The Cost of Capital

Bus 3019

Winter 2006

Outline of the Lecture

• Weighted Average Cost of Capital (WACC) • Best Practices in Estimating the Cost of Capital: Survey and Synthesis

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WACC Projects of levered firms are simultaneously financed with both debt and equity. The cost of capital is a weighted average of the cost of debt and the cost of equity. What weights must be used in WACC calculations? How to calculate cost of debt and cost of equity?

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WACC A firm’s balance sheet can be represented as follows: Assets

Debt & Equity

NWC

Debt (D)

Fixed Assets

Equity (E)

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WACC The value of a firm, V , can then be defined as V = NWC + Fixed Assets = D+E and its weighted average cost of capital is given by WACC = WE KE + WD (1 − t)KD .

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WACC A firm has a book value and a market value. Book Value: Calculated using the values on the balance sheet (historical cost of assets) Market Value: Calculated using market values (market value of equity (stock price × number of shares outstanding) + market value of debt)

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WACC When considering equity, there usually is a significant difference between market and book values. Market and book values of debt are often very similar. In WACC calculations, market-value weights are more appropriate that book-value weights. Technically, target weights are ideal: If the firm expects to reduce debt in the future, this must be taken into account.

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WACC: The Cost of Debt The cost of debt of a firm is its after-tax borrowing rate. This before-tax rate can be: • The interest rate the firm would pay were bonds issued today (marginal cost) • The average interest rate paid on current debt

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WACC: The Cost of Debt Bond prices are usually expressed as percentages of par values. That is, a price of 110.29 means that the bond is actually worth 110.29% of its par value, or P = 1.1029. F Hence a bond issue with par value of $125 millions and price 110.29 has a market value of 1.1029 × 125 = $137.86 millions.

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WACC: The Cost of Debt Interest payments are tax deductible. A firm’s cost of debt is therefore its after-tax interest rate. The tax rate (t) used can be: • The firm’s marginal tax rate • The firm’s average (historical) tax rate

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WACC: The Cost of Equity The cost of equity is the cost of retaining earnings as well as the cost of issuing new shares. The cost of equity is the return required by shareholders. This return can be calculated using: • The CAPM • The DDM • The average historical return of the firm’s stock

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WACC: The Cost of Equity According to the CAPM, KE = K f + β Km − K f




= k f + β × RP, where RP represents the “equity risk premium”.

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WACC: The Cost of Equity Risk Premium The cost of equity is a “forward-looking” cost of equity. That is, it is based on what will happen rather than what has happened. Hence, its calculation should involve a forward-looking risk premium.

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WACC: The Cost of Equity Risk Premium According to Arnott and Bernstein (2002), the forward-looking risk premium was around 0-2% in 2002 Computing a forward-looking risk premium can be quite cumbersome and is very subjective. An average of past risk premia is often used. What average to use for the risk premium? An arithmetic average? A geometric average? Both have advantages and disadvantages. 14

WACC: The Cost of Equity Risk Premium Based on Ibbotson Associates’ data from 1926 to 1995, the equity risk premium is as follows: Equity Market Risk Premium (Km − Kf ) K f = T-Bill Return

K f = T-Bond Return

Arithmetic Mean

8.5%

7.0%

Geometric Mean

6.5%

5.4%

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WACC: The Cost of Equity Beta Which β to use? • Calculate your own: Run the regression KE,t = α + βKm,t . • Use beta from a published source (Bloomberg, Value Line, Standard & Poor’s, etc.)

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WACC: The Cost of Equity Beta When calculating your own β, what type of data to use? Monthly returns? Weekly returns? Increasing the number of period increases the reliability of the estimate but incorporates information that may be irrelevant. Reducing the observation period from monthly to weekly may increase the number of observations but may yield observations that are not normally distributed.

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WACC: The Cost of Equity Risk-Free Rate What should be used for K f ? Textbooks often suggest to use the 90-day T-bill rate. The life of an investment is usually more than 90 days. Firms mostly use yields on government bonds that match the life of their investments (10-year government bonds for 10-year investment horizons, for instance).

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“Best Practices” in Estimating the Cost of Capital

• Telephone interview of the most senior financial officer of 27 firms, of 10 financial advisers and 7 textbooks • Mostly open-ended questions • More diversified variety of answers than with a questionnaire

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Best Practices: Survey Results DCF and Weights • 89% of corporations use discounted cash flow techniques as a primary tool to evaluate investment opportunities • 52% of corporations and 90% of financial advisors use target weights • 59% of corporations and 90% of financial advisors use market weights

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Best Practices: Survey Results Cost of Debt • 52% of corporations use marginal (before-tax) cost of debt, 37% use current average • 52% of corporation use marginal tax rate, 37% use historical average

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Best Practices: Survey Results Cost of Equity Capital • 81% of corporations use the CAPM. • Risk-free rate: 70% of corporations use government bonds with 10 or more years to maturity, of corporation use 90-day T-Bill • 52% of corporations use beta from published source, 30% calculate their own • Risk premium: Varies a lot 22