# LECTURE 07. Cost of Capital Berk, De Marzo Chapter 14 and 15

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1 1 LECTURE 07 Cost of Capital Berk, De Marzo Chapter 14 and 15

2 2 Equity Versus Debt Financing Capital Structure: The relative proportions of debt, equity, and other securities that a firm has outstanding. You are considering an investment opportunity. For an initial investment of \$800 this year, the project will generate cash flows of either \$1400 or \$900 next year, depending on whether the economy is strong or weak, respectively. Both scenarios are equally likely. The project cash flows depend on the overall economy and thus contain market risk. As a result, you demand a 10% risk premium over the current risk-free interest rate of 5% to invest in this project. What is the NPV of this investment opportunity?

3 3 Financing a Firm with Equity The cost of capital for this project is 15%. The expected cash flow in one year is: ½(\$1400) + ½(\$900) = \$1150. The NPV of the project is: \$1150 NPV = \$800 + = \$800 + \$1000 = \$ If you finance this project using only equity, how much would you be willing to pay for the project? \$1150 PV (equity cash flows) = = \$ If you can raise \$1000 by selling equity in the firm, after paying the investment cost of \$800, you can keep the remaining \$200, the NPV of the project NPV, as a profit.

4 4 Financing a Firm with Equity Unlevered Equity Equity in a firm with no debt. Because there is no debt, the cash flows of the unlevered equity are equal to those of the project. Shareholder s returns are either 40% or 10%. The expected return on the unlevered equity is: ½ (40%) + ½( 10%) = 15%. Because the cost of capital of the project is 15%, shareholders are earning an appropriate return for the risk they are taking.

5 5 Financing a Firm with Debt and Equity Suppose you decide to borrow \$500 initially, in addition to selling equity. Because the project s cash flow will always be enough to repay the debt, the debt is risk free and you can borrow at the risk-free interest rate of 5%. You will owe the debt holders: \$ = \$525 in one year. Levered Equity: Equity in a firm that also has debt outstanding. Given the firm s \$525 debt obligation, your shareholders will receive only \$875 (\$1400 \$525 = \$875) if the economy is strong and \$375 (\$900 \$525 = \$375) if the economy is weak.

6 What price E should the levered equity sell for? Which is the best capital structure choice for the entrepreneur? 6

7 7 Financing a Firm with Debt and Equity Modigliani and Miller argued that with perfect capital markets, the total value of a firm should not depend on its capital structure. They reasoned that the firm s total cash flows still equal the cash flows of the project, and therefore have the same present value. Because the cash flows of the debt and equity sum to the cash flows of the project, by the Law of One Price the combined values of debt and equity must be \$1000. Therefore, if the value of the debt is \$500, the value of the levered equity must be \$500. E = \$1000 \$500 = \$500.

8 8 Modigliani-Miller I: Leverage, Arbitrage, and Firm Value The Law of One Price implies that leverage will not affect the total value of the firm. Instead, it merely changes the allocation of cash flows between debt and equity, without altering the total cash flows of the firm. Modigliani and Miller (MM) showed that this result holds more generally under a set of conditions referred to as perfect capital markets: 1. Investors and firms can trade the same set of securities at competitive market prices equal to the present value of their future cash flows. 2. There are no taxes, transaction costs, or issuance costs associated with security trading. 3. A firm s financing decisions do not change the cash flows generated by its investments, nor do they reveal new information about them. MM Proposition I: In a perfect capital market, the total value of a firm is equal to the market value of the total cash flows generated by its assets and is not affected by its choice of capital structure.

9 9 Modigliani-Miller II: Leverage, Risk, and the Cost of Capital Leverage and the Equity Cost of Capital MM s first proposition can be used to derive an explicit relationship between leverage and the equity cost of capital. Leverage and the Equity Cost of Capital MM Proposition I states that: The total market value of the firm s securities is equal to the market value of its assets, whether the firm is unlevered or levered. Leverage and the Equity Cost of Capital E=Market value of equity in a levered firm. D=Market value of debt in a levered firm. U=Market value of equity in an unlevered firm. A=Market value of the firm s assets. E + D = U = A

10 10 Modigliani-Miller II: Leverage, Risk, and the Cost of Capital Leverage and the Equity Cost of Capital The cash flows from holding unlevered equity can be replicated using homemade leverage by holding a portfolio of the firm s equity and debt. The return on unlevered equity (R U ) is related to the returns of levered equity (R E ) and debt (R D ): R = R + D ( R R ) E { U U D E R i s k w i t h o u t l e v e r a g e A d d i t i o n a l r i s k d u e t o l e v e r a g e E D R + R = R E + D E + D E D U The levered equity return equals the unlevered return, plus a premium due to leverage. The amount of the premium depends on the amount of leverage, measured by the firm s market value debt-equity ratio, D/E. MM Proposition II: The cost of capital of levered equity is equal to the cost of capital of unlevered equity plus a premium that is proportional to the market value debt-equity ratio. Note: Homemade leverage: when investors use leverage in their own portfolios to adjust the leverage choice made by the firm.

