Problems and Questions

1. Suppose you are analyzing a new store for The Limited, a leading clothing retailer, and the store is expected to have the following characteristics:

Size of the store = 10,000 square feet

Sales/square foot = \$ 500/square foot

Cost of setting up store = \$ 2.5 million (Depreciated straight line over 10 years to \$ 500,000)

Variable Costs = 40% of Revenues

Fixed Costs = \$ 1 million/ year

The store is expected to have a life of 10 years and the firm is expected to pay 40% of its income as taxes and has a cost of capital of 14%.

a. Estimate the base case net present value and IRR.

b. Estimate the sensitivity of both measures to sales/square foot and the variable costs as a percent of revenues.

c. Estimate the breakeven in financial and accounting terms, in terms of sales per square foot.

2. Suppose you are analyzing the cash flows on a new manufacturing plant to produce a new type of computer disk drive. The plant will cost \$ 10 million to build, and have the capacity to sell 20,000 drives a year. Each drive is expected to retail for \$ 250, and the cost of making each drive is expected to be \$ 100. The fixed costs amount to \$ 500,000 a year, not including depreciation, which is assumed to be straight line over 5 years on the initial investment of \$ 10 million, with no salvage value. The inflation rate in both revenues and costs is expected to be 5%, and the cost of capital is 15%.

a. Estimate the NPV and IRR for the base case analysis.

b. Estimate the sensitivity of these measures to changes in assumptions on the number of units sold and the sales price per unit.

c. Estimate the accounting and financial breakeven on this project.

3. Consider again the example described above. Instead of providing base case estimates, assume that you are given the following probability distributions for each of the following variables:

Number of Units Sold Sales Price/Unit

# Units Sold Probability Sales Price Probability

15,000 0.25 \$ 200 0.20

20,000 0.50 \$ 225 0.20

25,000 0.25 \$ 250 0.20

\$ 275 0.20

\$ 300 0.20

Assume that all of the other base case assumptions hold.

a. How would you go about structuring the simulation for this problem?

b. If you repeated this simulation for a large number of times and calculated the expected net present value and IRR across these simulations, what would you expect to find (relative to the base case)?

c. What other information from the simulation would you use in your decision making?

4. You have just analyzed a project, requiring an initial investment in plant and equipment and with a 10-year life and estimated the cash flows over the 10 years:
 Year Initial Investment AT Operating CF Salvage Value 0 \$ (10,000,000.00) 1 \$ 1,500,000 2 \$ 1,575,000 3 \$ 1,653,750 4 \$ 1,736,438 5 \$ 1,823,259 6 \$ 1,914,422

7

\$ 2,010,143

a. Estimate the net present value, assuming a cost of capital of 12%.

b. Since the life of the project is arbitrarily set at 10 years, recalculate the net present value, assuming that

1. the project continues for 5 more years, and that cash flows continue to grow 5% a year during this period (the salvage value remains unchanged).

2. the project continues for 10 more years, and cash flows are frozen at year 10 levels. (the salvage value remains unchanged).

3. the project continues forever, and cash flows are frozen at year 10 levels.

5. Assume that you are analyzing a new menu entry for a fast-food chain, that has three stages:

Stage 1: The project requires a test marketing expense of \$ 5 million. This test market is expected to last a year, and there is a 60% chance of success.

Stage 2: If the test market is a success, the firm plans an introduction into one region of the country at a cost of \$ 20 million (at the start of the second year), and there is a 75% chance of success.

Stage 3: If the regional introduction succeeds, the firm plans to introduce the product country wide at a cost of \$ 50 million (at the start of the third year). If it does so, there are three possibilities:

a. The product sells much better than expected and generates \$ 40 million in after cash flows for the next 5 years.

b. The product sells as well as expected and generates \$ 20 million in after-tax cash flows for the next 5 years.

c. The product sells less well than expected and generates \$ 5 million in after-tax cash flows for the next 5 years.

Each has an equal probability of occurring.

a. Draw the decision tree for this project.

b. Estimate the expected net present value of this decision.

c. If you were given the right to abandon the project one year into the full introduction, estimate the value of the option to abandon.

6. You are helping Hersheyís, the chocolate manufacturer, decide whether it should introduce a new low-fat candy. To help the company make this decision, you have done simulations of the cash flows from introducing the new product, and arrived at the following distribution of net present values.

NPV Number of Simulations

< -10 million 150

-10 million to 0 350

0 to + 10 million 500

10 to 20 million 1000

20 to 30 million 1000

30 to 40 million 500

40 to 50 million 300

> 50 million 200

a. Estimate the expected net present value of this project.

b. What is the likelihood that this project is a bad one?

b. How would you use the output from these simulations in your decision making?

7. You work for a newspaper and magaizing publisher who has asked you to look into the feasibility of introducing a weekly magazine directed to reporting financing news from overseas for U.S. investors. After your research, you conclude the following ñ

• It will cost you approximatly \$ 20 million to start the newspaper.
• The annual fixed cost of preparing the magazine will be approximately \$ 10 million; there will be a production cost of a \$1 for every issue sold.
• Based upon the overall market size, you expect to sell about 100,000 copies of your magazine each week and receive about \$ 2.50 per issue sold. You also expect advertising revenues to be about \$ 15 million a year.
• You have estimated a life of 5 years for the magazine.
• You have estimated a tax rate of 40% for the firm, and your cost of capital is 12%.

a. Estimate the base case NPV and IRR for this project.

b. How senstive is your conclusion to the number of issues that you sell a week.

c. How many issues would you have to sell to breakeven on an accounting basis? on a financial basis?

