AFM 372 Fall 2006 Key Midterm Examination

I. Multiple choice questions: Circle one answer that is the best. (2.5 points each)

1. A bond issued by Owers Divestiture Corporation on July 1, 2005 has the following features: face value $1,000, annual interest rate of 8%, maturity date July 1, 2010, semi-annual interest payments on July 1 and January 1 each year. How much is the accrued interest if an investor buys the bond on Sept. 1, 2006?

A) $13.33 B) $26.67 C) $40.00 D) $80.00 E) $120.00

1. Answer: A. Accrued interest on Sept 1 = (.08/12) (2) (1000) = $13.33

Use the information below to answer questions 2 and 3: The shareholders of the Unicorn Company need to elect five new directors. There are one million shares outstanding.

2. At least how many shares should you own to be certain that you can elect two directors if the company has straight voting?

A) 500,001 B) 500,000 C) 1 million D) 333,334 E) 166,667

3. At least how many shares should you own to be certain that you can elect one director if the company has cumulative voting?

A) 500,001 B) 500,000 C) 1 million D) 333,334 E) 166,667

4. Consider two corporations, G and H, that have exactly the same risk. They both have a current price of $60. Corporation G pays no dividend and will have a price of $66 one year from now. Corporation H pays dividends and will have a price of $63 one year from now after payment of a dividend. Corporations pay no income taxes. Investors pay no taxes on capital gains, but they pay a 30% income tax on dividends. What is the value of the dividend that investors expect Corporation B to pay?

A) $4.29 (66-60)/60 = 10% = [63 + X(1-.3)]/60 -1 Æ X = 4.29 B) $3.00 C) $3.15 D) $3.30 E) It is impossible to calculate expected dividend without the discount rate.

5. may exist because:

A) losses before income taxes prevent a company from enjoying the tax advantages of debt interest while none exist for preferred dividends. B) an advantage exists for the firm; preferred shareholders can not force the company into bankruptcy because of unpaid dividends. C) corporations get a tax exemption on preferred dividends received. D) all of the above. E) none of the above.

1 6.A firm has a debt-to-equity ratio of 1.20. If it had no debt, its cost of equity would be 15%. Its cost of debt is 10%. What is its cost of equity if there are no taxes or other imperfections?

A) 21%. B) 18%. C) 15%. D) 10%. E) None of the above. R_0 = r_0 + B/S (r_0 – r_B) = .15 + 1.2 (.15-.10) = .21

7. The pecking-order theory of is at odds with the tradeoff theory of capital structure in that pecking-order theory says

A) There should be no target book/equity ratio. B) Profitable firms should use less debt. C) One should take advantage of of debt. D) Both A) and B). E) Both B) and C).

8. Your aunt is in a high tax bracket and would like to minimize the tax burden of her investment portfolio which is subject to high taxes. She is willing to buy and sell in order to maximize her after-tax returns and she has asked for your advice. There are several choices for her: i). Buy high dividend yield because high dividend stocks are safer with cash in hand. ii) Buy low dividend yield stocks to avoid paying high taxes on dividends. iii) Sell low dividend yield stocks because those stocks tend to be overpriced. iv) Move high dividend yield stocks that are currently in her portfolio to a tax-deferred account such as retirement account.

You think she should do:

A) Both i) and ii). B) Both ii) and iv). C) i) only. D) Both i) and iii).

9. A firm commitment arrangement with an investment banker occurs when:

A) the syndicate is in place to handle the issue. B) The spread between the buying and selling price is less than one percent. C) The issue is solidly accepted in the market evidenced by a large price increase. D) When the investment banker buys the securities for less than the offering price and accepts the risk of not being able to sell them. E) When the investment banker sells as much of the security as the market can bear without a price decrease.

10. You estimate that Canadian Tire’s stock beta is 0.35. Its current debt has market value of $1.25 billion, and its equity value is $10 billion. From past market data, you estimate that the riskfree interest rate is 5%, and the market return is 20%. Current yield on Canadian Tire’s bonds is 8%. The corporate tax rate is 36%. Ignore personal taxes and financial distress costs. What’s Canadian Tire’s cost of equity if it were an all-equity firm?

