Question

Two firms, U and L, are identical except for their capital structure. Both will earn $100 in a boom and $50 in a slump. There is a 50% chance of each event. U is entirely equity-financed, and therefore shareholders receive the entire income. Its shares are valued at $1000. L has issued $600 of risk-free debt at an interest rate of 10%. There are no taxes or other market imperfections. Assume that, investors can borrow and lend at the risk-free rate of interest.

a. What is the value of L’s stock?

b. Show that MM’s proposition II with no taxes hold.

Answer 1

Answer :

(a.) Calculation of Value of L's Stock :

As Firms are identical but there capital structure are dfferent , and there are no taxes or other market imperfections,

Value of Stock L = 1000 - 600

= $400

(b.)  MM’s proposition II with no taxes hold.

Return on Equity = Return on Assets + [(Debt / Equity) * (Return on Assets - Cost of Debt)]

Calculation of Return on Assets = Net Income / Total Assets(Invested Capital)

= [(100 * 0.50) + (50 * 0.50)] / 1000

= [50 + 25] / 1000

= 75 / 1000

= 7.5%

Therefore return on Assets is same for Firm U and L

For L expected Return on Equity = [Expected (EBIT - Interest)] / Equity value

= {[(100 - 60) * 0.50] + [(50 - 60) * 0.50]} / 400

= (20 - 5) / 400

= 3.75%

Now as per MM’s proposition II

Return on Equity = 7.5% + [(600 / 400) * (7.5% - 10%)]

= 7.5 % - 3.75%

= 3.75%