8. You have the opportunity to invest in a real estate project with significant risks associated with it. The investment is only marginally acceptable and you are considering rejecting it. The promoter of the project offers you the option to sell back your share of the project at 75% of your investment anytime in the first 5 years of the project. Would it make a difference to your decision? Why or why not?

9. You are considering whether to test market a new breakfast bar that you have just developed. It is estimated that the test marketing will cost approximately \$ 10 million. Based upon your prior experiences with similar products, there is a 60% chance that the test market will be successful; if it is, a plant will be built at a cost of \$ 50 million and the product can expect to generate after-tax cash flows of \$ 10 million a year for 10 years; if it is not, the product will be abandoned. The cost of capital is 10%.

a. Draw the decision tree for this project.

b. Would you do the test market for the proect? Why?

10. Coca Cola Corporation is considering the introduction of a grape flavored cola, and has asked you to do the analysis of the feasibility of the project. The initial cost of promotion and advertising is expected to be \$ 100 million; the advertising cost per year after that is expected to be \$ 10 million. All advertising costs are tax deductible in the year in which they are made. The cost per can sold is \$ 0.20, and the expected revenue per can to the company is \$ 0.50. The product is expected to have a 20-year life, and the cost of capital for Coca Cola is 11%. The corporate tax rate is 40%.

a. Estimate how many cans of the new soda Coca Cola will have to sell to reach an accounting breakeven.

b. Estimate how many cans of the new soda Coca Cola will have to sell to reach a financial breakeven.

11. You are the owner of a small appliance store and you are thinking of ways of increasing your sales. One option that you are considering is to start offering credit to your customers. By doing so, you expect to increase your sales from \$ 4 million a year to \$ 6 million, and your after-tax operating margins to remain unchanged at 10%. The credit, however, will increase your working capital needs from 10% of revenues to 20% of revenues. Your cost of capital is 14%.

a. Assuming that you plan to stay in business for 10 years, should you offer credit?

b. How much would your sales have to increase for you to reach breakeven (from a financial standpoint)?

c. How many years would you have to stay in business to recoup your investment in working capital?

12. You are looking at the results of a sensitivity and breakeven analysis done on the new chemical plant that your firm is considering.

Variable Base Case Assumption Breakeven for NPV=0

Volume Sold 100,000 tonnes 92,000 tonnes

Price/unit \$ 1000/tonne \$ 875/tonne

Operating Margin 15% 14.1%

Discount Rate 12.5% 14.0%

Life of Project 15 years 12.7 years

a. Estimate the margin for error you have on each of these assumptions.

b. How would you use this information in your decision making?

c. If you were concerned about the small margin for error on operating margin, how would you go about reducing your discomfort with that assumption?

13. GDT Corporation is a new Internet service company that is planning to offer subscribers unlimited access to the Internet for \$ 15 a month. It will cost the company \$ 10 million initially to set up the service, and \$ 5 a month to provide the service to each subscriber. GellComm is not sure how long it will be able to stay in business before it is overwhelmed by the competition from phone companies. It has a cost of capital of 14%, and a tax rate of 40%.

a. Assuming that it stays in business for 2 years, how many subscribers will it need to breakeven on a NPV basis?

b. Assuming that it signs up 100,000 subscribers, how long will it need to stay in business to breakeven on a NPV basis?

14. Doing sensiitivity analysis on a project can lead to the double counting of risk, since the discount rates used already reflect the project risk. Comment.

15. You run a software firm and you are considering a major upgrade of your product. The upgrade will cost \$ 15 million, but it will increase the sales significantly. You will keep the price per unit at \$ 200, and your after-tax operating margin is expected to remain at 40%. Your cost of capital is 15%.

a. If your product has an expected life of 3 years (before becoming obsolete), how many additional units would you have to sell to breakeven?

16. An oil company is considering whether it should drill for oil in the Gulf of Mexico. Based upon prior experience, it has estimated the following ñ

• The initial cost of the exploratory rig is \$ 10 million; the probability of finding sufficient oil with the exploratory rig is 60%.
• The cost of the full rig is \$ 50 million; if this investment is made, there are three possible scenarios ñ
• Mega Well: The well will yield 500,000 barrels of oil a year for 20 years.
• Typical Well: The well will yield 250,000 barrels of oil a year for 20 years.
• Bust: The well will yield only 50,000 barrels of oil a year for 20 years.

The company has a pre-tax operating profit of \$ 12 per barrel currently, and this is expected to grow 3% a year over the next 20 years. The annual fixed cost of operating the rig is \$ 1 million, and the rig will be depreciated straight line over 20 years. The cost of capital is 10%, and the corporate tax rate is 40%.

a. Show the decision tree for this investment.

b. Should the oil company invest in the exploratory righ.

c. How much is the value of the option to abandon the well? (Assume that there is no salvage.)