Question

The EXES Company is assessing its present capital structure and that structure’s implications for the welfare of its investors. EXES is currently financed entirely with common stock, of which 1,000 shares are outstanding. Given the risk of the underlying cash flows (EBIT) generated by EXES, investors currently require a 20-percent return on the EXES common stock. The company pays out all earnings as dividends to common stockholders. EXES expects that for each year in the future operating income will be $1,000, $2,000, or $4,200 with respective probabilities of 0.1, 0.4, and 0.5. EXES is contemplating issuing $7,500 in bonds and using the proceeds to repurchase shares.

1. Suppose that the corporate tax rate is 40 percent and all personal income tax rates are zero. Calculate the value of the firm with and without the leverage.
2. Suppose that the corporate tax rate is 40 percent, the personal tax rate on interest income is 40 percent, and the effective tax rate on equity income (earnings) is zero. Calculate the value of the firm with and without leverage.

Answer 1

a) Statement showing value of unlevered firm

Particulars	Operating Income	Probability	Amount
EBIT	1000	0.1	100
	2000	0.4	800
	4200	0.5	2100
Expected EBIT			3000
Less tax @40%			1200
PAT			1800
Capitalization rate			20%
Value of unlevered firm			9000

Value of levered firm = Value of unlevered firm + (Debt*tax rate)
=9000 + (7500*40%)
=9000+3000
12000$

B)Value of unlevered firm remains the same ie 9000$

Value of levered firm = Value of unlevered firm + ([1-(1-corporate tax)(1- capital gains )/(1-personal tax)]*Debt)
=9000 + [1-(1-0.4)(1-0)/(1.04)]*7500
9000+[1-(1.04/1.04)]*7500
9000+[1-1]*7500
9000+(0*7500)
=9000$