# Corporate finance

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1 Bonds (3 points)

A company aims to takeover one of its suppliers valued at 2 million Euros and is planning to fund the takeover by issuing three-year zero coupon bonds, each with face value C1000. After having their credit rating checked, executives have decided that they need to issue 2400 of these bonds to raise the 2 million needed to fund this takeover. What is the YTM of the bonds issued by the company? (a) 5.79% (b) 7.13% (c) 6.27% (d) 5.34% If the company’s credit rating changes due to recent earnings announcements and the YTM of the bonds should now be 4.4% how many bonds must the company issue to raise 2 million Euros? (a) 2351 (b) 2276 (c) 2248 (d) 2302 Suppose that the company may default on these bonds with a 25% probability. In case of default, bondholders will receive 60% of the face value of bonds. If the price of the bonds is same as in part (a), what is the YTM in this case? (a) 3.1% (b) 2.9% (c) 2.6% (d) 3.4%

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2 Financial statements (4 points)

Use the following information for ECE incorporated: Assets Shareholder Equity Sales $200 million $100 million $300 million

If ECE reported $15 million in net income, then ECE’s Return on Equity (ROE) is: (a) 5.0% (b) 7.5% (c) 10.0% (d) 15.0% If ECE’s return on assets (ROA) is 12% , then ECE’s return on equity (ROE) is (a) 10% (b) 12% (c) 18% (d) 24% If ECE’s net proﬁt margin is 8% , then ECE’s return on equity (ROE) is: (a) 10% (b) 12% (c) 24% (d) 30% If ECE’s earnings are $10 million, its price-earnings ratio is (a) 10 (b) 5 (c) 20 (d) Cannot be determined

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3 Capital budgeting (3 points)

Fancypants Fashion is going to purchase new sewing machines worth 50 million Euros to manufacture purple trousers for the coming ﬁve years, after which purple trousers will be out of fashion and no longer in demand. The machines will be depreciated on a straightline basis over ﬁve years, and after ﬁve

years will be sold at an estimated 20 million Euros. The company estimates that the EBITDA from the sale of purple trousers will be 12 million Euros per year for the coming 5 years. The company’s earnings are subject to a corporate tax rate of 40%. If the ﬁrm’s equity cost of capital is 9.6% what is the NPV of this project? (a) 0.48 million Euros (b) 0.72million Euros (c) 0.26 million Euros (d) 0.92 million Euros Instead of selling the machines after ﬁve years, the company can use them to produce grey trousers starting in year 6. If they do so, using these machines the company will generate free cash ﬂows of 2 million Euros per year in perpetuity, since grey trousers are classics and never go out of fashion. What is the NPV of the project if the company chooses this option? (a) 5.89 million Euros (b) 5.72 million Euros (c) 6.36 million Euros (d) 6.07 million Euros Suppose that the company has decided that they will use the machines to produce grey trousers after ﬁve years. The company can ﬁnance the purchase of new sewing machines entirely by debt by issuing 5-year bonds with 6% coupon rate sold at par. Assuming this additional borrowing is project-speciﬁc and hence will not alter the company’s capital structure, what is the value of the project with the tax shield? (a) 11.56 (b) 11.94 (c) 12.25 (d) 11.12

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4 More capital budgeting (4 points)

Use the following information for “Iota Industries” (all ﬁgures in $ Millions) Iota Industries Market Value Balance Sheet Assets Liabilities Cash 250 Debt 650 Other Assets 1200 Equity 800 The company considers a new project with the following free cash ﬂows: Iota Industries New Project Free Cash Flows Year 0 1 2 3 Free CFs -250 75 150 100 Assume that Iota Industries has a debt cost of capital of 7% and an equity cost of capital of 14%. Furthermore, it faces a marginal corporate tax rate of 35%. If the project is of average risk and the company wants to keep its debt-to-equity ratio constant, its weighted average cost of capital is closest to: (a) 8.40% (b) 9.75% (c) 10.85% (d) 11.70% The NPV for Iota’s new project is closest to: (a) $25.25 million (b) $13.25 million (c) $9.00 million (d) $18.50 million The Debt Capacity for Iota’s new project in year 0 is closest to: (a) $263.25 million (b) $87.75 million (c) $50.25 million (d) $118.00 million If

instead of maintaining a ﬁxed debt-equity ratio Iota ﬁnances the project with $100 million of permanent debt, the NPV of the project is closest to (a) $44.28 million (b) $48.10 million (c) $53.44 million (d) $48.14 million 4

5 Arbitrage (4 points)

An exchange traded fund (ETF) is a security that represents a portfolio of individual stocks. Consider an ETF for which each share represents a portfolio of two shares of International Business Machines (IBM), three shares of Merck (MRK), and three shares of Citigroup Inc. (C). Suppose the current market price of each individual stock are shown in the following table: Stock IBM MRK C Current Price $121.57 $36.59 $3.15

What is the price per share of the ETF in a normal market:

Assume that the ETF is trading for $366.00, what (if any) arbitrage opportunity exists? What (if any) trades would you make?

