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 and how many shares would AJC repurchase in the recapitalization?

Answer 1

A. If this restructuring plan were carried out, what would be AJC’s new levered beta and new cost of equity?

Levered beta

Note: AJC's current unlevered beta is 0.5, and its tax rate is 40 percent. Capital structure that is comprised of 40 percent debt and 60 percent equity.

= Unlevered beta * ( 1 + (1 - tax rate) * (debt / equity) )

= 0.5 * ( 1+ (1- 0.4) * ( 0.4 / 0.6 ) )

= 0.7

Cost of equity:

Note: The risk free rate is 6 percent and the market risk premium is 5 percent. Required debt cost is 7%.

Re = Rf + beta * ( Rm- Rf )

Re = Rf + B( Risk premium )

= 6% + 0.7(5%)

= 9.5%

B. What would be AJC's new WACC and total corporate value?

WACC

= Cost of debt * Weight of debt * (1 - tax rate) + Cost of equity * weight of equity

= 7% * 0.40 * (1- 0.40) + 9.5% * 0.60

= 7.38%

Corporate Value

= EBIT (1 - tax rate) / WACC

= 100000 ( 1- 0.40) / 7.38%

= 60,000 / 0.0738

= 813,008.13

C. What would be its new total market value of debt and total market value of equity respectively?

Debt value

= Value of firm * 0.40

= 325,203.25

Equity value

= value of firm * 0.60

= 813,008.13 * 0.60

= 487,804.88

D. What would be its new stock price per share and how many shares would AJC repurchase in the recapitalization?

New stock price per share

= (Value of equity + change in debt) / original number of shares

= ( 487804.88 + (325203.25 - 200000) ) / 10000

= 61.3

How many shares would AJC repurchase in the recapitalization:

= Existing number of shares - (Value of equity / New price per share)

= 10000 - (487804.88 / 61.3)

= 10000 - 7958

= 2024