Question

Xerxes Manufacturing has 20 million shares outstanding with price 32. It has no debt. After-tax return on equity is 15%. In order to increase return on equity, it borrows x and uses it to repurchase shares. It pays 6% interest on the loan. Xerxes’s corporate tax rate is 25%. Calculate the amount to borrow so that after-tax return on equity is 20%.

Answer 1

Equity sharecapital = 20 Million shares * 32 = 640 Million

ROE = 15%

	Amount
EAT	96,000,000.00	15%*640,000,000
Tax	32,000,000.00	96000000 * 25/75
EBIT	128,000,000.00	EAT - Tax

Let x be the sum borrowed and interest = 6% of x = 0.06x

Equity sharecapital after repurchase would be 640 Million - Loan x = 640 - X

ROE = Profit after tax / Equity share capital

(EBIT - Interest - Tax)/Equity sharecapital = ROE

(128Million - 0.06x) * (1 - 0.25) / (640-x) = 0.20

(96 - 0.045x) / (640-x) = 0.20

(96 - 0.045x) = 0.20 (640-x)

- 0.045x + 0.20 x = 128 - 96

0.155x = 32 M

x = 32 M/0.155 = 206.45 M

Loan amount = 206.45

Answer: Amount to be borrowed to repurchase loan = 206.45

validation

Interest = 12.387 M

EAT = ( 128 - 12.387 ) * .75 = 86.71

Equity share capital = (640-206.45) = 433.55

ROE = 86.71/433.55 *100

ROE = 20%