BFC3140 Corporate Finance 2 Week 02
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BFC3140 Corporate Finance 2
Week 02 Tutorial Answers - Capital Structure (Chapters 14 & 15)
Chapter 14
14-4. Wolfrum Technology (WT) has no debt. Its assets will be worth $476 million in one year if the
economy is strong, but only $262 million in one year if the economy is weak. Both events are equally likely. The market value today of its assets is $286 million.
a. What is the expected return of WT stock without leverage?
b. Suppose the risk-free interest rate is 5%. If WT borrows $93 million today at this rate and uses the proceeds to pay an immediate cash dividend, what will be the market value of its equity just after the dividend is paid, according to MM?
c. What is the expected return of WT stock after the dividend is paid in part (b)?
a. (0.5 × 476 + 0.5 × 262)/286 = 1.2902 29.02%
b. E + D = 286, D = 93 E = 193
c. (0.5 × (476 - 93 × 1.05) + 0.5 × (262 - 93 × 1.05))/193 = 1.4060 40.60%
14-6. Suppose Alpha Industries and Omega Technology have identical assets that generate identical cash
flows. Alpha Industries is an all-equity firm, with 10 million shares outstanding that trade for a price of $22 per share. Omega Technology has 20 million shares outstanding as well as debt of $60 million.
a. According to MM Proposition I, what is the stock price for Omega Technology?
b. Suppose Omega Technology stock currently trades for $11 per share. What arbitrage opportunity is available? What assumptions are necessary to exploit this opportunity?
a. V(Alpha) = 10 × 22 = 220m = V(Omega) = D + E E = 220 - 60 = 160m p = $8 per share.
b. According to MM, in perfect capital markets the value of Omega has to be equal to the value of Alpha (VL = VU). As Omega is overpriced, an arbitrage strategy can be conducted to exploit themispricing as follows:
Sell 20m Omega shares and borrow $60m
Buy 10mAlpha shares
And get total profit of 20*11 + 60 - 10*22 = $60m, or 60/20 = $3 per Omega share (consistent with the gap between the current price and the fair price: 11 - 8).
Assumes we can trade shares at current prices and that we can borrow at the same terms as Omega (or own Omega debt and can sell at same price).
14-12. Hardmon Enterprises is currently an all-equity firm with an expected return of 12%. It is
considering a leveraged recapitalization in which it would borrow and repurchase existing shares.
a. Suppose Hardmon borrows to the point that its debt-equity ratio is 0.50. With this amount of debt, the debt cost of capital is 5%. What will the expected return of equity be after this transaction?
b. Suppose instead Hardmon borrows to the point that its debt-equity ratio is 1.50. With this amount of debt, Hardmon’s debt will be much riskier. As a result, the debt cost of capital will be 7%. What will the expected return of equity be in this case?
c. A senior manager argues that it is in the best interest of the shareholders to choose the capital structure that leads to the highest expected return for the stock. How would you respond to this argument?
a. re = ru + d/e(ru – rd) = 12% + 0.50(12% – 5%) = 15.5%
b. re = 12% + 1.50(12% – 7%) = 19.5%
c. Returns are higher because risk is higher—the return fairly compensates for the risk. There is no free lunch.
Chapter 15
15-2. Grommit Engineering expects to have net income next year of $20.75 million and free cash flow of
$22.15 million. Grommit’s marginal corporate tax rate is 20%.
a. If Grommit increases leverage so that its interest expense rises by $1 million, how will its net income change?
b. For the same increase in interest expense, how will free cash flow change?
a. Net income will fall by the after-tax interest expense to $20.75 – (1× (1 − 0.20)) = $19.95 million.
b. Free cash flow is not affected by interest expenses.
15-6. Arnell Industries has just issued $10 million in debt (at par). The firm will pay interest only on this
debt. Arnell’s marginal tax rate is expected to be 21% for the foreseeable future.
a. Suppose Arnell pays interest of 6% per year on its debt. What is its annual interest tax shield?
b. What is the present value of the interest tax shield, assuming its risk is the same as the loan?
c. Suppose instead that the interest rate on the debt is 5%. What is the present value of the interest tax shield in this case?
a. Interest tax shield = $10 × 6% × 21% = $0.126 million
b. PV(Interest tax shield) = = $2.1 million
c. Interest tax shield = $10 ×5% ×21% = $0.105 million. PV = = $2.1 million.
15-19. Rally, Inc., is an all-equity firm with assets worth $25 billion and 10 billion shares outstanding. Rally
plans to borrow $10 billion and use these funds to repurchase shares. The firm’s corporate tax rate is 21%, and Rally plans to keep its outstanding debt equal to $10 billion permanently.
a. Without the increase in leverage, what would Rally’s share price be?
b. Suppose Rally offers $2.60 per share to repurchase its shares. Would shareholders sell for this price?
c. Suppose Rally offers $3.00 per share, and shareholders tender their shares at this price. What will Rally’s share price be after the repurchase?
d. What is the lowest price Rally can offer and have shareholders tender their shares? What will its stock price be after the share repurchase in that case?
a. Share price = 10(25) = $2.50 per share
b. When securities are fairly priced, the original shareholders of firm capture the full benefit of the interest tax shield from an increase in leverage. So the value of equity will rise by the PV of the tax shield on the increase in leverage, immediately upon the repurchase announcement.
VL = VU + PV (ITS) = 25 + 10* 21% = $27.1 billion
VE = SP * No. of shares SP = 27.1/10 = $2.71
Therefore, shareholders will not sell for $2.60 per share.
c. VL = VU + PV (ITS) = 25 + 10* 21% = $27.1 billion
VE = VL-VD=27. 1 - 10 = 17. 1 billion
Shares = 10 − 13(0) = 6.667 billion. Share price = 6166(7.1)7 = $2.565 share.
d. From (b), fair value of the shares prior to repurchase is $2.71. At this price, Rally will have 10 − 217(0)1 = 6.31 million shares outstanding, which will be worth 6(1)3(7.)1(1) = $2.71 after the repurchase. Therefore, shares will be willing to sell at this price.
2023-08-26
Tutorial Answers – Capital Structure