E Risk of cash flow to shareholders WACC R A EV R E DV R D 1 TC Case 1 No

E risk of cash flow to shareholders wacc r a ev r e

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E Risk of cash flow to shareholders WACC = R A = (E/V) R E + (D/V) R D (1-T C ) Case 1: No corporate/personal taxes, no bankruptcy costs Proposition I The value of the firm is NOT affected by changes in the capital structure The cash flows of the firm do not change, therefore value doesn’t change Proposition II The WACC of the firm is NOT affected by capital structure
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54 Example of Case 1 Data Required return on assets = 16%, cost of debt = 10%; percent of debt = 45% What is the cost of equity? R E = R A + (R A R D ) x (D/E) = 0.16 + (0.16 0.10) x (0.45/0.55) = 0.2091 = 20.91% Suppose instead that the cost of equity is 25%, what is the debt-to-equity ratio? D/E = (R E R A ) / (R A R D ) = (0.25 0.16) / (0.16 0.10) = 1.5 Based on this information, what is the percent of equity in the firm? E/V = 1 / 2.5 = 0.40% Comparison of the different capital structures Scenario 1: R E = 0.2091, R D = 0.10 o D/E = 0.45/0.55 = 0.8182 o WACC = 0.55(0.2091) + 0.45(0.10) = 0.1600 Scenario 2: R E = 0.25, R D = 0.10 o New D/E = 1.5 o WACC = 0.40(0.25) + 0.60(0.10) = 0.16 Note: R A or WACC does not change despite R E increasing, R E merely changes the capital structure. Case 2: Corporate taxes (no personal taxes), no bankruptcy costs Interest is tax deductible o Therefore, when a firm adds debt, it reduces taxes, all else equal o The reduction in taxes increases the cash flow of the firm Interest Tax Shield Illustration Suppose Firm U and L have the same operations and assets but Firm L issued $1,000 worth of perpetual bonds on which is pays 8% interest annually. Also assume corporate tax rate is 30%. Firm (Unlevered) Firm (Levered) EBIT $1,000 $1,000 Interest 0 80 Taxable Income $1,000 $920 Tax (30%) (300) (276) Net Income $700 $644 Cash Flow from Assets Firm (Unlevered) Firm (Levered) EBIT $1,000 $1,000 Tax (30%) (300) (276) Total $700 $724 To stockholders $700 $644 To bondholders 0 80 Total $700 $724 Total cash flows to Firm L is higher
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55 Proposition I PV (Interest Tax Shield) = (T C x D x R D ) / R D = T C x D Explanation o Every year, the interest tax shield will cause Firm L’s cash flow to be $24 greater than Firm U. o Therefore, the tax shield generated by paying interest has the same risk as the debt and 8% (Cost of debt) is the appropriate discount rate. o PV (Interest Tax Shield) = $24 / 0.08 = [(0.30 x $1,000 x 0.08)] / 0.08 = $300 𝑉 ? = ??𝐼? × (1 − ? ? ) ? ? = $ 700 0.1 = $7,000 ?ℎ??? ? ? 𝑖? ?ℎ? ????????? ???? ?? ???𝑖??? (???????) 𝑉 ? = 𝑉 ? + (? × ? ? ) = $7,000 + (1,000 × 0.3) = $7,300 Hence, we can see that: o V Levered = V Unlevered + PV (Interest Tax Shield) o V L = V U + (T C x D) o Value of the firm increases as total debt increases because of the interest tax shield. Proposition II From Proposition I under the given assumptions, we can conclude that the best capital structure is 100% debt by examining the WACC. o WACC = (E/V) x R E + (D/V) x R D x (1 T C ) o R E = R U + (R U R D ) x (D/E) x (1 T c ) Example Previously, we established that V L = $7,300. Therefore, equity must be worth $7,300 1,000 = $6,300. For Firm L, the cost of equity is thus: R E = 0.10 + (0.10 0.08) x ($1,000/6,3000) x (1 0.3) = 0.1022 = 10.22% WACC = ($6,300 / 7,300) x 10.22% + (1,000 / 7,300) x 8% x (1 0.30) = 0.096 = 9.6% Without debt, WACC is over 10%. With debt, it is 9.6%. Hence, the firm is better off with debt.
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