 million and several
years. Buying Tungsram seemed a more promising alternative, since the Hungarian firm already
exported 70% of its output to the West. Thus, it offered a tempting mix of Western European
market share and low Eastern European wages. In effect, by investing in Tungsram, GE is buying
options on: (a) the Western European market; (b) introducing new technologies and higher-priced
products to Tungsram; and (c) a low-cost export platform. In response to GE’s purchase, Philips
recently took over Poland’s leading lamp producer and another Western European competitor,
Siemens’ Osram unit, has acquired an East German producer.
A biotech firm must decide whether to purchase the patent to a new food additive, a low-cal
starch substitute. It is estimated that the funds required to bring the additive to the market can be
as high as $50 million or as low as $25 million. The payoff is uncertain as well: The present value of
profits could be as high as $500 million or as low as $30 million. The risk-free rate is 10 percent,
and the standard deviation of rate of return on biotech products is 35 percent. The patent’s life is
estimated at one year.
In a worst-case scenario, how much is the patent worth?
Answer: We need to make a few assumptions to solve this problem. We assume that in one year,
the present value of profits will take values of $500M and $30M with equal probability. We further
assume that the risk-free discount rate is the appropriate capitalization rate for the firm.
In a worst-case scenario, the costs will be $50M. The firm will only adopt the project if NPV > 0,
or PV(Benefits) = $500M. The expected net present value is 0.5(500 Ä 50) + 0.5(0) = $225M. The
present value is $225M/(1.10) = $204.55M, which represents the maximum value of the patent.
In a best-case scenario, how much is the patent worth?
Answer: In a best-case scenario, the costs will be $25M, and the project will be adopted no matter
what. The expected NPV is 0.5(500 Ä 25) + 0.5(30 Ä 25) = $240M. The present value is $218.18.
The managers of a firm are asked to consider two possible new product lines for the firm.
Project 1 is quite risky and may result in a market value for the firm of $50 million in two years, or
nothing. Project 2 is much more certain in outcome and may result in a firm market value as high as
$25 million or as low as $15 million.
The face value of the company’s debt, payable in two years, is $20 million.
What are the possible payoffs to the bondholders under projects 1 and 2?
Chapter 4: Real Options and Project Analysis
Answer: (Payoffs in 2 years, in millions of dollars)
Total Payoff
Debt Distribution
Total Payoff
Debt Distribution
What are the possible payoffs to the shareholders under projects 1 and 2?
Answer: (Payoffs in 2 years, in millions of dollars)
Total Payoff
Equity Distribution
Total Payoff
Equity Distribution
Which will the shareholders favor? The bondholders?
Answer: Shareholders will favor project 1, which provides an equal or higher payoff in each state.
Bondholders favor project 2 for the same reason.
Eastern Shallow, Ltd., is a gold mining company operating a single mine. The present price of
gold is $300 an ounce and it costs the company $250 an ounce to produce the gold. Last year,
50,000 ounces were produced and engineers estimate that at this rate of production the mine will
be exhausted in seven years. The required rate of return on gold mines is 10 percent.
What is the value of the mine?
Answer: The present value of the mine is the present value of 7 years of payments of $50/oz ?
50,000 oz = $2.5M, discounted at r = 10%. This present value is $12.171M.
Suppose inflation is expected to increase the cost of producing gold by 10 percent a year but
the price of gold does not change because of large sales of stock-piled gold by foreign governments.
Furthermore, imagine that the inflation raises the required rate of return to 21 percent. Now, what is
the value of the mine?
Answer: If the costs rise by 10% per year while the price remains the same, we will not operate the
mine after one year. In the first year, profits are (300 Ä 275) ? 50,000 = $1.25M, discounted one
year at r = 21%. In the second year, profits are zero; we will not mine gold at $302.50 per ounce to
sell at $300 per ounce. The value of the mine is $1.25M/1.21 = $1.033M.
