Problems and Questions

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:
H
\$25
\$20
 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

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:
J
\$25
\$15
\$10
ĦI
 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 F \$10 \$10 \$10 G \$20 \$15 \$20 H \$30 \$25 \$35 I \$35 \$25 \$25

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 much 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?

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, with a new machine that 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%.
• 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 e a small business owner and are 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.

ï Project A has an initial investment of \$5 million and after-tax cashflows of \$ 2.5 million a year for the next 5 years.

ï 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).

ï 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?

12. You are the manager of a pharmaceutical company and are considering what type of laptops to buy for your salesmen 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 ñ

• In the first option, you will patch up the roads for \$100,000, but you will then have to repeat this expenditure every year to keep the roads in reasonable shape.
• Alternatively, you can spend \$ 400,000 to repave and repair the roads, in which case, the annual expenditures you will have 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 firmís 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 which 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 out all of the projects.

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 swould 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 employeeís computers every three years. You have 500 employees, and each computer costs \$ 2,500 currently ññ 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 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?