Tax Saving Methods Of Overseas Corporation

Beta and the Cost of Equity

12.1 Furniture Depot, Inc., is an all-equity firm with a beta of 0.95. The market-risk premium is 9 percent and the risk-free rate is 5 percent. The company must decide whether or not to undertake the project that requires an immediate investment of $1.2 million and will generate annual after-tax cash flows of $340,000 at year-end for five years. If the project has the same risk as the firm as a whole, should Furniture Depot undertake the project?

12.2 The returns for the past five years on Douglas stock and the New York Stock Exchange Composite Index (NYSE) are listed below:

Douglas NYSE

a. What are the average returns on Douglas stock and on the market?

b. Compute the beta of Douglas stock.

12.3 Mitsubishi Inc. is a levered firm with a debt-to-equity ratio of 0.25. The beta of common stock is 1.15, while the beta of debt is 0.3. The market-risk premium is 10 percent and the risk-free rate is 6 percent. The corporate tax rate is 35 percent. The SML holds for the company.

a. If a new project of the company has the same risk as the common stock of the firm, what is the cost of equity on the project?

b. If a new project of the company has the same risk as the overall firm, what is the weighted average cost of capital on the project?

12.4 The correlation between the returns on Ceramics Craftsman, Inc., and the returns on the S&P 500 is 0.675. The variance of the returns on Ceramics Craftsman, Inc., is 0.004225,

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330 Part III Risk and the variance of the returns on the S&P 500 is 0.001467. What is the beta of Ceramics Craftsman stock?

12.5 The returns from the past 13 quarters on Mercantile Bank Corporation and the market are listed below.

0.009 |
0.023 |

0.051 |
0.058 |

0.001 |
—0.020 |

0.045 |
—0.050 |

0.085 |
0.071 |

0.000 |
0.012 |

0.080 |
—0.075 |

0.020 |
0.050 |

0.125 |
0.120 |

0.110 |
0.049 |

0.100 |
—0.030 |

0.040 |
0.028 |

a. What is the beta of Mercantile Bank Corporation stock?

b. Is Mercantile's beta higher or lower than the beta of the average stock?

12.6 The following table lists possible rates of return on two risky assets, M and J. The table also lists their joint probabilities, that is, the probabilities that they will occur simultaneously.

rm |
rj |
prob(rm, rj) |

0.16 |
0.16 |
0.10 |

0.16 |
0.18 |
0.06 |

0.16 |
0.22 |
0.04 |

0.18 |
0.18 |
0.12 |

0.18 |
0.20 |
0.36 |

0.18 |
0.22 |
0.12 |

0.20 |
0.18 |
0.02 |

0.20 |
0.20 |
0.04 |

0.20 |
0.22 |
0.04 |

0.20 |
0.24 |
0.10 |

a. List the possible values for RM and the probabilities that correspond to those values.

b. Compute the following items for RM.

i. Expected value ii. Variance iii. Standard deviation c. List the possible values for RJ and the probabilities that correspond to those values.

d. Compute the following items for RJ.

i. Expected value ii. Variance iii. Standard deviation e. Calculate the covariance and correlation coefficient of RM and RJ.

f. Assume M is the market portfolio. Calculate the beta coefficient for security J.

12.7 If you use the stock beta and the security market line to compute the discount rate for a project, what assumptions are you implicitly making?

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Chapter 12 Risk, Cost of Capital, and Capital Budgeting 331

12.8 Pacific Cosmetics is evaluating a project to produce a perfume line. Pacific currently produces no body-scent products. Pacific Cosmetics is an all-equity firm.

a. Should Pacific Cosmetics use its stock beta to evaluate the project?

b. How should Pacific Cosmetics compute the beta to evaluate the project?

12.9 The following table lists possible rates of return on Compton Technology's stock and debt, and on the market portfolio. The corporate tax rate is 35 percent. The corresponding probabilities are also listed.

State |
Probability |
Equity (%) |
Debt (%) |
the Market (%) |

1 |
0.1 |
3% |
8% |
5% |

2 |
0.3 |
8 |
8 |
10 |

3 |
0.4 |
20 |
10 |
15 |

4 |
0.2 |
15 |
10 |
20 |

a. What is the beta of Compton Technology debt?

b. What is the beta of Compton Technology stock?

c. If the debt-to-equity ratio of Compton Technology is 0.5, what is the asset beta of Compton Technology?

