Question

Assume that two firms, U and L, are identical in all respects except for one: Firm U is debt-free, whereas Firm L has a capital structure that is 50% debt and 50% equity by market value. Further suppose that the assumptions of M&M's "irrelevance" Proposition I hold (no taxes or transaction costs, no bankruptcy costs, etc.) and that each firm will have income before interest and taxes of $800,000.

If the required return on assets, rA, for these firms is 12.5% and if the risk-free debt yields 5%. calculate the following values for both Firm U and Firm L: (1) total firm value, (2) market value of debt and equity, and (3) required return on equity.

Now, recompute these values while assuming that the market mistakenly assigns Firm L's equity a required return of 15%, and describe the arbitrage operation that will force Firm L's valuation back into equilibrium.

Answer 1

The market value of Firm U which does not have debt
Ve = Earnings before interest and tax/K0
800000/0.125	6400000
Market value of Firm U = $6400000
Return On Equity = 12.5%
Firm L
Total Firm Value = 800000/0.125	6400000
Firm's market value of Equity = Total firm value - Debt
Assuming debt is 32 lacs
6400000-3200000	3200000
Required return on equity = 12.50% +(12.50%-5%)
20%

The arbitrage operation would work that investors would buy the share in the market and later sell due to higher return of equity which will bring equilbrium in the market