Question

Kido Corp. currently has 35 million common stocks each trading at $24. Moreover, it has 1 million, 2.947%

coupon, 10 year bonds ($1000 par) each trading at 84. Interest is paid annually. The management wants to

change the firm’s capital structure by either changing the debt-to-equity ratio to:

(i) 0.43 by selling more stocks and paying off debt or

(ii) 2.33 by issuing more debt and do stock repurchase

More Information:

Current beta is 1.5

The risk free rate is 2.5%

Market risk premium is 10%.

Corporate tax rate is 40%.

The current cost of debt (before tax) is 5%.

If the debt-to-equity ratio changes to 0.43, the cost of debt (before tax) will be 3%.

If the debt-to-equity ratio is 2.33, the cost of debt (before tax) will be 8%.

Find the following:

a) What is the firm’s WACC at current debt-to-equity ratio?

b) What is the firm’s WACC using debt-to-equity ratio of 0.43?

c) What is the firm’s WACC using debt-to-equity ratio of 2.33?

d) What is the optimal capital structure and why?

Answer 1

Part (a)

D = P x N = 84% x 1,000 x 1 million = 840 million

E = P x N = 24 x 35 million = 840 million

Wd = Proportion of debt in capital structure = D / (D + E) = 840 / (840 + 840) = 0.5

We = 1 - Wd = 1 - 0.5 = 0.5

Kd = 5%; Tax rate, T = 40%; Ke = Rf + beta x Rmp = 2.5% + 1.5 x 10% = 17.5%

Hence, the firm’s WACC at current debt-to-equity ratio = Wd x Kd x (1 - T) + We x Ke = 0.5 x 5% x (1 - 40%) + 0.5 x 17.5% = 10.25%

Part (b)

D/E₀ = Earlier debt to equity ratio = 840 / 840 = 1

D/E₁ = Debt to equity ratio now = 0.43

Unlevered beta = Bu = Levered beta / [1 + D/E₀ x (1 - T)] = 1.5 / [1 + 1 x (1 - 40%)] = 0.9375

Levered beta = Unlevered beta x [1 +  D/E₁ x (1 - T)] = 0.9375 x [1 + 0.43 x (1 - 40%)] = 1.1794

Ke = Rf + beta x Rmp = 2.5% + 1.1794 x 10% = 14.29%

Kd = 3%

Wd = D / (D + E) = 0.43 / (0.43 + 1) = 0.3007

We = 1 - Wd = 1 - 0.3007 = 0.6993

Hence, WACC = = Wd x Kd x (1 - T) + We x Ke = 0.3007 x 3% x (1 - 40%) + 0.6993 x 14.29% = 10.54%

Part (c)

D/E₀ = Earlier debt to equity ratio = 840 / 840 = 1

D/E₂ = Debt to equity ratio now = 2.33

Unlevered beta = Bu = Levered beta / [1 + D/E₀ x (1 - T)] = 1.5 / [1 + 1 x (1 - 40%)] = 0.9375

Levered beta = Unlevered beta x [1 +  D/E₂ x (1 - T)] = 0.9375 x [1 + 2.33 x (1 - 40%)] = 2.2481

Ke = Rf + beta x Rmp = 2.5% + 2.2481 x 10% = 24.98%

Kd = 8%

Wd = D / (D + E) = 2.33 / (2.33 + 1) = 0.6997

We = 1 - Wd = 1 - 0.6997 = 0.3003

Hence, WACC = = Wd x Kd x (1 - T) + We x Ke = 0.6997 x 8% x (1 - 40%) + 0.3003 x 24.98% = 10.86%

Part (d)

WACC was least in part (a) i.e. under the current capital structure (D/E = 1). Hence the optimal capital structure is the current (existing) capital structure of debt / equity ratio of 1