Question

One year estimates suggest that Mulligan Manufacturing (MM) has a 20% probability of being worth $100 million, a 50% probability of being worth $200 million, a 10% probability of being worth $330 million and a 20% probability of being worth $400 million. The firm has two discount bonds outstanding: a senior bond outstanding with a face value of $100 million and a promised rate of return of 5% and a junior bond outstanding with a face value of $40 million and a promised return of 20%. If the firms required rate of return its assets is 12%, then what is the firm’s levered cost of equity?

Answer 1

Given
20% probability of being worth $100 million
50% probability of being worth $200 million
10% probability of being worth $330 million
20% probability of being worth $400 million

Worth of company = (0.20 * 100) + (0.50 * 200) + (0.10 * 330) + (0.20 * 400)
= 233

Income After One Year (Estimated) = 233

Given
Outstanding Bonds (Debt Instrument used to get debt and cost of debt is RR)

Face Vale = 100
RR = 5%

Face Value = 40
RR = 20%

Total Debt = 100 + 40 = 140
Cost of Debt = (100/140 * 5%) + (40/140 * 20%)
= 9.286%

Given
Rate of return on asset = 12%
ROA = net income / total assets

Total Assets = 233/0.12 = 1941.6
Equity = Total asset = 1941.6
Debt = 140
Cost of equity (Umlevered) = E/E+D * ROA + D/E+D * Cost of Debt
=.9327 * .12 + .06725 * .09286
= 11.8175%

Levered Cost of Equity = Unlevered cost of equity + D/E(ROA - Cost of Debt)

= 11.8175% + 0.07210 * ( .12 - 0.09286)
= 12.013%