6-1. Your brother wants to borrow $10,000
from you. He has offered to pay you back $12,000 in a year. If the cost of
capital of this investment opportunity is 10%, what is its NPV? Should you
undertake the investment opportunity? Calculate the IRR and use it to determine
the maximum deviation allowable in the cost of capital estimate to leave the
6-2. You are considering investing in a
start-up company. The founder asked you for $200,000 today and you expect to
get $1,000,000 in nine years. Given the riskiness of the investment
opportunity, your cost of capital is 20%. What is the NPV of the investment
opportunity? Should you undertake the investment opportunity? Calculate the IRR
and use it to determine the maximum deviation allowable in the cost of capital
estimate to leave the decision unchanged.
6-3. You are considering opening a new
plant. The plant will cost $100 million upfront. After that, it is expected to
produce profits of $30 million at the end of every year. The cash flows are
expected to last forever. Calculate the NPV of this investment opportunity if
your cost of capital is 8%. Should you make the investment? Calculate the IRR
and use it to determine the maximum deviation allowable in the cost of capital
estimate to leave the decision unchanged.
6-4. Your firm is considering the launch of
a new product, the XJ5. The upfront development cost is $10 million, and you
expect to earn a cash flow of $3 million per year for the next five years. Plot
the NPV profile for this project for discount rates ranging from 0% to 30%. For
what range of discount rates is the project attractive?
6-5. Bill Clinton reportedly was paid $10
million to write his book My Way. The book took three years to write. In
the time he spent writing, Clinton
could have been paid to make speeches. Given his popularity, assume that he
could earn $8 million per year (paid at the end of the year) speaking instead
of writing. Assume his cost of capital is 10% per year.
a. What is the NPV of agreeing to write the
book (ignoring any royalty payments)?
b. Assume that, once the book is finished, it is expected to
generate royalties of $5 million in the first year (paid at the end of the
year) and these royalties are expected to decrease at a rate of 30% per year in
perpetuity. What is the NPV of the book with the royalty payments?
6-6. FastTrack Bikes, Inc. is thinking of
developing a new composite road bike. Development will take six years and the
cost is $200,000 per year. Once in production, the bike is expected to make
$300,000 per year for 10 years. Assume the cost of capital is 10%.
a. Calculate the NPV of this investment
opportunity, assuming all cash flows occur at the end of each year. Should the
company make the investment?
b. By how much must the cost of capital
estimate deviate to change the decision? (Hint: Use Excel to calculate
c. What is the NPV of the investment if the
cost of capital is 14%?
6-8. You are considering an investment in a clothes
distributor. The company needs $100,000 today and expects to repay you $120,000
in a year from now. What is the IRR of this investment opportunity? Given the
riskiness of the investment opportunity, your cost of capital is 20%. What does
the IRR rule say about whether you should invest?
6-9. You have been offered a very long term
investment opportunity to increase your money one hundredfold. You can invest
$1000 today and expect to receive $100,000 in 40 years. Your cost of capital
for this (very risky) opportunity is 25%. What does the IRR rule say about
whether the investment should be undertaken? What about the NPV rule? Do they
6-10. Does the IRR rule agree with the NPV rule
in Problem 3? Explain.
6-11. How many IRRs are there in part (a) of
Problem 5? Does the IRR rule give the right answer in this case? How many IRRs
are there in part (b) of Problem 5? Does the IRR rule work in this case?
6-12. Professor Wendy Smith has been offered
the following deal: A law firm would like to retain her for an upfront payment
of $50,000. In return, for the next year the firm would have access to 8 hours
of her time every month. Smith’s rate is $550 per hour and her opportunity cost
of capital is 15% (EAR). What does the IRR rule advise regarding this
opportunity? What about the NPV rule?
6-13. Innovation Company is thinking about
marketing a new software product. Upfront costs to market and develop the
product are $5 million. The product is expected to generate profits of $1
million per year for 10 years. The company will have to provide product support
expected to cost $100,000 per year in perpetuity. Assume all profits and
expenses occur at the end of the year.
a. What is the NPV of this investment if the
cost of capital is 6%? Should the firm undertake the project? Repeat the
analysis for discount rates of 2% and 12%.
b. How many IRRs does this investment
c. Can the IRR rule be used to evaluate this
6-14. You own a coal mining company and are
considering opening a new mine. The mine itself will cost $120 million to open.
If this money is spent immediately, the mine will generate $20 million for the
next 10 years. After that, the coal will run out and the site must be cleaned
and maintained at environmental standards. The cleaning and maintenance are
expected to cost $2 million per year in perpetuity. What does the IRR rule say
about whether you should accept this opportunity? If the cost of capital is 8%,
what does the NPV rule say?
If the opportunity cost of capital is between 2.93% and 8.72%, the investment
should be undertaken.