12.10 Is the discount rate for the projects of a levered firm higher or lower than the cost of equity computed using the security market line? Why? (Consider only projects that have similar risk to that of the firm.)

12.11 What factors determine the beta of a stock? Define and describe each. Weighted Average Cost of Capital

12.12 The equity beta for Adobe Online Company is 1.29. Adobe Online has a debt-to-equity ratio of 1.0. The expected return on the market is 13 percent. The risk-free rate is

7 percent. The cost of debt capital is 7 percent. The corporate tax rate is 35 percent.

a. What is Adobe Online's cost of equity?

b. What is Adobe Online's weighted average cost of capital?

12.13 Calculate the weighted average cost of capital for the Luxury Porcelain Company. The book value of Luxury's outstanding debt is $60 million. Currently, the debt is trading at 120 percent of book value and is priced to yield 12 percent. The 5 million outstanding shares of Luxury stock are selling for $20 per share. The required return on Luxury stock is 18 percent. The tax rate is 25 percent.

12.14 First Data Co. has 20 million shares of common stock outstanding that are currently being sold for $25 per share. The firm's debt is publicly traded at 95 percent of its face value of $180 million. The cost of debt is 10 percent and the cost of equity is 20 percent. What is the weighted average cost of capital for the firm? Assume the corporate tax rate is 40 percent.

12.15 Calgary Industries, Inc., is considering a new project that costs $25 million. The project will generate after-tax (year-end) cash flows of $7 million for five years. The firm has a debt-to-equity ratio of 0.75. The cost of equity is 15 percent and the cost of debt is 9 percent. The corporate tax rate is 35 percent. It appears that the project has the same risk as that of the overall firm. Should Calgary take on the project?

12.16 Suppose Garageband.com has a 28 percent cost of equity capital and a 10 percent before-tax cost of debt capital. The firm's debt-to-equity ratio is 1.0. Garageband is interested in investing in a telecomm project that will cost $1,000,000 and will provide $600,000 pretax annual earnings for 5 years. Given the project is an extension of its core business, the project risk is similar to the overall risk of the firm. What is the net present value of this project if Garageband's tax rate is 35%?

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Part III Risk

Minicase: AlliedProducts

AlliedProducts, Inc., has recently won approval from the Federal Aviation Administration (FAA) for its Enhanced Ground Proximity Warning System (GPWS). This system is designed to give airplane pilots additional warning of approaching ground danger and thus help prevent crashes. AlliedProducts has spent $10 million in research and development the past four years developing GPWS. The GPWS will be put on the market beginning this year and AlliedProducts expects it to stay on the market for a total of five years.

As a financial analyst specializing in the aerospace industry for USC Pension & Investment, Inc., you are asked by your managing partner, Mr. Adam Smith, to evaluate the potential of this new GPWS project.

Initially, AlliedProducts will need to acquire $42 million in production equipment to make the GPWS. The equipment is expected to have a seven-year useful life. This equipment can be sold for $12 million at the end of five years. AlliedProducts intends to sell two different versions of the GPWS:

1. New GPWS—intended for installation in new aircraft. The selling price is $70,000 per system and the variable cost of production is $50,000 per system. (Assume cash flows occur at year-end.)

2. Upgrade GPWS—intended for installation on existing aircraft with an older version ground proximity radar in place. The selling price of the Upgrade system is $35,000 per system and the variable cost to produce it is $22,000 per system.

AlliedProducts intends to raise prices at the same rate as inflation. Variable costs will also increase with inflation. In addition, the GPWS project will also incur $3 million in marketing and general administration costs the first year (expected to increase at the same rate as inflation).

AlliedProducts' corporate tax rate is 40 percent. Assume that the equity beta listed in Value Line Investment Survey (the latest edition) is the best estimate of AlliedProducts' beta. A five-year U.S. Treasury Bond has a rate of 6.20 percent and the S&P 500 recent years' historical average excess return (i.e., the market return less the Treasury bond rate) is 8.3 percent. Annual inflation is expected to remain constant at 3 percent. Further, suppose AlliedProducts' cost of debt is 6.2 percent and (although somewhat unrealistic) its debt-to-equity ratio is 50 percent and will remain at 50 percent for at least five years.