A) 10.25% B) 10.08% C) 10.00% D) 9.86% E) Not enough information.

r_s = .05 + .35 (.20 - .05) = .1025 = r0 + 1.25/10 (1-.36) (r0 - .08) r0 = 10.0833%

2 II. Short answer questions (5 points each.)

1. If Miller-Modigliani Proposition II (with corporate taxes) is correct, every firm should take (almost) 100% debt to maximize the firm value. But you do not observe that in real life. Give three reasons that why firms do not follow Miller-Modigliani Proposition II and brief explain your reasons.

Possible reasons: 1. Financial distress—more debt, higher bankruptcy risk. 2. Agency cost of equity in financial distress—bondholders know that they will be taken advantage of by distressed firms and may ask for higher interest rates Æ less debt. 3. Financial flexibility: Firms want to preserve financing flexibility for future opportunities. 4. Pecking-order of financing: Firm may follow pecking order theory in financing, i.e., internal cash first. Therefore, if they have enough internal cash, no need for debt. 5. Credit ratings concern: The more you borrow, the less credit worthiness you are. 6. Not able to take advantage of tax shield –e.g., firms in red.

2. You just read the following from The Financial Post on Thursday, October 12, 2006: “Gannett Co. Inc. the largest U.S. newspaper publisher, reported a lower third-quarter profit yesterday because of weak advertising growth and lower-than-expected revenues, sending shares down 3.4%. Revenue rose 2.7% to US$1.91-billion, but fell short of analysts’ views ranging from US$1.92-billion to US$1.99-billion, according to Reuters Estimates.” Assume nothing happens before the event. Comment whether this event is consistent with, against, or uncertain with the efficient markets hypothesis.

This event is consistent with semi-strong form EMH. Analysts were forecasting a higher earnings but the firm did not reach the expectation. This is a bad news. If nothing happens before bad news, then EMH says that price will drop. The stock price action is consistent with semi-strong form EMH.

3 III. True or false. Choose only one true/false question to answer. If you answer both questions, you will get the average mark of the two.

Assess whether each of the following statements is true, false, or uncertain. Justify your answer. All marks are based on the quality of your arguments supporting your answer.

1. (4 points) If the efficient–market hypothesis is true, then the pension fund manager might as well select a portfolio with a pin.

False. The efficient markets hypothesis does not imply that portfolio selection should be done with a pin, for several reasons:

(1) The manager still must make sure that the portfolio is well diversified. It should be noted that a large number of stocks alone is not enough to ensure diversification; they could all be in similar industries. (2) Second, she must make sure the risk of the diversified portfolio is appropriate for her clients. In the case of pension fund, she should choose “safe” investments, i.e., choose those stocks/bonds or combined portfolios with lower beta.

2. (4 points) As the firm borrows more and debt becomes risky, both stockholders and bondholders demand higher rates of return. Thus by reducing the debt equity ratio we can reduce both the cost of debt and the cost of equity, making everybody better off.

False. Borrowing has some benefits, such as tax shield of interest, added discipline to the management. It has costs as well, such as financial distress costs, agency costs of debt, and loss of financial flexibility. If the marginal benefit of adding debt is greater than the marginal cost, firms should borrow. In this case, borrowing will reduce the for the whole firm, generally through a higher portion of debt whose cost is less than the cost of equity.

(This question can also be answered in the following ways: 1. You can use MM-I without tax. In this world, the cost of capital of the firm is not affected by the choice of capital structure under Proposition I in the no tax scenario. As the debt-equity ratio decreases, it is true that the cost of equity decrease, but a smaller proportion of the firm is financed by the lower cost debt. Hence, the overall effect is to leave the firm’s cost of capital unchanged. 2. You can also use MM-II with taxes. In this world, the cost of capital is decreasing in the amount of debt. As firm borrows more, it is true that stock becomes riskier and hence the required return on equity is higher. However, firm value increases with debt because of the tax shield of debt, meaning that the cost of capital for the firm is smaller.)