6-15. Your firm spends $500,000 per year in
regular maintenance of its equipment. Due to the economic downturn, the firm
considers forgoing these maintenance expenses for the next three years. If it
does so, it expects it will need to spend $2 million in year 4 replacing failed
a. What is the IRR of the decision to forgo
maintenance of the equipment?
b. Does the IRR rule work for this decision?
c. For what costs of capital is forgoing
maintenance a good decision?
6-16. You are considering investing in a new
gold mine in South Africa.
Gold in South Africa
is buried very deep, so the mine will require an initial investment of $250
million. Once this investment is made, the mine is expected to produce revenues
of $30 million per year for the next 20 years. It will cost $10 million per
year to operate the mine. After 20 years, the gold will be depleted. The mine
must then be stabilized on an ongoing basis, which will cost $5 million per
year in perpetuity. Calculate the IRR of this investment. (Hint: Plot
the NPV as a function of the discount rate.)
6-17. Your firm has been hired to develop new
software for the university’s class registration system. Under the contract,
you will receive $500,000 as an upfront payment. You expect the development
costs to be $450,000 per year for the next three years. Once the new system is
in place, you will receive a final payment of $900,000 from the university four
years from now.
a. What are the IRRs of this opportunity?
b. If your cost of capital is 10%, is the
you are able to renegotiate the terms of the contract so that your final
payment in year 4 will be $1 million.
c. What is the IRR of the opportunity now?
d. Is it attractive at these terms?
6-18. You are considering constructing a new
plant in a remote wilderness area to process the ore from a planned mining
operation. You anticipate that the plant will take a year to build and cost
$100 million upfront. Once built, it will generate cash flows of $15 million at
the end of every year over the life of the plant. The plant will be useless 20
years after its completion once the mine runs out of ore. At that point you
expect to pay $200 million to shut the plant down and restore the area to its
pristine state. Using a cost of capital of 12%,
a. What is the NPV of the project?
b. Is using the IRR rule reliable for this
c. What are the IRR’s of this project?
6-19. You are a real estate agent thinking of
placing a sign advertising your services at a local bus stop. The sign will
cost $5000 and will be posted for one year. You expect that it will generate
additional revenue of $500 per month. What is the payback period?
6-20. You are considering making a movie. The
movie is expected to cost $10 million upfront and take a year to make. After
that, it is expected to make $5 million when it is released in one year and $2
million per year for the following four years. What is the payback period of
this investment? If you require a payback period of two years, will you make
the movie? Does the movie have positive NPV if the cost of capital is 10%?
6-21. You are deciding between two mutually
exclusive investment opportunities. Both require the same initial investment of
$10 million. Investment A will generate $2 million per year (starting at the
end of the first year) in perpetuity. Investment B will generate $1.5 million
at the end of the first year and its revenues will grow at 2% per year for
every year after that.
a. Which investment has the higher IRR?
b. Which investment has the higher NPV when
the cost of capital is 7%?
c. In this case, for what values of the cost
of capital does picking the higher IRR give the correct answer as to which
investment is the best opportunity?
6-22. You have just started your summer
internship, and your boss asks you to review a recent analysis that was done to
compare three alternative proposals to enhance the firm’s manufacturing
facility. You find that the prior analysis ranked the proposals according to
their IRR, and recommended the highest IRR option, Proposal A. You are concerned
and decide to redo the analysis using NPV to determine whether this
recommendation was appropriate. But while you are confident the IRRs were
computed correctly, it seems that some of the underlying data regarding the
cash flows that were estimated for each proposal was not included in the
report. For Proposal B, you cannot find information regarding the total initial
investment that was required in year 0. And for Proposal C, you cannot find the
data regarding additional salvage value that will be recovered in year 3. Here
is the information you have:
the appropriate cost of capital for each alternative is 10%. Using this
information, determine the NPV of each project. Which project should the firm
is ranking the projects by their IRR not valid in this situation?
6-23. Use the incremental IRR rule to correctly
choose between the investments in Problem 21 when the cost of capital is 7%. At
what cost of capital would your decision change?
6-24. You work for an outdoor play structure manufacturing
company and are trying to decide between two projects:
can undertake only one project. If your cost of capital is 8%, use the
incremental IRR rule to make the correct decision.
Since the incremental IRR of 7.522% is less
than the cost of capital of 8%, you should take the Playhouse.
6-25. You are evaluating the following two
the incremental IRR to determine the range of discount rates for which each
project is optimal to undertake. Note that you should also include the range in
which it does not make sense to take either project.
6-26. Consider two investment projects, which
both require an upfront investment of $10 million, and both of which pay a
constant positive amount each year for the next 10 years. Under what conditions
can you rank these projects by comparing their IRRs?