The state of the economy has a major impact on the airplane manufacturing industry. Airline industry analysts have the following production expectations, depending on the annual state of the economy for the next five years:

State of Economy Probability of State New Aircraft (year 1)

Annual Growth

Strong growth Moderate growth Mild recession Severe recession

35G 25G 15G 5G

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Chapter 12 Risk, Cost of Capital, and Capital Budgeting

While probabilities of each state of the economy will not change during the next five years, airplane production for each category will increase, as shown in Table 12.4, each year after year 1. The FAA requires that these planes have new ground proximity warning systems, of which there are a number of manufacturers besides AlliedProducts.

AlliedProducts estimates that there are approximately 12,500 existing aircraft that comprise the market for its GPWS Upgrade package. Due to FAA regulations, all existing aircraft will be required to get an upgraded ground proximity warning system within the next five years, again, not necessarily from AlliedProducts. AlliedProducts believes the upgrades of the existing aircraft fleet will be spread evenly over the five years (the time value of money would suggest manufacturers defer purchasing upgrades until the fifth year; however, consumer demand for the additional safety will induce earlier upgrades).

AlliedProducts uses the MACRS depreciation schedule (seven-year property class). The immediate initial working capital requirement is $2 million and thereafter the net working capital requirements will be 5 percent of sales.

AlliedProducts has a number of competitors both in the new GPWS and upgrade GPWS markets but expects to dominate the market with a 45 percent share.

Assignment:

First, use the CAPM to determine the appropriate discount rate for this product. Then, use computer spreadsheets such as Excel or Lotus 1-2-3 to analyze the project.

Will the GPWS project improve the wealth of AlliedProducts' shareholders, such as your firm—USC Pension & Investment, Inc.?

Economic Value Added and the Measurement of Financial Performance

Chapter 12 shows how to calculate the appropriate discount rate for capital budgeting and other valuation problems. We now consider the measurement of financial performance. We introduce the concept of economic value added, which uses the same discount rate developed for capital budgeting. We begin with a simple example.

Many years ago, Henry Bodenheimer started Bodie's Blimps, one of the largest highspeed blimp manufacturers. Because growth was so rapid, Henry put most of his effort into capital budgeting. His approach to capital budgeting paralleled that of Chapter 12. He forecasted cash flows for various projects and discounted them at the cost of capital appropriate to the beta of the blimp business. However, these projects have grown rapidly, in some cases becoming whole divisions. He now needs to evaluate the performance of these divisions in order to reward his division managers. How does he perform the appropriate analysis?

Henry is aware that capital budgeting and performance measurement are essentially mirror images of each other. Capital budgeting is forward-looking by nature because one must estimate future cash flows to value a project. By contrast, performance measurement is backward-looking. As Henry stated to a group of his executives, "Capital budgeting is like looking through the windshield while driving a car. You need to know what lies further down the road to calculate a net present value. Performance measurement is like looking into the rearview mirror. You find out where you have been."

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Henry first measured the performance of his various divisions by return on assets (ROA), an approach, which we treated in the appendix to Chapter 2. For example, if a division had earnings after tax of $1,000 and had assets of $10,000, the ROA would be12

$10,000

He calculated the ROA ratio for each of his divisions, paying a bonus to each of his division managers based on the size of that division's ROA. However, while ROA was generally effective in motivating his managers, there were a number of situations where it appeared that ROA was counterproductive.

For example, Henry always believed that Sharon Smith, head of the supersonic division, was his best manager. The ROA of Smith's division was generally in the high double digits, but the best estimate of the weighted average cost of capital for the division was only 20%. Furthermore, the division had been growing rapidly. However, as soon as Henry paid bonuses based on ROA, the division stopped growing. At that time, Smith's division had after tax earnings of $2,000,000 on an asset base of $2,000,000, for an ROA of 100% ($2 million/$2 million).

Henry found out why the growth stopped when he suggested a project to Smith that would earn $1,000,000 per year on an investment of $2,000,000. This was clearly an attractive project with an ROA of 50% ($1 million/$2 million). He thought that Smith would jump at the chance to place his project into her division, because the ROA of the project was much higher than the cost of capital of 20%. However, Smith did everything she could to kill the project. And, as Henry later figured out, Smith was rational to do so. Smith must have realized that if the project were accepted, the division's ROA would become

$2,000,000 + $1,000,000 = $2,000,000 + $2,000,000 = %

Thus, the ROA of Smith's division would fall from 100% to 75% if the project were accepted, with Smith's bonus falling in tandem.

