# Cost of Capital. Session 7

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1 Cost of Capital Session 7

2 Cost of Capital Cost of Capital - The return the firm s investors could expect to earn if they invested in securities with comparable degrees of risk Capital Structure - The firm s mix of long term financing and equity financing

3 Cost of Capital The cost of capital represents the overall cost of financing to the firm The cost of capital is normally the relevant discount rate to use in analyzing an investment The overall cost of capital is a weighted average of the various sources: WACC = Weighted Average Cost of Capital WACC = After-tax cost x weights

4 Cost of Debt The cost of debt to the firm is the effective yield to maturity (or interest rate) paid to its bondholders Since interest is tax deductible to the firm, the actual cost of debt is less than the yield to maturity: After-tax cost of debt = yield x (1 - tax rate) The cost of debt should also be adjusted for flotation costs (associated with issuing new bonds)

5 Example: Tax effects of financing with debt with stock with debt EBIT 400, ,000 - interest expense 0 (50,000) EBT 400, ,000 - taxes (34%) (136,000) (119,000) EAT 264, ,000 Now, suppose the firm pays \$50,000 in dividends to the shareholders

6 Example: Tax effects of financing with debt with stock with debt EBIT 400, ,000 - interest expense 0 (50,000) EBT 400, ,000 - taxes (34%) (136,000) (119,000) EAT 264, ,000 - dividends (50,000) 0 Retained earnings 214, ,000

7 Cost of Debt After-tax cost Before-tax cost Tax = - of Debt of Debt Savings 33,000 = 50,000-17,000 OR 33,000 = 50,000 ( ) Or, if we want to look at percentage costs:

8 Cost of Debt After-tax Before-tax Marginal % cost of % cost of x tax = 1- Debt Debt rate Kd = kd (1 - T).066 =.10 (1 -.34)

9 EXAMPLE: Cost of Debt Prescott Corporation issues a \$1,000 par, 20 year bond paying the market rate of 10%. Coupons are annual. The bond will sell for par since it pays the market rate, but flotation costs amount to \$50 per bond. What is the pre-tax and after-tax cost of debt for Prescott Corporation?

10 EXAMPLE: Cost of Debt Pre-tax cost of debt: 950 = 100(PVIFA 20, K d ) (PVIF 20, K d ) using a financial calculator: K d = 10.61% After-tax cost of debt: K d = K d (1 - T) K d =.1061 (1 -.34) K =.07 = 7%

11 Cost of New Preferred Preferred stock: Stock has a fixed dividend (similar to debt) has no maturity date dividends are not tax deductible and are expected to be perpetual or infinite Cost of preferred stock = dividend price - flotation cost

12 Cost of Preferred stock: Example Baker Corporation has preferred stock that sells for \$100 per share and pays an annual dividend of \$ If the flotation costs are \$4 per share, what is the cost of new preferred stock? \$10.50 K P = =.1094 = 10.94% \$100-4

13 Cost of Equity: Retained Earnings Why is there a cost for retained earnings? Earnings can be reinvested or paid out as dividends Investors could buy other securities, and earn a return. Thus, there is an opportunity cost if earnings are retained

14 Cost of Equity: Retained Earnings Common stock equity is available through retained earnings (R/E) or by issuing new common stock: Common equity = R/E + New common stock

15 Cost of Equity: New Common Stock The cost of new common stock is higher than the cost of retained earnings because of flotation costs selling and distribution costs (such as sales commissions) for the new securities

16 Cost of Equity There are a number of methods used to determine the cost of equity We will focus on two Dividend growth Model CAPM

17 The Dividend Growth Model Approach Estimating the cost of equity: the dividend growth model approach According to the constant growth (Gordon) model, D P 1 0 = R E - g Rearranging D 1 R E = g P 0

18 Example: Estimating the Dividend Growth Rate Percentage Year Dividend Dollar Change Change 1990 \$ \$ % Average Growth Rate ( )/4 = 9.025%

19 Dividend Growth Model This model has drawbacks: Some firms concentrate on growth and do not pay dividends at all, or only irregularly Growth rates may also be hard to estimate Also this model doesn t adjust for market risk Therefore many financial managers prefer the capital asset pricing model (CAPM) - or security market line (SML) - approach for estimating the cost of equity

20 Capital Asset Pricing Model (CAPM) kj = R f + β ( m f R R ) Cost of capital Risk-free return Co-variance of returns against the portfolio (departure from the average) B < 1, security is safer than WIG average B > 1, security is riskier than WIG average Average rate of return on common stocks (WIG)