6-27. You are considering a safe investment
opportunity that requires a $1000 investment today, and will pay $500 two years
from now and another $750 five years from now.
a. What is the IRR of this investment?
b. If you are choosing between this investment
and putting your money in a safe bank account that pays an EAR of 5% per year
for any horizon, can you make the decision by simply comparing this EAR with
the IRR of the investment? Explain.
6-28. AOL is considering two proposals to
overhaul its network infrastructure. They have received two bids. The first
bid, from Huawei, will require a $20 million upfront investment and will
generate $20 million in savings for AOL each year for the next three years. The
second bid, from Cisco, requires a $100 million upfront investment and will
generate $60 million in savings each year for the next three years.
a. What is the IRR for AOL associated with
b. If the cost of capital for this investment
is 12%, what is the NPV for AOL of each bid? Suppose Cisco modifies its bid by
offering a lease contract instead. Under the terms of the lease, AOL will pay
$20 million upfront, and $35 million per year for the next three years. AOL’s
savings will be the same as with Cisco’s original bid.
c. Including its savings, what are AOL’s net
cash flows under the lease contract? What is the IRR of the Cisco bid now?
d. Is this new bid a better deal for AOL than
Cisco’s original bid? Explain.
6-29. Natasha’s Flowers, a local florist,
purchases fresh flowers each day at the local flower market. The buyer has a
budget of $1000 per day to spend. Different flowers have different profit
margins, and also a maximum amount the shop can sell. Based on past experience,
the shop has estimated the following NPV of purchasing each type:
combination of flowers should the shop purchase each day?
6-30. You own a car dealership and are trying
to decide how to configure the showroom floor. The floor has 2000 square feet
of usable space.You have hired an analyst and asked her to estimate the NPV of
putting a particular model on the floor and how much space each model requires:
addition, the showroom also requires office space. The analyst has estimated
that office space generates an NPV of $14 per square foot. What models should
be displayed on the floor and how many square feet should be devoted to office
6-31. Kaimalino Properties (KP) is evaluating
six real estate investments. Management plans to buy the properties today and
sell them five years from today. The following table summarizes the initial
cost and the expected sale price for each property, as well as the appropriate
discount rate based on the risk of each venture.
has a total capital budget of $18,000,000 to invest in properties.
a. What is the IRR of each investment?
b. What is the NPV of each investment?
c. Given its budget of $18,000,000, which
properties should KP choose?
d. Explain why the profitably index method
could not be used if KP’s budget were $12,000,000 instead. Which properties
should KP choose in this case?
6-32. Orchid Biotech Company is evaluating
several development projects for experimental drugs. Although the cash flows
are difficult to forecast, the company has come up with the following estimates
of the initial capital requirements and NPVs for the projects. Given a wide
variety of staffing needs, the company has also estimated the number of
research scientists required for each development project (all cost values are
given in millions of dollars).
a. Suppose that Orchid has a total capital budget of $60 million.
How should it prioritize these projects?
b. Suppose in addition that Orchid currently
has only 12 research scientists and does not anticipate being able to hire any
more in the near future. How should Orchid prioritize these projects?
c. If instead, Orchid had 15 research
scientists available, explain why the profitability index ranking cannot be
used to prioritize projects. Which projects should it choose now?
Lecture Five - Payout Policy
17-1. What options does a firm
have to spend its free cash flow (after it has satisfied all interest
17-2. ABC Corporation announced that it will
pay a dividend to all shareholders of record as of Monday, April 3, 2006. It
takes three business days of a purchase for the new owners of a share of stock
to be registered.
a. When is the last day an investor can
purchase ABC stock and still get the dividend payment?
b. When is the ex-dividend day?
17-3. Describe the different mechanisms
available to a firm to use to repurchase shares
17-4. RFC Corp. has announced a $1 dividend. If
RFC’s price last price cum-dividend is $50, what should its first ex-dividend
price be (assuming perfect capital markets)?
17-5. EJH Company has a market capitalization
of $1 billion and 20 million shares outstanding. It plans to distribute $100
million through an open market repurchase. Assuming perfect capital markets:
a. What will the price per share of EJH be
right before the repurchase?
b. How many shares will be repurchased?
c. What will the price per share of EJH be
right after the repurchase?
17-7. Natsam Corporation has $250 million of
excess cash. The firm has no debt and 500 million shares outstanding with a
current market price of $15 per share. Natsam’s board has decided to pay out
this cash as a one-time dividend.
a. What is the ex-dividend price of a share in
a perfect capital market?
b. If the board instead decided to use the
cash to do a one-time share repurchase, in a perfect capital market what is the
price of the shares once the repurchase is complete?
c. In a perfect capital market, which policy,
in part (a) or (b), makes investors in the firm better off?
17-8. Suppose the board of Natsam Corporation
decided to do the share repurchase in Problem 7(b), but you, as an investor,
would have preferred to receive a dividend payment. How can you leave yourself
in the same position as if the board had elected to make the dividend payment