11 11 Example- Modigliani-Miller II Problem Suppose the entrepreneur in Alternative Example 14.1 borrows only \$700 when financing the project. Recall, the expected return on unlevered equity is 15% and the risk-free rate is 5%.According to MM Proposition II, what will be the firm s equity cost of capital? Because the firm s assets have a market value of \$1000, by MM Proposition I the equity will have a market value of \$300. \$700 r E = 15% + ( 15% 5% ) = 38.33% \$300 This result matches the expected return calculated in Example 14.1.

12 Capital Budgeting and the Weighted Average Cost of Capital If a firm is unlevered, all of the free cash flows generated by its assets are paid out to its equity holders If a firm is levered, project r A is equal to the firm s weighted average cost of capital. Unlevered Cost of Capital (pretax WACC) r wacc Fraction of Firm Value Equity Fraction of Firm Value Debt + Financed by Equity Cost of Capital Financed by Debt Cost of Capital E D = re + rd E + D E + D rwacc = ru = ra With no debt, the WACC is equal to the unlevered equity cost of capital. 12

13 13 WACC and Leverage with Perfect Capital Markets (a) Equity, debt, and weighted average costs of capital for different amounts of leverage. The rate of increase of rd and re, and thus the shape of the curves, depends on the characteristics of the firm s cash flows. (b) Calculating the WACC for alternative capital structures. Data in this table correspond to the example in Section 14.1.

14 14 Example-WACC Problem Honeywell International Inc. (HON) has a market debt-equity ratio of 0.5.Assume its current debt cost of capital is 6.5%, and its equity cost of capital is 14%. If HON issues equity and uses the proceeds to repay its debt and reduce its debt-equity ratio to 0.4, it will lower its debt cost of capital to 5.75%. With perfect capital markets, what effect will this transaction have on HON s equity cost of capital and WACC?

15 15 Alternative Example 14.5 (cont d) Solution Current WACC E D 2 1 rwacc = re + rd = 14% + 6.5% = 11.5% E + D E + D New Cost of Equity D re = ru + ( ru rd ) = 11.5% +.4(11.5% 5.75%) = 13.8% E New WACC 1.4 r NEWwacc = 13.8% % = 11.5% The cost of equity capital falls from 14% to 13.8% while the WACC is unchanged.

16 16 Levered and Unlevered Betas The effect of leverage on the risk of a firm s securities can also be expressed in terms of beta: Unlevered Beta β E D U = E D E D β + + E + D β A measure of the risk of a firm as if it did not have leverage, which is equivalent to the beta of the firm s assets.if you are trying to estimate the unlevered beta for an investment project, you should base your estimate on the unlevered betas of firms with comparable investments

17 17 Unlevered Beta Levered and Unlevered Betas A measure of the risk of a firm as if it did not have leverage, which is equivalent to the beta of the firm s assets. If you are trying to estimate the unlevered beta for an investment project, you should base your estimate on the unlevered betas of firms with comparable investments. D βe = βu + ( βu βd ) E Leverage amplifies the market risk of a firm s assets, β U, raising the market risk of its equity.

18 Example-Levered and Unlevered Betas 18

19 Example-Levered and Unlevered Betas 19

20 20 Example-Example-Levered and Unlevered Betas

21 21 Example-Example-Levered and Unlevered Betas

22 Modigliani-Miller II: Leverage, Risk, and the Cost of Capital Corporations must pay taxes on the income that they earn. Because they pay taxes after interest payments are deducted, interest expenses reduce the amount of corporate tax firms must pay.this creates an incentive in using debt fo finance the firm. In general the gain to investor from the tax deducibility of interest payments is referred to as the interest tax shield. Interest Tax Shield = Corporate Tax Rate x Interest Payments MM Proposition I with Taxes: The total value of the levered firm exceeds the value of the firm without leverage due to the present value of the tax savings from debt. L U V = V + PV (Interest Tax Shield)

23 The Interest Tax Shield with Permanent Debt Suppose a firm borrows debt D and keeps the debt permanently. If the firm s marginal tax rate is τ c, and if the debt is riskless with a risk-free interest rate r f, then the interest tax shield each year is τ c r f D, and the tax shield can be valued as a perpetuity. PV (Interest T ax Shield) τ c Interest = = r = τ c ( r D ) If the debt is fairly priced, no arbitrage implies that its market value must equal the present value of the future interest payments. Market Value of Debt = D = PV (Future Interest Payments) f D τ c r f f

24 The Interest Tax Shield with Permanent Debt If the firm s marginal tax rate is constant, then: PV (Interest Tax Shield) = PV ( τ Future Interest Payments) = τ c = τ c c PV (Future Interest Payments) D

25 The Weighted Average Cost of Capital with Taxes With tax-deductible interest, the effective after-tax borrowing rate is r(1 τ c ) and the weighted average cost of capital becomes E D rwacc = re + rd (1 τ c ) E + D E + D r = E wacc r D D E rd rd c E + D + E + D E + D τ Pretax WACC Reduction Due to Interest Tax Shield

26 The WACC with and without Corporate Taxes

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