M&M II with taxes; no bankruptcy costs Lecture 19 M&M II with taxes; no bankruptcy costs

Topics covered Assumptions General interpretation Formulae Implications Graph Numerical example Practice problem with check answer

Assumptions Perfect market No bankruptcy costs Going concern

General Interpretation of M&M II with taxes Cost of equity of a levered firm depends on the cost of unlevered capital (RU), cost of debt (RD), financial leverage (D/E ratio), and marginal corporate tax rate (TC). A firm’s weighted cost of capital (WACC) will be reduced by the interest tax shields.

Formulae Cost of equity: RE = RU + [(RU – RD) x (D/E) x (1 - TC)] WACC: WACC = [(E/V) x RE] + [(D/V) x RD x (1 - TC)]

Variables defined RE = Cost of equity RU = Cost of capital for an unlevered firm = WACCU = Cost of equity on unlevered firm (REU) RD = Cost of debt (assumed to be constant) D = $ amount of debt E = $ amount of equity D/E = Debt-equity ratio TC = Marginal corporate tax rate V = Total asset value of the firm = D + E E/V = Weight of equity in the capital structure D/V = Weight of debt in the capital structure

Implications Cost of equity goes up as financial leverage goes up. D/E => RE Risk of equity depends on business risk and financial risk. E = A(1 + D/E) WACC goes down as financial leverage goes up. D/E => WACC

Graph Cost of capital (R) RE RU WACC RD (1 – TC) D/E

Numerical example ABC Inc. and XYZ Co. are identical except for their financing policy. ABC is financed with all equity, whereas XYZ has $1,000,000 in debt financing. Both firms have earnings before interest and taxes of $500,000, and both are subject 35% corporate tax rate. ABC’s cost of capital is estimated to be 18%. Cost of debt is 9%. By using M&M I with taxes, we obtain the following: Value of unlevered firm: VU = $1,805,555.56 Value of levered firm: VL = $2,155,555.56 Value of levered firm’s equity: EL = $1,155,555.56 a. What is ABC’s cost of equity? b. What is XYZ’s cost of equity? c. Compare the two firms’ cost of equity. Which one is higher? d. What is ABC’s weighted average cost of capital? e. What is XYZ’s weighted average cost of capital? f. Compare the two firms’ WACC. Which one is lower?

Numerical example (cont.) Information given: D = $1,000,000 EBIT = $500,000 TC = 0.35 RU = 0.18 RD = 0.09 Value of unlevered firm: VU = $1,805,555.56 Value of levered firm: VL = $2,155,555.56 Value of levered firm’s equity: EL = $1,155,555.56

Numerical example (cont.) We have the following information: RE = 0.230625 RD = 0.09 TC = 0.35 D = $1,000,000 Value of unlevered firm: VU = $1,805,555.56 Value of levered firm: VL = $2,155,555.56 Value of levered firm’s equity: EL = $1,155,555.56

The road to finance heaven… We have two firms, Firm U and Firm L, that are identical in every respect except for their financing policy. Firm U has zero debt, and its assets have an estimated value of $10 million. Firm L is partly financed with debt at an interest rate of 8%, and its assets have an estimated value of $12.5 million. Given that both firms are subject to a corporate tax rate of 40%, and both have an EBIT of $2 million. Using M&M Proposition I with taxes, we find the cost of capital of Firm U is 12% and debt-equity ratio is 1. a. What is the cost of equity for Firm U? b. What is the cost of equity for Firm L? c. What is the WACC for Firm L? d. Is the cost of equity higher or lower for Firm L? e. Is the WACC higher or lower for Firm L?

Check answer Information given: VU = $10,000,000 VL = $12,500,000 RD = 0.08 TC = 0.4 EBIT = $2,000,000 RU = 0.12 D/E = 1 a. Firm U’s Cost of equity = RU = 0.12 b. Firm L’s Cost of equity = RE = RU + [(RU - RD) x (D/E) x (1 - TC)] = 0.12 + [(0.12 - 0.08) x 1 x (1 – 0.4)] = 0.12 + 0.024 = 0.144

Check answer (cont.) c. Information needed to calculate Firm L’s WACC are: RD = 0.08 TC = 0.4 RU = 0.12 D/E = 1 RE = 0.144 We can use D/E to find the capital structure weights: For every dollar of debt, there is one dollar of equity. Therefore, if we imagine the total assets are made up of two parts, then the weight on debt is ½ and the weight on equity is also ½: D/V = E/V = 0.5 WACC is then calculated as: WACC = [(E/V) x RE] + [(D/V) x RD x (1 - TC)] = [0.5 x 0.144] + [0.5 x 0.08 x (1 - 0.4)] = 0.072 + 0.024 = 0.096 d. Cost of equity of 0.144 for Firm L is higher than the cost of equity for Firm U (0.12). e. WACC for Firm L (0.096) is lower than the WACC for Firm U (0.12).

End of Lecture 19: M&M II with taxes No bankruptcy costs