Measuring Investment Returns: Questions and Exercises

1. You have been given the following information on a project:

• It has a 5-year lifetime
• The initial investment in the project will be \$25 million, and the investment will be depreciated straight line, down to a salvage value of \$10 million at the end of the fifth year.
• The revenues are expected to be \$20 million next year and to grow 10% a year after that for the remaining 4 years.
• The cost of goods sold, excluding depreciation, is expected to be 50% of revenues.
• The tax rate is 40%.

a. Estimate the pre-tax return on capital, by year and on average, for the project.

b. Estimate the after-tax return on capital, by year and on average, for the project.

c. If the firm faced a cost of capital of 12%, should it take this project.

2. Now assume that the facts in problem 1 remain unchanged except for the depreciation method, which is switched to an accelerated method with the following depreciation schedule:
 Year % of Depreciable Asset 1 40% 2 24% 3 14.4% 4 13.3% 5 13.3%

Depreciable Asset = Initial Investment - Salvage Value

a. Estimate the pre-tax return on capital, by year and on average, for the project.

b. Estimate the after-tax return on capital, by year and on average, for the project.

c. If the firm faced a cost of capital of 12%, should it take this project?

3. Consider again the project described in problem 1 (assume that the depreciation reverts to straight line). Assume that 40% of the initial investment for the project will be financed with debt, with an annual interest rate of 10% and a balloon payment of the principal at the end of the fifth year.

a. Estimate the return on equity, by year and on average, for this project.

b. If the cost of equity is 15%, should the firm take this project?

4. Answer true or false to the following statements:

a. The return on equity for a project will always be higher than the return on capital on the same project.

b. If the return on capital is less than the cost of equity, the project should be rejected.

c. Projects with high financial leverage will have higher interest expenses and lower net income than projects with low financial leverage and thus end up with a lower return on equity.

d. Increasing the depreciation on an asset will increase the estimated return on capital and equity on the project.

e. The average return on equity on a project over its lifetime will increase if we switch from straight line to double declining balance depreciation.

5. Under what conditions will the return on equity on a project be equal to the internal rate of return, estimated from cashflows to equity investors, on the same project?

6. You are provided with the projected income statements for a project:
 Year 1 2 3 4 Revenues \$ 10,000 \$ 11,000 \$12,000 \$13,000 - Cost of Goods Sold \$ 4,000 \$ 4,400 \$ 4,800 \$ 5,200 - Depreciation \$ 4,000 \$ 3,000 \$ 2,000 \$ 1,000 = EBIT \$ 2,000 \$ 3,600 \$ 5,200 \$ 6,800

• The tax rate is 40%.
• The project required an initial investment of \$15,000 and an additional investment of \$2,000 at the end of year 2.
• The working capital is anticipated to be 10% of revenues, and the working capital investment has to be made at the beginning of each period.

a. Estimate the free cash flow to the firm for each of the 4 years.

b. Estimate the payback period for investors in the firm.

c. Estimate the net present value to investors in the firm, if the cost of capital is 12%. Would you accept the project?

d. Estimate the internal rate of return to investors in the firm. Would you accept the project?

7. Consider the project described in problem 6. Assume that the firm plans to finance 40% of its net capital expenditure and working capital needs with debt. The interest rate on debt is 10%.

a. Estimate the free cash flow to equity for each of the 4 years.

b. Estimate the payback period for equity investors in the firm.

c. Estimate the net present value to equity investors if the cost of equity is 16%. Would you accept the project?

d. Estimate the internal rate of return to equity investors in the firm. Would you accept the project?

8. You are provided with the following cash flows on a project:
 Year Cash Flow to Firm 0 - 10,000,000 1 \$ 4,000,000 2 \$ 5,000,000 3 \$ 6,000,000

Plot the net present value profile for this project. What is the internal rate of return? If this firm had a cost of capital of 10% and a cost of equity of 15%, would you accept this project?

9. You have estimated the following cash flows on a project:
 Year Cashflow to Equity 0 -\$ 4,750,000 1 \$4,000,000 2 \$ 4,000,000 3 - \$3,000,000

Plot the net present value profile for this project. What is the internal rate of return? If the cost of equity is 16%, would you accept this project?

10. Estimate the modified internal rate of return for the project described in problem 8. Does it change your decision on accepting this project?

11. You are analyzing two mutually exclusive projects with the following cash flows:
 Year A B 0 -\$4,000,000 -\$4,000,000 1 \$2,000,000 \$1,000,000 2 \$1,500,000 \$1,500,000 3 \$ 1,250,000 \$1,700,000 4 \$1,000,000 \$2,400,000

a. Estimate the net present value of each project, assuming a cost of capital of 10%. Which is the better project?

b. Estimate the internal rate of return for each project. Which is the better project?

c. What reinvestment rate assumptions are made by each of these rules? Can you show the effect on future cash flows of these assumptions?

d. What is the modified internal rate of return on each of these projects?

