Question

The A. J. Croft Company (AJC) currently has $200,000 market value (and book value) of perpetual debt outstanding carrying a coupon rate of 6 percent. Its earnings before interest and taxes (EBIT) are $100,000, and it is a zero-growth company. AJC's current unlevered beta is 0.5, and its tax rate is 40 percent. The firm has 10,000 shares of common stock outstanding selling at a price per share of $60.00.

The firm is considering moving to a capital structure that is comprised of 40 percent debt and 60 percent equity, based on market values. The new funds would be used to replace the old debt and to repurchase stock. It is estimated that the increase in riskiness resulting from the leverage increase would cause the required rate of return on debt to rise to 7 percent. The risk free rate is 6 percent and the market risk premium is 5 percent.

1. If this restructuring plan were carried out, what would be AJC’s new levered beta and new cost of equity?
2. What would be AJC's new WACC and total corporate value?
3. What would be its new total market value of debt and total market value of equity respectively?
4. What would be its new stock price per share?
5. How many shares would AJC repurchase in the recapitalization?
6. Should AJC make the capital structure change?

Answer 1

1). Bu (unlevered beta) = 0.50; New D/E = 40/60 = 0.6667; Tax rate = 40%

Bl (new levered beta) = Bu*(1+(1-Tax rate)*D/E) = 0.5*(1+(1-40%)*0.6667) = 0.70

New cost of equity (using CAPM) (Rsl) = risk-free rate + beta*market risk premium = 6%+(0.70*5%) = 9.50%

New cost of debt (Rd) = 7%

2). New WACC = (Weight of debt*Rd*(1-Tax rate)) + (Weight of equity*Rsl)

= (40%*7%*(1-40%))+(60%*9.50%) = 7.38%

Total corporate value (or firm value) (Vl) = EBIT*(1-Tax rate)/WACC = 100,000*(1-40%)/7.38% = 813,008.13

3). Market value of equity = weight of equity*Vl = 60%*813,008.13 = 487,804.88

Market value of debt = weight of debt*Vl = 40%*813,008.13 = 325,203.25

4). New stock price = (value of equity + change in debt)/shares outstanding

= (487,804.88 + (325,203,25-200,000))/10,000 = $61.30 per share

5). Share repurchased = debt amount used to repurchase stock/new share price = (new debt value - old debt value)/new share price

= (325,203.25-200,000)/61.30 = 2,042.44 or 2,042 shares

6). The new capital structure change can be made as it results in increase in firm value.