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 cost of equity is 8.8 percent, 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.

1. What is AJC's current total market value and weighted average cost of capital?
2. 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, while the required rate of return on equity would increase to 9.5 percent. If this plan were carried out, what would be AJC's new WACC and total value?
3. Now assume that AJC is considering changing from its original capital structure to a new capital structure with 50 percent debt and 50 percent equity. If it makes this change, its resulting market value would be $820,000. What would be its new stock price per share?
4. Now assume that AJC is considering changing from its original capital structure to a new capital structure that results in a stock price of $64 per share. The resulting capital structure would have a $336,000 total market value of equity and $504,000 market value of debt. How many shares would AJC repurchase in the recapitalization?

Answer 1

1. current market value = $800000, WACC = 7.5%
2. new WACC = 7.38%, Total value of firm = $ 813,008.13
3. stock price per share = $62.00
4. 4750 shares

Step-by-step explanation:

1) Calculate AJC's current total market value and weighted average cost of capital

current market value = value of equity + value of debt

= ( 10000 * $60 ) + $200000

= $800000

Weighted average cost of capital = ( weight of equity * cost of equity ) + ( weight of debt * cost of debt * ( 1 - tax rate )

= (75% * 8.8% ) + (25% * 6% * 0.6 ) = 7.5%

2) what would be AJC's new WACC and total value

WACC = ( weight of equity * cost of equity ) + ( weight of debt * cost of debt * ( 1 - tax rate )

= ( 60% * 9.5% ) + ( 40% * 7% * 0.6 ) = 7.38%

Total value of the firm =

= ( Cash flow after tax / WACC )

= (( 100000 * ( 1-40%)) / 7.38%

= 100000 * 0.6 / 7.38% = $ 813,008.13

3) Calculate the new stock price per share

new stock price = ( value of equity + change in debt ) / original number of outstanding shares

value of equity = weight of equity * firm value

change in debt =( weight of debt * firm value ) - initial debt value

Hence new stock price =

( 50% *$820000) + (( 50% * $820000)- $200000)) / 10000

= $62.00

4) calculate how many shares AJC would repurchase in the recapitalization

= original shares - Remaining shares

= 10000 - 5250 = 4750 shares

while ;

Remaining shares = value of equity / stock price = $336000 / $64 = 5250

original shares = 10000