Henry was later exposed to the economic-value-added (EVA) approach,13 which seems to obviate this particular problem. The formula for EVA is

[ROA — Weighted average cost of capital] X Total capital

Without the new project, the EVA of Smith's division would be:

This is an annual number. That is, the division would bring in $1.6 million above and beyond the cost of capital to the firm each year.

With the new project included, the EVA jumps to

If Sharon Smith knew that her bonus was based on EVA, she would now have an incentive to accept, not reject, the project. Although ROA appears in the EVA formula, EVA differs substantially from ROA. The big difference is that ROA is a percentage number and

12Earnings after tax is EBIT (1 — Tc) where EBIT is earnings before interest and taxes and Tc is the tax rate.

13Stern Stewart & Company have a copyright on the terms economic value added and EVA. Details on the Stern Steward & Company EVA can be found in J. M. Stern, G. B. Stewart, and D. A. Chew, "The EVA Financial Management System," Journal of Applied Corporate Finance (Summer 1999).

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Chapter 12 Risk, Cost of Capital, and Capital Budgeting

EVA is a dollar value. In the preceding example, EVA increased when the new project was added even though the ROA actually decreased. In this situation, EVA correctly incorporates the fact that a high return on a large division may be better than a very high return on a smaller division. The situation here is quite similar to the scale problem in capital budgeting that we discussed in Section 6.6.

Further understanding of EVA can be achieved by rewriting the EVA formula. Because ROA X total capital is equal to earnings after tax, we can write the EVA formula as:

Thus, EVA can simply be viewed as earnings after capital costs. Although accountants subtract many costs (including depreciation) to get the earnings number shown in financial reports, they do not subtract out capital costs. One can see the logic of accountants, because the cost of capital is very subjective. By contrast, costs such as COGS (cost of goods sold), SGA (sales, general and administration), and even depreciation can be measured more objectively. However, even if the cost of capital is difficult to estimate, it is hard to justify ignoring it completely. After all, this textbook argues that the cost of capital is a necessary input to capital budgeting. Shouldn't it also be a necessary input to performance measurement?

This example argues that EVA can increase investment for those firms that are currently underinvesting. However, there are many firms in the reverse situation; the managers are so focused on increasing earnings that they take on projects for which the profits do not justify the capital outlays. These managers either are unaware of capital costs or, knowing these costs, choose to ignore them. Because the cost of capital is right in the middle of the EVA formula, managers will not easily ignore these costs when evaluated on an EVA system.

One other advantage of EVA is that it is so stark; the number is either positive or it is negative. Plenty of divisions have negative EVAs for a number of years. Because these divisions are destroying more value than they are creating, a strong point can be made for liquidating these divisions. Although managers are generally emotionally opposed to this type of action, EVA analysis makes liquidation harder to ignore.

The preceding discussion puts EVA in a very positive light. However, one can certainly find much to criticize with EVA as well. We now focus on two well-known problems with EVA. First, the preceding example uses EVA for performance measurement, where we believe it properly belongs. To us, EVA seems a clear improvement over ROA and other financial ratios. However, EVA has little to offer for capital budgeting because EVA focuses only on current earnings. By contrast, net-present-value analysis uses projections of all future cash flows, where the cash flows will generally differ from year to year. Thus, as far as capital budgeting is concerned, NPV analysis has a richness that EVA does not have. Although supporters may argue that EVA correctly incorporates the weighted average cost of capital, one must remember that the discount rate in NPV analysis is the same weighted average cost of capital. That is, both approaches take the cost of equity capital based on beta and combine it with the cost of debt to get an estimate of this weighted average.

A second problem with EVA is that it may increase the shortsightedness of managers. Under EVA, a manager will be well rewarded today if earnings are high today. Future losses may not harm the manager, because there is a good chance that she will be promoted or have left the firm by then. Thus, the manager has an incentive to run a division with more regard for short-term than long-term value. By raising prices or cutting quality, the manager may increase current profits (and, therefore, current EVA). However, to the extent that customer satisfaction is reduced, future profits (and therefore future EVA) are likely to fall. However, one should not be too harsh with EVA here, because the same problem occurs with ROA. A manager who raises prices or cuts quality will increase current ROA at the expense of future ROA. The problem, then, is not EVA per se but with the use of accounting numbers in

Earnings after tax - Weighted average cost of capital X Total capital

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Part III Risk general. Because stockholders want the discounted present value of all cash flows to be maximized, managers with bonuses based on some function of current profits or current cash flows are likely to behave in a shortsighted way.

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