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The fact that the option to abandon has value provides a rationale for firms to
build the flexibility to scale back or terminate projects if they do not measure up to
expectations. Firms can do this in a number of ways. The first, and most direct way, is to
build in the option contractually with those parties that are involved in the project. Thus,
contracts with suppliers may be written on an annual basis, rather than long term, and
employees may be hired on a temporary basis, rather than permanently. The physical
plant used for a project may be leased on a short term basis, rather than bought, and the
financial investment may be made in stages rather than as an initial lump sum. While
there is a cost to building in this flexibility, the gains may be much larger, especially in
volatile businesses.

Conclusions
Projects often create side costs and benefits that are not captured in the initial
estimates of cash flows used to estimate returns. In this chapter, we examined some of
these indirect costs and benefits:
Investing in one project may prevent us from taking alternative investments if these

are mutually exclusive. If projects have equal lives and there are no capital rationing
constraints, we can pick the investment with the higher net present value. If this is not
the case, we have to find ways of controlling for differences in project lives (by
computing an equivalent annuity) and for differences in scale (by computing
profitability indices).
Opportunity costs measure the costs of resources that the company already owns that

might be used for a new project. While the business might not spend new money
acquiring these resources, there are consequences in terms of the cash flows which
have to be reflected in the returns.
Projects may also provide synergistic benefits for other projects that a firm might

have. These benefits, which also take the form of cash flows, should be reflected in
the returns.
Projects may also create options that are valuable - options to expand into new

markets and to produce new products.
In summary, the project returns have to reflect all of the side costs and benefits.
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Problems

1. A small manufacturing firm, which has limited access to capital, has a capital rationing
constraint of $ 150 million and is faced with the following investment projects:
Project Initial Investment NPV
A $25 $10
B $30 $25
C $40 $20
D $10 $10
E $15 $10
F $60 $20
G $20 $10
H $25 $20
I $35 $10
J $15 $5


a. Which of these projects would you accept? Why?
b. What is the cost of the capital rationing constraint?

2. A closely held, publicly traded firm faces self-imposed capital rationing constraints of
$ 100 million in this period and $75 million in the next period. It has to choose among the
following projects:
Investment Outlay
Project Current Period Next Period NPV
A $20 $10 $20
B $25 $15 $20
C $30 $30 $15
D $15 $15 $20
E $40 $25 $30
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F $10 $10 $10
G $20 $15 $20
H $30 $25 $35
I $35 $25 $25
J $25 $15 $10

Set up the linear programming problem, assuming that fractions and multiples of projects
cannot be taken.

3. You own a rental building in the city and are interested in replacing the heating system.
You are faced with the following alternatives:
a. A solar heating system, which will cost $ 12,000 to install and $ 500 a year to
run and will last forever (assume that your building will too).
b. A gas-heating system, which will cost $ 5,000 to install and $ 1000 a year to
run and will last 20 years.
c. An oil-heating system, which will cost $ 3,500 to install and $ 1200 a year to
run and will last 15 years.
If your opportunity cost is 10%, which of these three options is best for you?

4. You are trying to choose a new siding for your house. A salesman offers you two
choices:
a. Wooden siding, which will last 10 years and cost $5000 to install and
$1000/year to maintain
b. Aluminium siding, which will last forever, cost $15,000 to install, and will
have a lower maintentance cost per year
If your discount rate is 10%, how low would your maintenance costs have to be for you
to choose the aluminium siding?

5. You have just been approached by a magazine with an offer for re-subsription. You
can renew for 1 year at $20, 2 years for $36, or 3 years at $45. Assuming that you have
an opportunity cost of 20% and the cost of a subscription will not change over time,
which of these three options should you choose?
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6. You have been hired as a capital budgeting analyst by a sporting goods firm that
manufactures athletic shoes and has captured 10% of the overall shoe market (the total
market is worth $100 million a year). The fixed costs associated with manufacturing
these shoes is $2 million a year, and variable costs are 40% of revenues. The company's
tax rate is 40%. The firm believes that it can increase its market share to 20% by
investing $10 million in a new distribution system (which can be depreciated over the
system's life of 10 years to a salvage value of zero) and spending $1 million a year in
additional advertising. The company proposes to continue to maintain working capital at
10% of annual revenues. The discount rate to be used for this project is 8%.


a. What is the initial investment for this project?
b. What is the annual operating cash flow from this project?
c. What is the NPV of this project?
d. How much would the firm's market share have to increase for you to be indifferent to
taking or rejecting this project?

7. You are considering the possibility of replacing an existing machine that has a book
value of $500,000, a remaining depreciable life of 5 years and a salvage value of $
300,000. The replacement machine will cost $ 2 million and have a 10-year life.
Assuming that you use straight line depreciation and that neither machine will have any
salvage value at the end of the next 10 years, how much would you need to save each
year to make the change (the tax rate is 40%)?

8. You are helping a book store decide whether it should open a coffee shop on the
premises. The details of the investment are as follows:
The coffee shop will cost $ 50,000 to open; it will have a 5-year life and be

depreciated straight line over the period to a salvage value of $10,000.
The sales at the shop are expected to be $15,000 in the first year and grow 5% a year

for the following 5 years.
The operating expenses will be 50% of revenues.

The tax rate is 40%.