12. You have a project that does not require an initial investment but has its expenses spread over the life of the project. Can the IRR be estimated for this project? Why or why not?

13. Businesses with severe capital rationing constraints should use IRR more than NPV. Do you agree? Explain.

14. You have to pick between three mutually exclusive projects with the following cash flows to the firm:
 Year Project A Project B Project C 0 -\$10,000 \$ 5,000 -\$15,000 1 \$ 8,000 \$ 5,000 \$ 10,000 2 \$ 7,000 -\$8,000 \$10,000

The cost of capital is 12%.

a. Which project would you pick using the net present value rule?

b. Which project would you pick using the internal rate of return rule?

c. How would you explain the differences between the two rules? Which one would you rely on to make your choice?

15. You are analyzing an investment decision, in which you will have to make an initial investment of \$10 million and you will be generating annual cash flows to the firm of \$2 million every year, growing at 5% a year, forever.

a. Estimate the NPV of this project, if the cost of capital is 10%.

b. Estimate the IRR of this project.

16. You are analyzing a project with a 30-year lifetime, with the following characteristics:

• The project will require an initial investment of \$20 million and additional investments of \$ 5 million in year 10 and \$ 5 million in year 20.
• The project will generate earnings before interest and taxes of \$3 million each year. (The tax rate is 40%.)
• The depreciation will amount to \$500,000 each year, and the salvage value of the equipment will be equal to the remaining book value at the end of year 30.
• The cost of capital is 12.5%.

a. Estimate the net present value of this project.

b. Estimate the internal rate of return on this project. What might be some of the problems in estimating the IRR for this project?

17. You are trying to estimate the NPV of a 3-year project, where the discount rate is expected to change over time.
 Year Cash Flow to Firm Discount Rate 0 -\$15,000 9.5% 1 \$5,000 10.5% 2 \$ 5,000 11.5% 3 \$ 10,000 12.5%

a. Estimate the NPV of this project. Would you take this project?

b. Estimate the IRR of this project. How would you use the IRR to decide whether to take this project or not?

18. Barring the case of multiple internal rates of return, is it possible for the net present value of a project to be positive, while the internal rate of return is less than the discount rate. Explain.

19. You are helping a manufacturing firm decide whether it should invest in a new plant. The initial investment is expected to be \$ 50 million, and the plant is expected to generate after-tax cashflows of \$ 5 million a year for the next 20 years. There will be an additional investment of \$ 20 million needed to upgrade the plant in 10 years. If the discount rate is 10%,

a. Estimate the Net Present Value of the project.

b. Prepare a Net Present Value Profile for this project.

c. Estimate the Internal Rate of Return for this project. Is there any aspect of the cashflows that may prove to be a problem for calculating IRR?

20. You have been asked to analyze a project, where the analyst has estimated the return on capital to be 37% over the ten-year lifetime of the project. While the cost of capital is only 12%, you have concerns about using the return on capital as an investment decision rule. Would it make a difference if you knew that the project was employing an accelerated depreciation method to compute depreciation? Why?

21. Accounting rates of return are based upon accounting income and book value of investment, whereas internal rates of return are based upon cashflows and take into account the time value of money. Under what conditions will the two approaches give you similar estimates?

22. You have acquired new equipment for a project, costing \$ 15 million. The equipment is expected to have a salvage value of \$ 3 million and a depreciable life of 10 years. The cost of capital is 12%, and the firm faces a tax rate of 40%.

a. Estimate the present value and the nominal value of the tax benefits from depreciation, assuming that you use straight line depreciation.

b. Estimate the present value and the nominal value of the tax benefits from depreciation, assuming that you use double declining balance depreciation.

c. Why does double declining balance depreciation yield a higher present value?

23. You are analyzing the depreciation tax benefits from acquiring an asset that cost \$2.5 million and has a salvage value of \$0.5 million. The asset is classified as an asset with a 5-year depreciable life in the ACRS system. Using the depreciation rates provided in the ACRS table:

a. Estimate the depreciation tax benefits each year on this asset, assuming that the tax rate is 40%.

b. Estimate the present value of these tax benefits, assuming a cost of capital of 10%.

c. If you could expense this asset instead of using the ACRS rates, how much would you gain in present value terms from tax benefits?

24. In both the examples above, there is an estimated salvage value. Assuming that you have to pay capital gains taxes at 20% on any excess of salvage value over book value, would you gain or lose by depreciating the assets down to zero and paying the capital gains taxes. Illustrate using straight line depreciation on problem 1 and ACRS depreciation in problem 2.