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6 NPV and exchange rates (2 points)

You have an investment opportunity in Germany that requires an investment of $250,000 today and will produce a cash ﬂow of C208,650 in one year with no risk. Suppose the risk -free rate of interest in Germany is 7% and the current competitive exchange rate is C0.78 to $1.00. What is the NPV of this project? Would you take the project? (1 point) (a) NPV = 0; No (b) NPV = 2,358; No (c) NPV = 2,358; Yes (d) NPV = 13,650; Yes Explain in a few sentences the intuition behind your answer. (1 point)

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7 Options (4 points)

Which of the following statements is false? (a) The option delta, ∆, has a natural interpretation: It is the change in the price of the stock given a $1 change in the price of the option. (b) Because a leveraged position in a stock is riskier than the stock itself, this implies that call options on a

positive beta stock are more risky than the underlying stock and therefore have higher returns and higher betas. (c) Only one parameter input for the Black-Scholes formula, the volatility of the stock price, is not observable directly. (d) Because a stock’s volatility is much easier to measure (and forecast) than its expected return, the Black-Scholes formula can be very precise. The current price of KD Industries stock is $20. In the next year the stock price will either go up by 20% or go down by 20%. KD pays no dividends. The one year risk-free rate is 5% and will remain constant. Using the binomial pricing model, the price of a one-year call option on KD stock with a strike price of $20 is closest to: (1 point) (a) $2.40 (b) $2.00 (c) $2.15 (d) $1.45 The risk neutral probability of an up state for KD Industries is closest to: (a) 37.5% (b) 60.0% (c) 40.0% (d) 62.5% Using the risk-neutral pricing model, the price of a one-year call option on KD stock with a strike price of $20 is closest to: (1 point) (a) $2.40 (b) $2.00 (c) $2.15 (d) $1.45

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8 Financial Distress (3 points)

Suppose that you have received two job offers. Rearden Metal offers you a contract for $75,000 per year for the next two years while Wyatt Oil offers you a contract for $90,000 per year for the next two years. Both jobs are equivalent. Suppose that Rearden Metal’s contract is certain, but Wyatt Oil has a 60% chance of going bankrupt at the end of the year. In the event that Wyatt Oil ﬁles for bankruptcy, it will cancel your contract and pay you the lowest amount possible for you to not quit. If you do quit, you expect you could ﬁnd an new job paying $75,000 per year, but you would be unemployed for four months while searching for this new job. If you take the job with Wyatt Oil, then, in the event of bankruptcy, the least amount that Wyatt Oil would pay you next year is closest to: (a) $45,000 (b) $50,000 (c) $54,000 (d) $75,000 Assuming your cost of capital is 6 percent, the present value of your expected wage if you accept Rearden Metal’s offer is closest to: (a) $133,000 (b) $138,000 (c) $140,000 (d) $144,000 Assuming your cost of capital is 6 percent, the present value of your expected wage if you accept Wyatt Oil’s offer is closest to: (a) $138,000 (b) $140,000 (c) $144,000 (d)

$150,000

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9 Real Options (3 points)

You own a small manufacturing plant that currently generates revenues of $2 million per year. Next year, based upon a decision on a long-term government contract, your revenues will either increase by 20% or decrease by 25%, with equal probability, and stay at that level as long as you operate the plant. Other costs run $1.6 million dollars per year. You can sell the plant at any time to a large conglomerate for $5 million and your cost of capital is 10%. If you are awarded the government contract and your sales increase by 20%, then the value of your plant will be closest to: (a) $5 million (b) $8 million (c) $0 (d) $4 million If you are not awarded the government contract and your sales decrease by 25%, then the value of your plant will be closest to: (a) -$1 million (b) $5 million (c) $8 million (d) $0 Given the embedded option to sell the plant, the value of your plant will be closest to: (a) $5.0 million (b) $4.0 million (c) $6.5 million (d) $8.0 million

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