# Financial Planning Problems

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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 decision unchanged.
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
the IRR.)

c. What is the NPV of the investment if the
cost of capital is 14%?

i.

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 agree?

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. Smithâ€™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
opportunity have?

c. Can the IRR rule be used to evaluate this
investment? Explain.

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?

.

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 equipment.

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 universityâ€™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
opportunity attractive?

Suppose 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
project? Explain.

c. What are the IRRâ€™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%?

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# Financial Planning Problems

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Eleanor needs \$40,000 a year to live on in retirement net
of the income she will receive. She will be retiring in 22 years and is funding
for a 25-year retirement. The inflation rate is expected to be 3.5 percent a
year and the after-tax return on her investments 6 percent.

a) How much will she short fall amount to at the beginning
of the retirement period?

b) What lump sum will she need at the beginning of the
retirement period?

c) What is the required yearly savings?

Q2

.0pt;margin-left:0in; line-height:200%”=””>Frank, age 28, wants to calculate his resources in real
(inflation-adjusted) terms. Calculate the amount of resources made available by
age 65 retirement if \$18,000 a year is saved. Assume that outflows from ages 65
to 90 are at the rate of \$27,000 a year. The projected inflation rate is 4 percent,
and the anticipated investment return is 6 percent.

a) How much in new savings will Frank have available at age
65 before subsequent withdrawals?

b) How much will he have left at age 90?

c) What is the present value of that sum at age 65?

d) How much will he have to save per year to exactly meet
his need?

=”margin-top:0in;margin-right:0in;margin-bottom:6.0pt;margin-left:0in;>

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