4 IV. Calculations (Show your process to get partial credit).

Question 1. (15 points) Mellow-Dramas Inc. is expected to (1) earn an operating income of $2.2 million one year from now, which it pays as dividends on its 200,000 outstanding shares, and (2) dissolve and have a liquidating value of $6.05 million two years from now. The company is all equity financed with a required rate of return of 10%. At the dividend declaration board meeting, several board members claimed that given that the firm is dissolving in two years, the dividend is too meager and is probably depressing the firm’s stock price. They proposed that the firm sell enough new shares one year from now to raise the dividend by 50%. The new shares sold are entitled to the liquidating value but not the dividend. Assume that markets are perfect, there are no taxes, and issuing stock is the only financing alternative.

(a) (2 points) What is the stock price under the current dividend policy?

1. Firm value: 2.2/1.1 + 6.05/1.12 = $7m (1.5pt) 2. Share price: 7m / 200,000 = $35 (.5 pt)

(b) (5 points) One year from now, at what price and how many new shares must the firm issue to finance the new dividend policy?

Date 1 Date 2 (2 pts) Aggregate dividend to old S/H Funds to be raised: =2.2 (.5) = 1.1m 6.05 – 1.1 * (1.1) = 4.84 (1 pt for 1.1m)

Dividend per share No need. = 4.84m/200,.000 = 24.2

Share price at date 1: 24.2 / 1.1 = 22 (1 pt) Shares sold: 1.1m/22 = 50,000 (1pt)

(c) (4 points) Jones owns 1,000 shares and prefers the current dividend policy. How can he achieve it if the firm switches to the new policy?

Current dividend policy is $11 per share at date 1, and $30.25 per share at date 2. Jones will get $11,000 at date 1, and $30,250 at date 2 for 1,000 shares.

The proposed policy is $16.5 per share at date 1, and $24.2 per share at date 2, Or in total $16,500 at date 1, and $24,200 at date 2 for 1,000 shares.

He can simply invest the extra $5,500 (which is $16500-11000) to buy $5,500/22 = 250 shares. He will have 1000+250 = 1,250 shares, each share give him $24.2, or a total of 1,250 (24.2) = 30,250.

(You can simply say that he invests $5.50 per share or $5500 to buy stock without any further supporting illustration and get 2 points.)

(d) (4 points) Comment on the claim that the low dividend is depressing the stock price and relates your comments to the relevance of dividend policy. Support your answer with calculation.

Stock price under new dividend policy is 16.5/1.1 + 24.2/1.12 = 35 = stock price under old dividend policy. Same stock price. Implies that in an MM world with perfect markets and a constant investment policy, dividend policy is irrelevant since investors can use homemade dividends to create any dividend policy that they want. Hence the claim that low dividend is depressing stock price is wrong.

5 Question 2 (14 points)

Milano Pizza Club is a restaurant popular for its specialty pizzas. The restaurant has a debt-to- equity ratio of 30 percent and marks interest payments of $30,000 at the end of each year. The cost of the restaurant’s levered equity ( rs ) is 20%. The restaurant costs 130,000 to set up, which are financed according to the restaurant’s debt-to-equity ratio. Its estimated annual sales will be $1 million, annual cost of goods sold will be $400,000, and annual general and administrative costs will be $300,000. These cash flows are expected to remain the same forever. The corporate tax rate is 40%. Ignore personal taxes and financial distress.

a. (6 points) Determine Milano Pizza Club’s i) equity value and ii) firm value.

B/S = .3 Æ S/(B+S) = 10/13 (1pt)

Initial equity contribution = 130,000 * (10/13) = 100,000 (1 pt)

EBIT = 1,000,000 – 400,000 – 300,000 = 300,000 (1pt) LCF = (300,000 – 30,000) (1-.4) = 162,000 (1pt) Equity value = PV(future cashflows) = 162,000/0.2 = 810,000 = 810,000 (1 pt)

Firm value = equity value / (10/13) = 810,000 * (13/10) = 1,053,000 (1pt)

(The project has debt other than the set up costs.)

b. (3 points) Decide Milano Pizza Club’s weighted average cost of capital.

B = 1,053,000 (3/13) =243,000 (1pt) rB = 30,000/243,000 = 12.35% (1pt)

WACC = 10/13 (.20) + 3/13 (1 - .4) (12.35%) = .1710 (1pt)

c. If Milano Pizza Club were an all-equity firm, what is its cost of capital? (3 points) Generally, why is it different from the cost of levered equity? (2 points) r_s = r_0 + B/S (1-Tc) (r_0 – r_B) => .20 = r_0 + .3 (1-.4) ( r_0 - .1235) => r_0 = .1883

It is different because leverage adds risk to firm’s equity (by making the cashflow to equityholders more risky). Therefore cost of levered equity is greater than (different from) cost of unlevered equity.

