Question

Additional Information for All Question: Return on market is 10%, return on T-bills is 4%, and companies pay 40% corporate tax and 30% capital gains tax.

Greenleaf Inc. is a newly incorporated firm that requires $500 million in capital; and is raising capital through debt and equity only. The firm is comparing one of two options on capital raising.

Option A: The firm raises $200million through issuing bonds and $300 million through issuing 600,000 (0.6million) ordinary shares. Each bond offers a semi annual coupons of $26.0485, has a par value of $200, matures in 10 years, and offers a YTM of 10% to its investors. The firm is to offer an expected dividend of $0 at the end of the first year, and offers ordinary shareholders a return of 14.92% per year.

Option B: The firm raises a total of $500 million by issuing 1 million bonds and 500,000 (0.5million) ordinary shares. Each bond costs $250, offers semiannual coupons, has a par value of $200, matures in 10 years, and offer a YTM of 11% to its investors. Each ordinary share costs $500.

Q2. (a) All things being equal, does cost of debt or cost of equity cost more?

(b) When a firm increases its Debt/Equity ratio, how does its cost of debt, cost of equity and its beta change?

(C) Analyze options A and B Which of options A and B should be chosen by Greenleaf Inc.?

Answer 1

Q2. (a) All things being equal, does cost of debt or cost of equity cost more?

Debt is cheaper than equity. Further interest payments on debt are tax deductible. Hence, post tax cost of debt is even further lower. Lenders are assured of interest payments and repayments. They are secured. Hence, they have lesser risks than equity holders. As a result, they are available cheaper.

(b) When a firm increases its Debt/Equity ratio, how does its cost of debt, cost of equity and its beta change?

When a firm increases its Debt/Equity ratio,

• Cost of debt on the incremental debt increases. From the lender's perspective, the increasing leverage makes the incremental debt riskier and hence expensive.
• Cost of equity also increases with increasing leverage or with increasing proportion of debt in capital structure. Equity holders are residual claimants. They get what is left over. As debt levels in the firm increases, equity becomes riskier and hence cost of equity also increases.
• Beta increases with leverage. In fact beta measures the riskiness of the firm and specially the equity, it rises with rising proportion of debt in capital structure. In fact, it's increase in beta that increases the cost of equity on increase in leverage.

(C) Analyze options A and B Which of options A and B should be chosen by Greenleaf Inc.?

Cost of capital under option A = Wd x Kd x (1 - T) + We x Ke = 2/5 x 10% x (1 - 40%) + 3/5 x 14.92% = 11.352%

Ke = Rf + Beta x (Rm - Rf)

Hence, 14.92% = 4% + beta x (10% - 4%)

Hence, Beta = (14.92% - 4%) / (10% - 4%) = 1.82

Unlevered beta = Levered beta / [1 + (1 - T) x D/E] = 1.82 / [1 + (1 - 40%) x 2/3] = 1.30

Under Option A: D/E ratio = 250/250 = 1

Hence, levered beta under this capital structure = Unlevered beta x [1 + (1 - T) x D/E] = 1.30 x [1 + (1 - 40%) x 1] = 2.08

Hence, Ke = 4% + 2.08 x (110% - 4%) = 16.48%

Cost of capital under option B = 1/2 x 11% x (1 - 40%) + 1/2 x 16.48% = 11.54%

As cost of capital is lower under option A, hence the firm should choose option B for itself.