25. You have just acquired equipment for \$ 10 million, with a depreciable life of 5 years and no salvage value. You must decide whether you should be using straight line or double declining balance method in estimating taxes and cash flows. Your tax rate is expected to increase over the 5 years ñ
 Year Tax Rate 1 20% 2 25% 3 30% 4 35% 5 40%

a. Which depreciation method provides the larger nominal tax benefits?

b. Which depreciation method provides the larger present value in tax benefits, assuming your cost of capital is 12%?

26. You are analyzing a project with a life of 5 years, which requires an initial investment in equipment and machinery of \$10 million. The equipment is expected to have a 5-year lifetime and no salvage value and to be depreciated straight line. The project is expected to generate revenues of \$ 5 million each year for the 5 years and have operating expenses (not including depreciation) amounting to 30% of revenues. The tax rate is 40%, and the cost of capital is 11%.

a. Estimate the after-tax operating cash flow each year on this project.

b. Estimate the net present value for this project.

c. How much of the net present value can be attributed to the tax benefits accruing from depreciation?

d. Assume that the firm that takes this project is losing money currently, and expects to continue losing money for the first 3 years. Estimate the net present value of this project.

27. You are considering a capital budgeting proposal to make 'glow-in-the-dark' pacifiers for anxious first-time parents. You estimate that the equipment to make the pacifiers would cost you \$50,000 (which you can depreciate straight line over the lifetime of the project, which is 10 years) and that you can sell 15,000 units a year at \$2 a unit. The cost of making each pacifier would be \$0.80, and the tax rate you would face would be 40%. You also estimate that you will need to maintain an inventory at 25% of revenues for the period of the project and that you can salvage 80% of this working capital at the termination of the project. Finally, you will be setting up the equipment in your garage, which means you will have to pay \$2000 a year to have your car garaged at a nearby private facility (assume that you can deduct this cost for tax purposes). To estimate the discount rate for this project, you find that there are comparable firms being traded on the financial markets with the following betas:

Company Debt-Equity ratioTax rateBeta

Nuk-Nuk 0.50 0.401.3

Gerber1.000.50 1.5

You expect to finance this project entirely with equity, and the current T.Bond rate is 11.5%.

(a) What is the appropriate discount rate to use for this project?

(b) What is the after-tax operating cashflow each year for the lifetime of the project?

(c) What is the NPV of this project?

28. You are a financial analyst for a company that is considering a new project. If the project is accepted, it will use 40% of a storage facility that the company already owns but currently does not use fully. The project is expected to last 10 years, and the discount rate is 10%. You research the possibilities and find that the entire storage facility can be sold for \$100,000 and a smaller facility acquired for \$ 40,000. The book value of the existing facility is \$60,000, and both the existing and the new facilities (if it is acquired) would be depreciated straight line over 10 years. The ordinary tax rate is 40%, and the capital gains rate is 25%. What is the opportunity cost, if any, of using the storage capacity?

29. You have been observing the progressive gentrification of you city with interest. You realize that the time is ripe for you to open and run an aerobic exercise center. You find an abandoned warehouse which will meet your needs and rents for \$48,000/ year. You estimate that it will initially cost \$50,000 to renovate the place and buy Nautilius equipment for the center (there will be no salvage and the entire initial cost is depreciable). Your market research indicates that you can expect to get 500 members, each paying \$500/year. You have also found five instructors you can hire for \$24000 a year each. Your tax rate, if you start making profits, will be 40%, and you choose to use straight line depreciation on your initial investment. If your cost of capital is 15% and you expect to retire to the Bahamas in 10 years, answer the following questions:

a. Estimate the annual after tax cash flows on this project.

b. Estimate the net present value and internal rate of return for this investment. Would you take it?

30. Brooks Brothers is thinking of investing in a new line of ìpunk rockerî clothes for the new executive. You have been hired to evaluate the project. You find that, if the project is accepted, you could use an abandoned warehouse already owned by Brooks Brothers with a book value of \$500,000. Your superior had been planning to rent this warehouse out to another firm for \$100,000 a year. If your tax rate is 40%, your discount rate is 15%, your project lifetime is 10 years and you use straight line depreciation, what is the opportunity cost of this investment?

31. You are graduating in June and would like to start your own business manufacturing wine coolers. You collect the following information on the initial costs:

Cost of Plant and Equipment = \$ 500000

Licensing and Legal Costs = \$ 50000

You can claim an investment tax credit of 10% on plant and equipment. You also have been left a tidy inheritance that will cover the initial cost, and your estimated opportunity cost is 10%.

You estimate that you can sell 1 million bottles a year at \$1 a bottle. You estimate your costs as follows:

Variable costs/bottle = 50 cents

Fixed Costs/ year = \$ 200000

Adding up state, local, and federal taxes, you note that you will be in the 50% tax bracket. To be conservative, you assume that you will terminate the business in 5 years and that you will get nothing from the plant and equipment as salvage (you also use straight line depreciation). As a final consideration, you note that starting this business will mean that you will not be able to take the investment banking job you have been offered (which offered \$ 75000 a year for the next 5 years). Should you take on the project?

