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COURSERA AN INTRODUCTION TO CORPORATE FINANCE

Franklin Allen

Week 6 Example Exam for Class

Instructions: All four questions carry equal weight.

1. Consider a world with two points in time, dates 0 and 1, perfect capital markets and nouncertainty. Agnieszka owns 42% of the shares of the Napoli Corporation. She only values consumption at date 0. Varun owns the remaining 58% of shares. He wants to consume $0.6 million at date 0. Once he has consumed this amount then he only values consumption at date 1. In addition to their shares in Napoli, Agnieszka has $0.2 million at date 0 and Varun has $0.85 million at date 0. Apart from these amounts at date 0, the only other payments they receive at dates 0 and 1 are from the Napoli Corporation. Suppose initially they can lend and borrow as much as they like at 7%. The Napoli Corporation has $20 million on hand to undertake investments. It has 4 projects available to it.

Cost at date 0 Payoff at date 1 Project A $2,352,611 $2,494,947 Project B $6,543,111 $6,739,404 Project C $14,532,236 $16,130,782 Project D $4,631,000 $5,001,480

(a) What rule should Agnieszka and Varun tell the managers of the firm to follow?

(b) Which project(s) should the Napoli Corporation undertake?

(c) Suppose that at date 0 the Napoli Corporation pays out all that is left over from the $20 million or raises any deficit from the shareholders after undertaking the projects you answered in part (b). At date 1 it pays out all the payoffs from these projects. (i) What is the most that Agnieszka can consume at date 0 assuming she consumes

nothing at date 1? (ii) What is the most that Varun can consume at date 1 assuming he consumes $0.6

million at date 0?

(d) Suppose Agnieszka and Varun can now borrow from the bank at 9% and lend at 7%. (i) Which projects would Agnieszka like the firm to undertake? (ii) Which projects would Varun like the firm to undertake? (iii) Which projects will the firm undertake if there is majority voting?

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2. (a) Jai wants to buy a boat 6 years from now with a cost at that time of $185,000. She wants to go on vacation now and annually with her paying for the first vacation now and the last vacation 20 years from now. The vacation costs $6,000 now. The price of the vacation is expected to grow at 4 percent per year. She can lend and borrow as much as she wants at 5 percent per year at her bank. What is the constant amount per year she needs to save to have enough to purchase the boat and vacations assuming the first amount is saved now and the last amount is saved 16 years from now?

(b) The Dodexia Banking Corporation is not expected to pay dividends until 8

years from now, when it pays its first quarterly dividend of €1.12. The quarterly dividends are expected to grow at a rate of 2 percent per quarter for 5 years following the first payment. After that they are expected to grow at 0.5 percent per quarter in perpetuity. What is the current price of the stock if the appropriate discount rate is 1.8 percent per quarter?

3. ExxonMobil needs to replace some of its oil tankers. It is choosing between Chinese built ships and Korean built ones. The Chinese ones each cost $140 million today (nominal). They are expected to last for 25 years. The salvage value at the end of these 25 years is expected to be $18 million (real). The before-tax annual maintenance and fuel costs are expected to be $6.5 million (real) at the end of the first year. These are expected to remain constant in real terms. The Korean built ships each cost $108 million today (nominal). They are expected to last for 20 years. The salvage value at the end of these 20 years is expected to be $14 million (real). The before-tax annual maintenance and fuel costs are expected to be $7.8 million (real) at the end of the first year and these are expected to remain constant in real terms. The capacities and maintenance schedules of the ships are such that ExxonMobil will need to buy either 15 Chinese built ships or 19 Korean ones. The firm uses straight line depreciation and has a total tax rate of 35%. It is anticipated that it will be profitable for the foreseeable future. The firm has a discount rate for this type of project of 7% (nominal). The rate of inflation is expected to be 3% per year going forward. Assume all cash flows occur at the end of the year. The tax code is written in nominal terms. Which type of ships should ExxonMobil purchase assuming that similar ships will be available in the foreseeable future? Make your comparison between the ships in real terms to ensure that the comparison of costs across different years is valid.

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4. (The two parts are separate so you cannot use information from one in the other.) (a) Suppose the CAPM holds with rF = 3 percent and rM - rF = 6 percent. The standard deviation of the market portfolio is 23 percent. Yuanyuan has wealth of 90 million euros. (i) How could Yuanyuan construct a portfolio on the capital market line with a

standard deviation of 9 percent? (ii) What is the expected return on this portfolio? (iii) What is the beta of this portfolio? (b) You have discovered three well-diversified portfolios with the following characteristics. Investment Expected Return (%) Beta Unique Risk A 5.0 0.5 none B 9.4 0.8 none C 12.6 1.1 none (i) Is an arbitrage opportunity available? (ii) Give a zero-investment, zero-risk portfolio with a positive expected return that

has either +$1 or -$1 invested in A. (iii) What is the expected return on this portfolio?