21 The Security Market Line Required rate of return Percent (SML) Market risk premium SML = R f + β (K m R f ) R f Beta (risk)

22 Finding the Required Return on Common Stock using the Capital Asset Pricing Model The Capital Asset Pricing Model (CAPM) can be used to estimate the required return on individual stocks. The formula: K j = R + β K f j ( ) m R f where K j = Required return on stock j R f = Risk-free rate of return (usually current rate on Treasury Bill). β j = Beta coefficient for stock j represents risk of the stock K m = Return in market as measured by some proxy portfolio (index) Suppose that Baker has the following values: R f = 5.5% β = 1.0 j K m = 12%.

23 Finding the Required Return on Common Stock using the Capital Asset Pricing Model Then, using the CAPM we would get a required return of ( ) 12% K j = =.

24 CAPM/SML approach Advantage: Evaluates risk, applicable to firms that don t pay dividends Disadvantage: Need to estimate Beta the risk premium (usually based on past data, not future projections) use an appropriate risk free rate of interest

25 Estimation of Beta: Measuring Market Risk Market Portfolio - Portfolio of all assets in the economy In practice a broad stock market index, such as the WIG, is used to represent the market Beta - sensitivity of a stock s return to the return on the market portfolio

26 Estimation of Beta Theoretically, the calculation of beta is straightforward: Cov( Ri, RM ) σ β = = Problems Var( RM ) σ 1. Betas may vary over time. 2. The sample size may be inadequate. 3. Betas are influenced by changing financial leverage and business risk. Solutions Problems 1 and 2 (above) can be moderated by more sophisticated statistical techniques. Problem 3 can be lessened by adjusting for changes in business and financial risk. Look at average beta estimates of comparable firms in the industry. im 2 M

27 Stability of Beta Most analysts argue that betas are generally stable for firms remaining in the same industry That s not to say that a firm s beta can t change Changes in product line Changes in technology Deregulation Changes in financial leverage

28 What is the appropriate risk-free rate? Use the yield on a long-term bond if you are analyzing cash flows from a long-term investment For short-term investments, it is entirely appropriate to use the yield on short-term government securities Use the nominal risk-free rate if you discount nominal cash flows and real risk-free rate if you discount real cash flows

29 Survey evidence: What do you use for the risk-free rate? Corporations Financial Advisors 90-day T-bill (4%) 90-day T-bill (10%) 3-7 year Treasuries (7%) 5-10 year Treasuries (10%) 10-year Treasuries (33%) year Treasuries (30%) 20-year Treasuries (4%) 30-year Treasuries (40%) year Treasuries (33%) N/A (10%) 10-years or 90-day; depends (4%) N/A (15%) Source: Bruner et. al. (1998)

30 Weighted Average Cost of Capital (WACC) WACC weights the cost of equity and the cost of debt by the percentage of each used in a firm s capital structure WACC=(E/ V) x RE + (D/ V) x RD x (1-TC) (E/V)= Equity % of total value (D/V)=Debt % of total value (1-Tc)=After-tax % or reciprocal of corp tax rate Tc. The after-tax rate must be considered because interest on corporate debt is deductible

31 WACC Illustration ABC Corp has 1.4 million shares common valued at \$20 per share =\$28 million. Debt has face value of \$5 million and trades at 93% of face (\$4.65 million) in the market. Total market value of both equity + debt thus =\$32.65 million. Equity % =.8576 and Debt % =.1424 Risk free rate is 4%, risk premium=7% and ABC s β=.74 Return on equity per SML : RE = 4% + (7% x.74)=9.18% Tax rate is 40% Current yield on market debt is 11%

32 WACC Illustration WACC = (E/V) x RE + (D/V) x RD x (1-Tc) =.8576 x (.1424 x.11 x.60) = or 8.81%

33 Final notes on WACC WACC should be based on market rates and valuation, not on book values of debt or equity Book values may not reflect the current marketplace WACC will reflect what a firm needs to earn on a new investment. But the new investment should also reflect a risk level similar to the firm s Beta used to calculate the firm s RE. In the case of ABC Co., the relatively low WACC of 8.81% reflects ABC s β=.74. A riskier investment should reflect a higher interest rate.

34 Final notes on WACC The WACC is not constant It changes in accordance with the risk of the company and with the floatation costs of new capital

35 Marginal cost of capital and Percent A investment projects B C 10.41% D 10.77% E 11.23% Amount of capital (\$ millions) F G H K mc Marginal cost of capital

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