6 Question 3: (17 points)

Brice Co., is in the process of going public. Its pre-IPO equity accounts are as follows:

Common shares (1,500 shares outstanding) 100,000 Retained earnings 50,000 Total 150,000

Brice will issue 500 new common shares, each with a face value of $1 and an issuing price of $150. Assume no issuance costs.

a. (3 points) What’s the book equity per share i) before the IPO, and ii) after the IPO? What is the market to book ratio right after IPO?

Book equity per share before IPO: 150,000/1,500 = $100 (1pt) After IPO: (150,000+500*150) / (1,500 + 500) = $112.5 (1pt)

M/B = 150/102.5 = 1.33 (1pt)

b. (3 points) Construct the post-IPO equity accounts for Brice.

Common shares (1,500 shares outstanding) 100,500 Additional paid-in capital (or contributed surplus) =500 (150-1) = 74,500 Retained earnings 50,000 Total 225,000

c. (3 points) The lead underwriter has a option to issue an additional 10% of shares during the month following the IPO. The lead underwriter exercises the greenshoe option when the stock price climbs to $180 twenty days after the IPO. What’s the new book to equity ratio? (Assume no issuance costs.)

(Book to equity ratio is the inverse of market to book ratio).

After greenshoe, the book value is: 150,000 + 500 (150) + 50 (150) =232,500 And the total number of share is: 2,000 + 10% (500) = 2,050 The book equity per share is: 113.41 The book to equity ratio is: 113.41/180 = 0.6301

7 Question 3 cont’d: d. (4 points) Back to settings in a) where Brice issues 500 new shares only and there is no greenshoe option. Brice has a strong stock performance since IPO. Two years after its IPO, the stock price reaches $250. At that moment, the management is considering a rights offering to raise an additional $50,000 for a significant expansion. The subscription price for each new share is $100. Figure out the terms for the right offering: i) How many rights are needed for a share and ii) what’s the value for a right?

# of new shares: 50,000/100 = 500 # of rights: 2,000 (shares outstanding) # of rights needs for a share: 2,000/500 = 4 (2pt to here) Value of a right: R_0 = (M_0 – S) /(N+1) = (250-100) /(4+1) = 30 (2pt)

e. (4 points) Show how a shareholder with 100 shares and no desire (or money) to buy additional shares is not harmed by the rights offering.

She can either sell the rights or exercise the rights. In both cases, her wealth will be the same. (1 pt for saying this)

If sell the rights, her wealth will be:

100 (250 – 30) + 100 (30) = 25,000 (250-30 is the ex-right stock price).

If she exercises the rights, her wealth will be:

(100 + 100/4) (250-30) = 27,500, but she spends an additional (100/4) *($100) or 25,000 out of her pocket to buy the new shares. Her ex-right wealth net of her additional spending is still $25,000.

8 Question 4 (15 points): Consider two firms, U and L, both with $40,000 in assets on balance sheet, are identical in every way except their capital structure. Firm U is unlevered, and firm L has a market value of $20,000 of perpetual debt that pays 8% interest per annum. Each company expects to earn $7,500 before interest per year in perpetuity and distributes all its earnings as dividends. Firm U has 1,000 shares outstanding, while firm L has 600 shares outstanding. The required rate of return for firm U is 15%. Assume no taxes and no financial distress costs. a. (4 points) What is the share price for U and L respectively? (Hint: derive values of firms first.)

U: firm value 7,500/.15 = 50,000. share price = 50,000/1,000 = 50

L: firm value = Vu = 50,000 = S + B Æ S = 30,000 (since B = 20,000) Share price = 30,000/600 = 50

b. (5 points) Mike owns 20% of firm L and believes that leverage works in his favor. You tell Mike that this is an illusion, and that with the possibility of borrowing on your own account at 8% interest, your can replicate Mike's payoff from firm L using borrowing/lending and firm U. Show to Mike the replication.

