Question

Dye Trucking has no debt outstanding, and its financial position is given by the following data:Assets (Market Value)$4,875,000EBIT$900,000Cost of equity12%Stock Price$16.25Shares outstanding300,000Tax rate35%The firm is hoping to sell bonds and simultaneously repurchase some of its stock.If it moves to a capital structure with 30% debt based on market values, its cost of equity will increase to 13%to reflect the increased risk. Bonds can be sold at a cost of 9%. Dye Trucking is a no-growth firm. Hence, all its earnings are paid out as dividends. Earnings are expected to be constant over time.

i.What effect would this use of leverage have on the value of the firm?

ii.What would the price of the stock be after the repurchase?

iii.Compare the earnings per share of the unlevered scenario with the levered scenario (after the repurchase).

Answer 1

(i) Debt to be issued = 4,875,000 x 30%

= $1,462,500

Proceeds from the issue of debt will be used to repurchase common stock

Cost of debt = 9%

Interest on debt = 1,462,500 x 9%

= $131,625

Tax rate = 35%

Calculation of value of firm after debt issue

EBIT	900,000
Less: Interest on debt	- 131,625
EBT	768,375
Less: tax @35%	- 268,931
Earnings after tax (a)	499,444
Cost of equity (b)	13%
Market value of equity (a)/(b)	3,841,877

Market value of firm = Market value of equity + Market value of debt

= 3,841,877 + 1,462,500

= $5,304,377

Hence, market value of the firm will increse by = 5,304,377 - 4,875,000

= $429,377

(ii) Market value of equity after repurchase = $3,841,877

Debt proceeds = $1,462,500

Hence, number of shares repurchased = 1,462,500/16.25

= 90,000

Number of shares outstanding after repurchase = 300,000 - 90,000

= 210,000

Hence, price of stock after repurchase = 3,841,877/210,000

= $18.29

(iii) EPS (before repurchase) = {EBIT(1 - Tax rate)}/Number of shares

= {900,000(1 - 0.35)}/300,000

= 585,000/300,000

= $1.95

EPS (after repurchase) = Earnings after tax/Number of shares

= 499,444/210,000

= $2.38