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CALCULATING COMPANY COST OF CAPITAL AS A WEIGHTED AVERAGE

Calculating the company cost of capital is straightforward, though not always easy, when only common stock is outstanding. For example, a financial manager could estimate beta and calculate shareholders` required rate of return using the capital asset pricing model (CAPM). This would be the expected rate of return investors require on the company`s existing assets and operations and also the expected return they will require on new investments that do not change the company`s market risk. But most companies issue debt as well as equity.

The company cost of capital is a weighted average of the returns demanded by debt and equity investors. The weighted average is the expected rate of return investors would demand on a portfolio of all the firm`s outstanding securities.

Let`s review Jo Ann Cox`s calculations for Geothermal. To avoid complications, we`ll ignore taxes for the next two or three pages. The total market value of Geothermal, which we denote as V, is the sum of the values of the outstanding debt D and the equity E. Thus firm value is V = D + E = $194 million + $453 million = $647 million. Debt accounts for 30 percent of the value and equity accounts for the remaining 70 percent. If you held all the shares and all the debt, your investment in Geothermal would be V = $647 million. Between them, the debt and equity holders own all the firm`s assets. So V is also the value of these assetsБІАААдthe value of Geothermal`s existing business.

Suppose that Geothermal`s equity investors require a 14 percent rate of return on their investment in the stock. What rate of return must a new project provide in order that all investorsБІАААдboth debtholders and stockholdersБІАААдearn a fair rate of return? The debtholders require a rate of return of rdebt = 8 percent. So each year the firm will need to pay interest of rdebt АГАз D = .08 АГАз $194 million = $15.52 million. The shareholders, who have invested in a riskier security, require a return of requity = 14 percent on their investment of $453 million. Thus in order to keep shareholders happy, the company needs additional income of requity АГАз E = .14 АГАз $453 million = $63.42 million. To satisfy both the debtholders and the shareholders, Geothermal needs to earn $15.52 million + $63.42 million = $78.94 million. This is equivalent to earning a return of rassets = 78.94/647 = .122, or 12.2 percent.

Figure 4.17 illustrates the reasoning behind our calculations. The figure shows the amount of income needed to satisfy the debt and equity investors. Notice that debtholders account for 30 percent of Geothermal`s capital structure but receive less than 30 percent of its expected income. On the other hand, they bear less than a 30 percent share of risk, since they have first cut at the company`s income, and also first claim on its assets if the company gets in trouble. Shareholders expect a return of more than 70 percent of Geothermal`s income because they bear correspondingly more risk.

However, if you buy all Geothermal`s debt and equity, you own its assets lock, stock, and barrel. You receive all the income and bear all the risks. The expected rate of return you`d require on this portfolio of securities is the same return you`d require from unencumbered ownership of the business. This rate of returnБІАААд12.2 percent, ignoring taxesБІАААдis therefore the company cost of capital and the required rate of return from an equal-risk expansion of the business. The bottom line (still ignoring taxes) is

Company cost of capital = weighted average of debt and equity returns

The underlying algebra is simple. Debtholders need income of (rdebt АГАз D) and the equity investors need income of (requity АГАз E). The total income that is needed is (rdebt АГАз D) + (requity АГАз E). The amount of their combined existing investment in the company is V. So to calculate the return that is needed on the assets, we simply divide the income by the investment:

This figure is the expected return demanded by investors in the firm`s assets.

MARKET VERSUS BOOK WEIGHTS

The company cost of capital is the expected rate of return that investors demand from the company`s assets and operations.

The cost of capital must be based on what investors are actually willing to pay for the company`s outstanding securitiesБІАААдthat is, based on the securities` market values.

Market values usually differ from the values recorded by accountants in the company`s books. The book value of Geothermal`s equity reflects money raised in the past from shareholders or reinvested by the firm on their behalf. If investors recognize Geothermal`s excellent prospects, the market value of equity may be much higher than book, and the debt ratio will be lower when measured in terms of market values rather than book values.

Financial managers use book debt-to-value ratios for various other purposes, and sometimes they unthinkingly look to the book ratios when calculating weights for the company cost of capital. That`s a mistake, because the company cost of capital measures what investors want from the company, and it depends on how they value the company`s securities. That value depends on future profits and cash flows, not on accounting history. Book values, while useful for many other purposes, only measure net cumulative historical outlays; they don`t generally measure market values accurately.

Geothermal`s debtholders account for 30 percent of the company`s capital structure, but they get a smaller share of income because their return is guaranteed by the company. Geothermal`s stockholders bear more risk and receive, on average, greater return. Of course if you buy all the debt and all the equity, you get all the income.