Mike’s payout from 20% of L: 20% [(7,500 – 20,000 (8%)] = 1,180 each year, The cost is 20% (600) (50) = 6,000

To replicate, (1) Buy 20% of U, costs 20% (1,000) 50 = 10,000 (2) Borrow 4,000 at 8% per. The cost of doing (1) and (2) is 10,000-4,000 = 6,000, the same as Mike’s ownership. And the payout is the same each year: 20% (7,500) – 4,000 (8%) = 1,180. c. (4 points) You find that value of the unlevered firm is 10% lower than the combined value of the equity and bond of the levered firm. Is there an arbitrage opportunity? If yes, design an arbitrage strategy to take advantage of it. Show the cashflows of your arbitrage strategy. Yes. One arbitrage strategy can be sell high and buy low (and always make your initial investment to be zero). Let value of unlevered firm be 30,000 and value of levered firm be 33,000. I can do the following: Buy 10% of unlevered firm; cost 30,000 (10%) = 3,000 short sell 10% of levered firm’s equity, proceeds: (33,000 -20,000) (10%) = 1,300 And borrow the rest (3,000-1,300) = 1,700 at 8%. My initial investment is thus zero.

Cashflows: My annual payouts are:

10% (7,500) – 10% [7,500 – 20,000 (8%)] – 1,700 (8%) = 24, always positive.

This constitutes an arbitrage strategy. d. (2 points) S&P credit rating services assigns a credit rating of BBB+ to firm L (but still no taxes). Altman estimates that bankruptcy costs are 20% of firm value and that the probability of default with BBB+ is 5%. What is the firm value for L now?

Expected Bankruptcy costs = value (cost) (probability)

V_l = Vu = 50,000 And after bankruptcy costs, it is 50,000 [1 - .2(.05)] = 49,500

9 Bonus question (5 points)

There are $7,600 million of equity and $1,000 million of bond on the balance sheet of CanTire Inc. The firm has 90 million shares outstanding, and its current stock price is $100. Its bond has the following features: face value $1,000 million, maturity of 3 years from now, coupon rate 10%, annual coupon payment. The bond is callable 2 years from now (after coupon payment of that year), with a call premium of 5%. You estimate the term structure of interest rates to be the following: 1-year spot rate is 10%, and 2-year spot rate is 8%. Depending on economic expansion or recession, 3-year spot rate can either be 6% or 10% with equal probability. What’s the firm value today?

(Definition: spot rate is the yield on a zero coupon bond. That is, if we let the current price of the T-year zero-coupon bond to be P, the face value to be $1, then the T-year spot rate, r, is derived as P(1+ r)T = 1.) Step 1. Equity value: 90 (100) = 9,000 (.5 pt) Step 2. A short cut that will give you 4 marks in total is the following:

Bond value = 100/1.10 + 100/1.082 + 0.5 (1,050/1.082 + 1,100/1.103)

Then go to step 3.

To get full credit, the process will be:

Coupon payment each year is 100 million, for three years. The value of coupons for the first two years is:

100/1.10 + 100/1.082 = 176.64 (1 pt)

We need to figure out the interest rate from year 2 to year 3. In expansion, the interest rate is: (1 + 6%)3 / (1 + 8%)2 – 1 = 0.0211 In recession, the interest rate is: (1 + 10%)3 / (1 + 8%)2 – 1 = 0.1411

Case 1: (1 pt) If the interest rate b/w year 2 and 3 is 0.0211, then bond value at the end of year 2 (after- coupon payment of that year) will be: (100 + 1,000 ) /1.0211, which is greater than the call value of 1,000 (1 + 5%) = 1,050 and the bond will be called.

In that case, bond holders get call price whose present value is

1,050/1.082 = 900.21

(1 pt) Case 2: If the interest rate b/w year 2 and 3 is 0.1411, then bond value at the end of year 2 (after-coupon payment of that year) will be: (100 + 1,000 ) /1.1411 = 963.98 Which is smaller than the call price and the bond won’t be called.

The PV of these cashflows is: 963.98 /1.082 = 826.46

Case 1 and case 2 happen with equal probability. Therefore, the bond value is:

176.64 + .5(900.21 + 826.46) = 1,039.97 (1pt)

Step 3. The firm value is: 9,000 + 1,039.97 = 10,039.97. (.5 pt)

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