Q1. a. Suppose you are given the following rates:
|
Maturity (Years)
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1
|
2
|
3
|
4
|
5
|
|
Zero-coupon YTM
|
30%
|
4.5%
|
4.5%
|
4.0%
|
3.5%
|
You want to lock in an interest rate for an investment that begins in one year and matures in five years. What rate (call this rate f1, 5) would you obtain if there are no arbitrage opportunities?
Q1. b. Suppose the yield on a one-year, zero-coupon bond is 6%. The forward rate for year 2 is 4%, and the forward rate for year 3 is 3%. What is the yield to maturity of a zero-coupon bond that matures in three years?
Q2. You are the financial vice-president of the e-mba.com Corporation. Management is questioning whether or not the existing capital structure is optimal so you have been asked to consider the possibility of issuing $1 million of additional debt and using the proceeds to repurchase stock. The following data reflects the current financial conditions of the e.mba.com Corporation:
Value of debt (book = market) $1,000,000
Market value of equity $5,257,143
Sales, last 12 months $12,000,000
Variable operating costs (50% of sales) $6,000,000
Fixed operating costs $5,000,000
Tax rate, T (federal-plus-state) 40%
At the current level of debt, the cost of debt is Kd, is 8 percent and the cost of equity Ke, is 10.5 percent. It is estimated that if the leverage were increased by raising the level of debt to $2 million, the interest rate on new debt would rise to 9 percent and the cost of equity would rise to 11.5 percent. The old 8 percent debt is senior to the new debt, and it would remain outstanding, continue to yield 8 percent, and have a market value of $1 million. The firm is a zero-growth firm, with all of its earnings paid out as dividends.
a. Should the firm increase its debt to $2 million?
Hint: Find the new value of the firm using the following equation: V = D + E = D + [{EBIT - Int) (1 - T)} Ke] and compare it with the existing value of the firm.
b. If the firm decided to increase its level of debt to $3 million, its cost of the additional $2 million of debt would be 12 percent and the Ke would rise to 15 percent. The original 8 percent of debt would again remain outstanding, and its market value would remain $1 million. What level of debt should the firm choose: $1 million, $2 million, or $3 million?
c. The market price of the firm's stock was originally $20 per share. Calculate the new equilibrium stock prices at debt levels of $2 million and $3 million. (Hint: Shares outstanding = Value of Equity / Price. Note that the repurchase price is the equilibrium price that would prevail after the repurchase transaction. Original shareholders would sell only at the price which incorporated any increased value resulting from the repurchase).
d. What would happen to the value of the old bonds if EMBA.com Corporation uses more leverage and the old bonds are not senior to the new bonds? What would happen to the value of equity? Explain.
Q3. Crocker Engine Co. is considering increasing the amount of debt in its capital structure. The treasurer is worried about the ramifications of that action on the firm's cost of funds. The following information may be relevant to your analysis.
- The company's capital structure is as follows (Figures are in book values):
Short-Term Bank Debt $ 6.2 million
Long - Term Bond 26.0
Preferred Stock 5.6
Common equity (8.60 million shares) 136.0
Total $173.8 million
- The bank debt is currently costing 8.2%.
- The bonds have a fixed 11% annual coupon, and mature in fourteen years. The price of the bonds is $109 (based on $100 par value).
- The preferred stock has 100 par value, pays an annual dividend of 6% of par, and is selling for $63 ¼ per share.
- The common stock is selling for $19 per share.
- The company's marginal tax rate is 34%
- The beta of the firm's stock, given its current capital structure, is 0.9.
- Treasury bonds are currently yielding 7.1%
- The market has historically earned 8.3% more than Treasury bonds.
If the company sells $10 million in bonds (at the prevailing market rate), and uses the proceeds to repurchase common stock, what will be Crocker's weighted-average cost of funds?
i) Use the Beta (Unlevered) = E/V x Beta (Levered) relationship.
ii) Treat preferred stock as debt when calculating the weight of equity (E/V) for un-levering and re-levering the Beta.
Q4. Do you agree or disagree with the following statements? Briefly explain why.
(a) "In a world of no corporate or personal taxes, no agency costs or information asymmetries, a lower dividend payout will reduce a firms' cost of capital."
(b) "Unlike new capital, which needs a stream of new dividends to service it, retained earnings have zero cost."
(c) "If a company repurchases stock instead of paying a dividend, the number of shares falls and earnings per shares rise. Thus stock repurchases must always be preferred to paying dividends."
Need all formulas written down, no Excel.