IKA is an all equity firm with perpetual EBIT of $45,000 per year. It has 6,000
ID: 2739971 • Letter: I
Question
IKA is an all equity firm with perpetual EBIT of $45,000 per year. It has 6,000 shares outstanding and shareholders have a required return of 9%. IKA is planning to recapitalize to debt-to-equity of 0.8 by borrowing at 4%. The tax rate is 30%.
a) What is the firm value before recapitalization?
b) Calculate the WACC after the recapitalization.
c) Using the WACC in part b), calculate the firm value.
d) Using FTE method, calculate the equity value after the recapitalization.
e) How much debt does IKA borrow? What is the PV of tax shield?
Explanation / Answer
EBIT $45,000 Cost of capital 9.00% Tax Rate 30.00% Free cash flow = EBIT x (1-30%) $31,500 a)Firm value before recapitalisation = FCF/cost of capital = $31,500/9% $350,000 b) Weights calculated below Cost of Capital WACC Equity 55.56% 9.00% 5.00% Debt (cost of capital after tax )= 4% x (1-30%) 44.44% 2.80% 1.24% Total 6.24% WACC after recapitalization 6.24% The problem does not provide either debt-to-value ratio or equity-to-value ratio. However, the firm’s debt-to-equity ratio of 80% is given, which can be written algebraically as: B / S = 80% ; Solving for B = 80%S A firm’s debt-to-value ratio is: B / (B+S) = 80%S/80%S + S 44.44% A firm’s equity-to-value ratio is: 1- debt to value 55.56% c. Firm value = FCF/cost of capital = $31,500/6.24% $504,448.4 d) FTE method, calculate the equity value after the recapitalization rS = r0 + (B/S)(r0 – rB)(1 – TC) r0 = the required return on the equity of an unlevered firm 9.00% rS = the required return on the equity of a levered firm rB = the pre-tax cost of debt 4.00% TC = the corporate tax rate 30.00% B/S = the firm’s debt-to-equity ratio 0.80% rS = 9%+.80%X(9%-4%)*(1-30%) 9.03% The firm’s equity-to-value ratio is 55.56%, the value of equity = $504,448.40 x 55.56% $280,249.11 The firm’s debt-to-value ratio is 44.44%, the value of debt = $504,448.40 x 44.44% $224,199.29 Interest on debt 4% = $224,199.29 x 4% $8,967.97 Cash Flows Available to Equity Holders $215,231.32 Using the Flow-to-Equity approach, discount the cash flows available to equity holders at the cost of the firm’s levered equity (rS Equity (S) = Cash Flows Available to Equity Holders / rS $2,384,042.06 e) Debt calculated above $224,199.29 Present value of Tax shield Annual value of tax Shield = 30% x $8,967.97 $2,690.39 Present value of Tax shield = $2,690.39/4% $67,259.79