Question

Company "Boats" Ltd. has no debt and its total market value is $ 2M. The profit before interest and tax (EBIT) is expected to be either $50,000 during a recession, $150,000 during normal times, and $300,000 in an expansion period. "Boats" is considering issuing $500K debt at 4% interest. With the amount raised, the company intends to buy back shares from the public. There are currently 50,000 shares outstanding. Ignore taxes and assume that EPS is paid as a dividend to shareholders.

A. Calculate the Company's earnings per share (EPS) under each of the three possible states of the economy, both before and after the issuance of the debt.

B. Assuming that the probability of ending up in a recession or expansion is each 25% and the probability of ending up in normal times is 50%, what is the return on equity capital if the firm decides to take on debt? What is the WACC in such a situation?

C. Mr. Smith had planned to buy 200 shares of “Boats” when it was an all equity firm; however, in the meantime the company issued debt and Mr. Smith does not want to bear the added risk. What can Mr. Smith do in order to receive the same payoff as he would have received if Boats was still an all equity firm? Provide complete numerical calculation and show that payoff is the same.

Answer 1

Solution:

Answering first two sub-question as per Chegg's guidelines:

A.Calculation of EPS:

EPS=EBIT/No. of shares outstanding

i)During recession:

EPS=$50,000/50,000

=$1

ii)During normal times

EPS=$150,000/50,000

=$3

iii)During expansion period

EPS=$300,000/50,000

=$6

Bi)Calculation of return on equity:

If the company decides to take on debt,Net income is:

=[EBIT under recession*Probability+EBIT under normal times*Probability+EBIT under expansion*Probability]-interest on debt

=[$50,000*0.25+$150,000*0.25+$300,000*0.25]-[$500,000*0.04]

=$180,000

Return on equity=Net Income/Shareholders' equity

=$180,000/$2000,000

=0.09 or 9%

ii)Calculation of WACC

Total Capital=Equity value+Debt value

=$2000,000+$500,000

=$2500,000

Assuming return on equity as cost of equity,WACC is;

=(Cost of equity*Equity value/Total capital)+(Cost of debt*Debt value/Total capital)

=(9%*$2000,000/$2500,000)+(4%*$500,000/$2500,000)

=8%