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THE COST OF CAPITAL

You learned how to use the capital asset pricing model to estimate the expected return on a company`s common stock. If the firm is financed wholly by common stock, then the stockholders own all the firm`s assets and are entitled to all the cash flows. In this case, the expected return required by investors in the common stock equals the company cost of capital.1

Most companies, however, are financed by a mixture of securities, including common stock, bonds, and often preferred stock or other securities. Each of these securities has different risks and therefore investors in them look for different rates of return. In these circumstances, the company cost of capital is no longer the same as the expected return on the common stock. It depends on the expected return from all the securities that the company has issued. It also depends on taxes, because interest payments made by a corporation are tax-deductible expenses.

Therefore, the company cost of capital is usually calculated as a weighted average of the after-tax interest cost of debt financing and the ¬cost of equity, ­ that is, the expected rate of return on the firm`s common stock. The weights are the fractions of debt and equity in the firm`s capital structure. Managers refer to the firm`s weighted-average cost of capital, or WACC (rhymes with ¬quack ­).

Managers use the weighted-average cost of capital to evaluate average-risk capital investment projects. ¬Average risk ­ means that the project`s risk matches the risk of the firm`s existing assets and operations. This material explains how the weighted-average cost of capital is calculated in practice.

After studying this material you should be able to

_ Calculate a firm`s capital structure.

_ Estimate the required rates of return on the securities issued by the firm.

_ Calculate the weighted-average cost of capital.

_ Understand when the weighted-average cost of capital is ¤or isn`t ¤the appropriate discount rate for a new project. Managers calculating WACC can get bogged down in formulas. We want you to understand why WACC works, not just how to calculate it. Let`s start with ¬Why? ­ We`ll listen in as a young financial manager struggles to recall the rationale for project discount rates.

Geothermal`s Cost of Capital

Jo Ann Cox, a recent graduate of a prestigious eastern business school, poured a third cup of black coffee and tried again to remember what she once knew about project hurdle rates. Why hadn`t she paid more attention in Finance 101? Why had she sold her finance text the day after passing the finance final?

Costas Thermopolis, her boss and CEO of Geothermal Corporation, had told her to prepare a financial evaluation of a proposed expansion of Geothermal`s production. She was to report at 9:00 Monday morning. Thermopolis, whose background was geophysics, not finance, not only expected a numerical analysis; he expected her to explain it to him.

Thermopolis had founded Geothermal in 1993 to produce electricity from geothermal energy trapped deep under Nevada. The company had pioneered this business and had been able to obtain perpetual production rights for a large tract on favorable terms from the United States government. When the 1999 oil shock drove up energy prices worldwide, Geothermal became an exceptionally profitable company. It was currently reporting a rate of return on book assets of 25 percent per year.

Now, in 2001, production rights were no longer cheap. The proposed expansion would cost $30 million and should generate a perpetual after-tax cash flow of $4.5 million annually. The projected rate of return was 4.5/30 = .15, or 15 percent, much less than the profitability of Geothermal`s existing assets. However, once the new project was up and running, it would be no riskier than Geothermal`s existing business.

Jo Ann realized that 15 percent was not necessarily a bad return ¤though of course 25 percent would have been better. Fifteen percent might still exceed Geothermal`s cost of capital, that is, exceed the expected rate of return that outside investors would demand to invest money in the project. If the cost of capital was less than the 15 percent expected return, expansion would be a good deal and would generate net value for Geothermal and its stockholders.

Jo Ann remembered how to calculate the cost of capital for companies which used only common stock financing. Briefly she sketched the argument. ¬I need the expected rate of return investors would require from Geothermal`s real assets ¤the wells, pumps, generators, etc. That rate of return depends on the assets` risk. However, the assets aren`t traded in the stock market, so I can`t observe how risky they have been. I can only observe the risk of Geothermal`s common stock.

But if Geothermal issues only stock ¤no debt ¤then owning the stock means owning the assets, and the expected return demanded by investors in the stock must also be the cost of capital for the assets. ­ She jotted down the following identities:

Value of business = value of stock Risk of business = risk of stock Rate of return on business = rate of return on stock

Investors` required return from business = investors` required return from stock

Unfortunately, Geothermal had borrowed a substantial amount of money; its stockholders did not have unencumbered ownership of Geothermal`s assets. The expansion project would also justify some extra debt finance. Jo Ann realized that she would have to look at Geothermal`s capital structure ¤its mix of debt and equity financing ¤and consider the required rates of return of debt as well as equity investors.

Geothermal had issued 22.65 million shares, now trading at $20 each. Thus shareholders valued Geothermal`s equity at $20 ГЧ 22.65 million = $453 million. In addition, the company had issued bonds with a market value of $194 million. The market value of the company`s debt and equity was therefore $194 + 453 = $647 million. Debt was 194/647 = .3, or 30 percent of the total.

¬Geothermal`s worth more to investors than either its debt or its equity, ­ Jo Ann mused. ¬But I ought to be able to find the overall value of Geothermal`s business by adding up the debt and equity. ­ She sketched a rough balance sheet:

¬Holy Toledo, I`ve got it! ­ Jo Ann exclaimed. ¬If I bought all the securities issued by Geothermal, debt as well as equity, I`d own the entire business. That means. . . . ­ She jotted again:

Value of business = value of portfolio of all the firm`s debt and equity securities Risk of business = risk of portfolio Rate of return on business = rate of return on portfolio Investors` required return on business = investors` required return on (company cost of capital) portfolio

¬All I have to do is calculate the expected rate of return on a portfolio of all the firm`s securities. That`s easy. The debt`s yielding 8 percent, and Fred, that nerdy banker, says that equity investors want 14 percent. Suppose he`s right. The portfolio would contain 30 percent debt and 70 percent equity, so. . . . ­ Portfolio return = (.3 ГЧ 8%) + (.7 ГЧ 14%) = 12.2%

It was all coming back to her now. The company cost of capital is just a weighted average of returns on debt and equity, with weights depending on relative market values of the two securities.

¬But there`s one more thing. Interest is tax-deductible. If Geothermal pays $1 of interest, taxable income is reduced by $1, and the firm`s tax bill drops by 35 cents (assuming a 35 percent tax rate). The net cost is only 65 cents. So the cost of debt is not 8 percent, but .65 ГЧ 8 = 5.2 percent. ¬Now I can finally calculate the weighted-average cost of capital: WACC = (.3 ГЧ 5.2%) + (.7 ГЧ 14%) = 11.4% ¬Looks like the expansion`s a good deal. Fifteen`s better than 11.4. But I sure need a break. ­