Question

1. Unlevered (U) and Levered (L) are two forms identical in every way except for their capital structures.

U is an all equity firm has 15000 shares outstanding, currently worth $30/share.

L uses leverage. The market value of debt $65000 and the cost of debt is 9%. Each firm is expected to have earnings before interest of $75,000 in perpetuity. Neither firm pays taxes. Every investor can borrow at 9% a year.

1. What is the value of U and L?
2. What is the market value of L’s equity?
3. (iii)How much will it cost to buy 10% of each firm’s equity?
4. (iv)What will be the dollar return to each position in part (iii) over the next year?
5. Construct an investment strategy in which an investor buys 10% of U’s equity and replicated the cost and dollar return of purchasing 10% of L’s equity.
6. (vi)Is U’s equity more or less risky than L’s? explain.

Answer 1

a.

Since Unlevered Corporation is an all-equity firm, its value is equal to the market value of its outstanding shares. Unlevered has 15,000 shares of common stock outstanding, worth $30 per share, so the value of Unlevered Corporation is:

               V( Unlevered ) = 15,000($30) = $450,000

b.

Modigliani-Miller Proposition I states that in the absence of taxes, the value of a levered firm equals the value of an otherwise identical unlevered firm. Since Levered Corporation is identical to Unlevered Corporation in every way except its capital structure and neither firm pays taxes, the value of the two firms should be equal. So, the value of Levered Corporation is $450,000 as well.

c.

The value of a levered firm equals the market value of its debt plus the market value of its equity. So, the value of Levered’s equity is:

               VL= B + S

               $450,000 = $65,000 + S

               S = $385,000

d.

The investor would need to invest 10 percent of the total market value of Unlevered’s equity, which is:

               Amount to invest in Unlevered = .10($450,000) = $45,000

Levered has less equity outstanding, so to purchase 10 percent of Levered’s equity, the investor would need:

               Amount to invest in Beta = .10($385,000) = $38,500

e.

Unlevered has no interest payments, so the dollar return to an investor who owns 10 percent of the company’s equity would be:

               Dollar return on Alpha investment = .10($75,000) = $7,500

Levered Corporation has an interest payment due on its debt in the amount of:

               Interest on Levered’s debt = .09($65,000) = $5,850

               

So, the investor who owns 10 percent of the company would receive 10 percent of EBIT minus the interest expense, or:

               Dollar return on Levered investment= .10($75,000 – 5,850) = $6,915

        

f.   

From part d, we know the initial cost of purchasing 10 percent of Unlevered Corporation’s equity is $45,000, but the cost to an investor of purchasing 10 percent of Levered Corporation’s equity is only $38,500. In order to purchase $45,000 worth of Unlevered's equity using only $38,500 of his own money, the investor must borrow $6,500 to cover the difference. The investor will receive the same dollar return from the Unlevered investment, but will pay interest on the amount borrowed, so the net dollar return to the investment is:

               Net dollar return = $15,000 – .09($6,500) = $14,415

This amount exactly matches the dollar return to an investor who purchases 10 percent of Levered’s equity.

g.

The equity of Levered Corporation is riskier. Levered must pay off its debt holders before its equity holders receive any of the firm’s earnings. If the firm does not do particularly well, all of the firm’s earnings may be needed to repay its debt holders, and equity holders will receive nothing.