Michaely Inc. is an all-equity firm with 100,000 shares outstanding. It has $500
ID: 2753725 • Letter: M
Question
Michaely Inc. is an all-equity firm with 100,000 shares outstanding. It has $500,000 of EBIT, which is expected to remain constant in the future. The company pays out all of its earnings, so earnings per share (EPS) equal dividends per shares (DPS). Michaely's current stock price is $30.00 and its marginal tax rate is 40%.
The company is considering issuing $600,000 of debt at an annual before-tax cost of 10 percent and using the proceeds from the debt issue to repurchase stock. The risk-free rate is 5.5%, the market risk premium is 5.0%, and the firm's beta is currently 0.90, but the CFO believes beta would rise to 1.20 if the recapitalization occurs.
What would the stock price be following (or after) the recapitalization?
$33.00
$30.00
$28.70
$26.40
$22.96
a.$33.00
b.$30.00
c.$28.70
d.$26.40
e.$22.96
Explanation / Answer
EPS of the Michaely Inc = Total Earnings/ No. of shares ...............(1)
EBIT of the firm = $500,000
In the $600,000 debt on 10% I (interest) would be equal to 600,00 *0.1= $60,000 .
Hence EBT of the firm = $500,000-$60,000 = $440,000
Taking marginal tax rate at 40% we get after tax earnings,
EAT= $440,000x(1-0.4) = $264,000
Hence from equation (1) the EPS of the firm = $264,000/100,000= 2.64 which is also equal to dividend per share (D) in this case.
As per CAPM model, the required rate of return for Michaely Inc-
R = Rf + b (Rm -Rf), where R = Required rate of return, Rf= Risk free return & Rm -Rf =Risk premium, b = Beta
Putting values in above equation we get required rate of return
R = 0.055+ 0.05*1.2 = 0.115 = 11.5%
As per CAPM the share price is present value of the stream of expected future dividends or
V = D/R, where V = stock value, D = Dividend and R = Required rate of return
putting the values we get the new share price
V = 2.64/0.115 = $22.96