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The coffee shop is expected to generate additional sales of $20,000 next year for the

book shop, and the pre-tax operating margin is 40%. These sales will grow 10% a
year for the following 4 years.
a. Estimate the net present value of the coffee shop without the additional book sales.
b. Estimate the present value of the cash flows accruing from the additional book sales.
c. Would you open the coffee shop?

9. The lining of a plating tank must be replaced every 3 years at the cost of approximately
$2000. A new lining material has been developed that is more resistant to the corrosive
effects of the plating liquid and will cost approximately $4000. If the required rate of
return is 20% and annual property taxes and insurance amount to about 4% of the initial
investment, how long must the new lining last to be more economical than the present
one?

10. You are a small business owner considering two alternatives for your phone system.
Plan A Plan B
Initial cost $50,000 $120,000
Annual maintenance cost $ 9,000 $ 6,000
Salvage value $ 10,000 $ 20,000
Life 20 years 40 years
The discount rate is 8%. Which alternatve would you pick?

11. You have been asked to compare three alternative investments and make a
recommendation.
• Project A has an initial investment of $5 million and after-tax cashflows of $ 2.5
million a year for the next 5 years.
• Project B has no initial investment, after-tax cash flows of $ 1 million a year for the
next 10 years, and a salvage value of $2 million (from working capital).
• Project C has an initial investment of $10 million, another investment of $5 million in
10 years, and after-tax cashflows of $ 2.5 million a year forever.

The discount rate is 10% for all three projects. Which of the three projects would you
pick? Why?
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12. You are the manager of a pharmaceutical company and are considering what type of
laptops to buy for your salespeople to take with them on their calls.
You can buy fairly inexpensive (and less powerful) older machines for about $ 2,000

each. These machines will be obsolete in three years and are expected to have an
annual maintentance cost of $ 150.
You can buy newer and more powerful laptops for about $ 4,000 each. These

machines will last five years and are expected to have an annual maintenance cost of
$ 50.
If your cost of capital is 12%, which option would you pick and why?

13. You are the supervisor of a town where the roads are in need of repair. You have a
limited budget and are considering two options “
You can patch up the roads for $100,000, but you will have to repeat this expenditure

every year to keep the roads in reasonable shape.
You can spend $ 400,000 to re-pave and repair the roads, in which case your annual

expenditures on maintenance will drop.
If your discount rate is 10%, how much would the annual expenditures have to drop in
the second option for you to consider it?

14. You are the manager of a specialty retailing firm which is considering two strategies
for getting into the Malaysian retail market. Under the first strategy, the firm will make a
small initial investment of $ 10 million and can expect to capture about 5% of the overall
market share. Under the second strategy, the firm will make a much larger commitment
of $ 40 million for advertising and promotion and can expect to capture about 10% of the
market share. If the overall size of the market is $ 200 million, the firm™s cost of capital is
12% and the typical life of a project in the firm is 15 years, what would the operating
margin have to be for the firm to consider the second strategy? [You can assume that the
firm leases its stores and has no depreciation or capital expenditures.]

15. You work for a firm that has limited access to capital markets. As a consequence, it
has only $ 20 million available for new investments this year. The firm does have a ready
supply of good projects, and you have listed all the projects.
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Project Initial Investment NPV IRR
I $ 10 million $ 3 million 21%
II $ 5 million $ 2.5 million 28%
III $ 15 million $ 4 million 19%
IV $ 10 million $ 4 million 24%
V $ 5 million $ 2 million 20%
a. Based upon the profitability index, which of these projects would you take?
b. Based upon the IRR, which of these projects would you take?
c. Why might the two approaches give you different answers?

16. You are the owner of a small hardware store and you are considering opening a
gardening store in a vacant area in the back of the store. You estimate that it will cost you
$ 50,000 to set up the store, and that you will generate $ 10,000 in after-tax cash flows
from the store for the life of the store (which is expected to be 10 years). The one concern
you have is that you have limited parking; by opening the gardening store you run the
risk of not having enough parking for customers who shop at your hardware store. You
estimate that the lost sales from such occurrence would amount to $ 3,000 a year, and that
your after-tax operating margin on sales at the hardware store is 40%. If your discount
rate is 14%, would you open the gardening store?

17. You are the manager of a grocery store and you are considering offering baby-sitting
services to your customers. You estimate that the licensing and set up costs will amount
to $150,000 initially and that you will be spending about $ 60,000 annually to provide the
service. As a result of the service, you expect sales at the store which is $ 5 million
currently to increase by 20%; your after-tax operating margin is 10%. If your cost of
capital is 12%, and you expect the store to remain open for 10 years, would you offer the
service?

18. You run a financial service firm where you replace your employee™s computers every
three years. You have 500 employees, and each computer costs $ 2,500 currently ““ the
old computers can be sold for $ 500 each. The new computers are generally depreciated
straight line over their 3-year lives to a salvage value of $ 500. A computer-service firm
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offers to lease you the computers and replace them for you at no cost, if you will pay a
leasing fee of $ 5 million a year (which is tax deductible). If your tax rate is 40%, would
you accept the offer?

19. You are examining the viability of a capital investment that your firm is interested in.
The project will require an initial investment of $500,000 and the projected revenues are
$400,000 a year for 5 years. The projected cost-of-goods-sold is 40% of revenues and the
tax rate is 40%. The initial investment is primarily in plant and equipment and can be
depreciated straight-line over 5 years (the salvage value is zero). The project makes use
of other resources that your firm already owns:
(a) Two employees of the firm, each with a salary of $40,000 a year, who are

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