Suppose the company may shut, reopen, or abandon the mine in response to fluctuations in
the price of gold. Can the NPV method be used to value the mine under these conditions?
Chapter 4: Real Options and Project Analysis
Answer: The NPV method can be used to determine the value of the mine if the company can
choose an optimal extraction policy. The analysis requires a potentially complex decision tree
formulation, and the determination of the optimal strategy as a function of the path of the price for
gold. The correct solution of the problem requires option-pricing methodologies.
G.D. Sorrell is developing an anticancer drug. The project is in its preliminary stage. G.D.S.
must decide whether to initiate a large-scale drug test costing $1.5 million a year for two years. If
the test results are positive, a $17.5 million plant to produce the drug for commercial trials will be
built at the end of the testing period. If commercial sales of the drug meet the company’s forecast
for the next two years, a second, larger plant costing $50 million will be built to produce the drug in
quantity. The cash flows resulting from this larger plant are expected to be $76 million for eight
years after it is built. The following are the relevant cash flows associated with the three possible
Scenario 1
Scenario 2
Scenario 3
Year 0
($1,5000)* ($1,500)
With a cost of capital of 10 percent, value the research project using DCF analysis. Is the
project acceptable? (Assume the two plants are built.)
Chapter 4: Real Options and Project Analysis
Chapter 4: Real Options and Project Analysis
An oil company has paid $100,000 for the right to pump oil on a plot of land during the next
three years. A well has already been sunk and all other necessary facilities are in place. The land
has known reserves of 60,000 barrels. The company wishes to know the market value of this
operation. The interest rate is 8 percent and the marginal cost of pumping is $8 per barrel. Both of
these costs are expected to remain unchanged over the three-year period. The current price of oil
is $10 per barrel. Company economists have estimated the following:
Oil will increase in price by 10 percent with a probability of 40 percent, or decrease in price by
12 percent with a probability of 60 percent during each of the next three years.
(ii) The cost of storing oil in above-ground tanks is $.50 per year.
(iii) The company can pump a maximum of 20,000 barrels per year at the site.
(iv) The site may be shut down for a year and then reopened at a cost of $2,000.
Chapter 7: Corporate Strategy and the Capital Budgeting Decision
Determine the market value of the operation ignoring taxes. Assume that all cash flows occur at
the end of each year. (Hint: Chart all possible sequences of oil prices, and calculate the optimal
production decisions and payoffs associated with each sequence.)
Answer: The possible oil price paths are diagramed below.
┌────── 13.31
┌────── 12.10 ───────┤
└────── 10.65
┌─ 11.00 ────┤
┌────── 10.65
└────── 9.68 ───────┤
10.00 ─┤
└─────── 8.52
┌────── 10.65
┌────── 9.68 ───────┤
└─ 8.80 ────┤
└─────── 8.52
┌─────── 8.52
└────── 7.74 ───────┤
└─────── 6.81
It is never optimal to store oil above ground; the expected price appreciation is (0.4)(0.10) +
(0.6)(─0.12) = ─3%. Furthermore, the cost is $0.50 per barrel per year. When oil prices
are high (guaranteed to be over $8.00), it is always optimal to drill. However, at the point
where prices reach $7.74, it is optimal to close. If we drill, the expected profits next year
are 0.4(8.52 ─ 8.00) + 0.6(6.81 ─ 8.00) = ─0.45 per barrel. Note that there would be no
point in keeping the oil; the extraction costs would be sunk. By closing, we incur a $2000
(0.10 per barrel) cost next year, and lose $0.26 per barrel in selling last year’s production.
The results are summarized as follows:
Cash Flow/Barrel
0.216 0.80,─.26,─.10
The value of the project is the probability-weighted sum of the present values of the paths.
Project value = 20,000 ´ 3.6950 = $73,900.32. We ignored the value of the oil in the ground in
case of a big price drop. If that value is less than $26,099.68, it seems the oil company paid too
much for the property.

Shapiro CHAPTER 4

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