32. You are an expert at working with PCs and are considering setting up a software development business. To set up the enterprise, you anticipate that you will need to acquire computer hardware costing \$ 100,000 (the lifetime of this hardware is 5 years for depreciation purposes, and straight line depreciation will be used). In addition, you will have to rent an office for \$50000 a year. You estimate that you will need to hire five software specialists at \$ 50000 a year to work on the software and that your marketing and selling costs will be \$ 100000 a year. You expect to price the software you produce at \$100 per unit and to sell 6000 units in the first year. The actual cost of materials used to produce each unit is \$ 20. The number of units sold is expected to increase 10% a year for the remaining 4 years, and the revenues and costs are expected to increase at 3% a year, reflecting inflation. The actual cost of materials used to produce each unit is \$ 20, and you will need to maintain working capital at 10% of revenues (assume that the working capital investment is made at the beginning of each year). Your tax rate will be 40%, and the cost of capital is 12%.

a. Estimate the cash flows each year on this project.

b. Should you accept the project?

33. You are an analyst for a sporting goods corporation that is considering a new project that will take advantage of excess capacity in an existing plant. The plant has a capacity to produce 50000 tennis racquets, but only 25,000 are being produced currently though sales of the rackets are increasing 10% a year. You want to use some of the remaining capacity to manufacture 20,000 squash rackets each year for the next 10 years (which will use up 40% of the total capacity), and this market is assumed to be stable (no growth). An average tennis racquet sells for \$100 and costs \$40 to make. The tax rate for the corporation is 40%, and the discount rate is 10%. Is there an opportunity cost involved? If so, how much is it?

34. 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 currently employed by another division will be transferred to this project. The other division has no alternative use for them, but they are covered by a union contract which will prevent them from being fired for 3 years (during which they would be paid their current salary).

(b) The project will use excess capacity in the current packaging plant. While this excess capacity has no alternative use now, it is estimated that the firm will have to invest \$ 250,000 in a new packaging plant in year 4 as a consequence of this project using up excess capacity (instead of year 8 as originally planned).

(c) The project will use a van currently owned by the firm. While the van is not currently being used, it can be rented out for \$ 3000 a year for 5 years. The book value of the van is \$10,000 and it is being depreciated straight line (with 5 years remaining for depreciation).

The discount rate to be used for this project is 10%.

a. What (if any) is the opportunity cost associated with using the two employees from another division?

b. What, if any, is the opportunity cost associated with the use of excess capacity of the packaging plant?

c. What, if any, is the opportunity cost associated with the use of the van ?

d. What is the after-tax operating cashflow each year on this project?

e. What is the net present value of this project?

35. 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 cashflow from this project?

c. What is the NPV of this project?

36. Your company is considering producing a new product. You have a production facility that is currently used to only 50% of capacity, and you plan to use some of the excess capacity for the new product. The production facility cost \$50 million 5 years ago when it was built and is being depreciated straight line over 25 years (in real dollars, assume that this cost will stay constant over time).
 Product line Capacity used currently Growth rate/year Revenues currently Fixed Costs/Yr Variable Costs/yr Old product 50% 5%/year 100 mil 25 mil 50 mil/yr New product 30% 10%/year 80 mil 20 mil 44 mil/yr

The new product has a life of 10 years, the tax rate is 40%, and the appropriate discount rate (real) is 10%.

a. If you take on this project, when would you run out of capacity?

b. When you run out of capacity, what would you lose if you chose to cut back production (in present value after-tax dollars)? (You have to decide which product you are going to cut back production on.)

c. What would the opportunity cost to be assigned to this new product be if you chose to build a new facility when you run out of capacity instead of cutting back on production?

37. You run a mail-order firm, selling upscale clothing. You are considering replacing your manual ordering system with a computerized system to make your operations more efficient and to increase sales. (All the cash flows given below are in real terms.)

• The computerized system will cost \$10 million to install, and \$500,000 to operate each year. It will replace a manual order system that costs \$1.5 million to operate each year.
• The system is expected to last 10 years, and have no salvage value at the end of the period.
• The computerized system is expected to increase annual revenues from \$5 million to \$8 million for the next 10 years.
• The costs of goods sold is expected to remain at 50% of revenues.
• The tax rate is 40%.
• As a result of the computerized system, the firm will be able to cut its inventory from 50% of revenues to 25% of revenues immediately. There is no change expected in the other working capital components.

The real discount rate is 8%.

a. What is your expected cash flow at time=0?

b. What is the expected incremental annual cash flow from computerizing the system?

c. What is the net present value of this project?