University of Minnesota, Duluth - FINA 3001

Chapter 3 (2^nd edition) Problems

Arbitrage and Financial Decision Making

1)Honda Motor Company is considering offering a $2000 rebate on its minivan, lowering the vehicle’s price from $30,000 to $28,000. The marketing group estimates that this rebate will increase sales over the next year from 40,000 to 55,000 vehicles. Suppose Honda’s profit margin with the rebate is $6000 per vehicle. If the change in sales is the only consequence of this decision, what are its costs and benefits? Is it a good idea?

2. You are an international shrimp trader. A food producer in the Czech Republic offers to pay you 2 million Czech koruna today in exchange for a year’s supply of frozen shrimp. Your Thai supplier will provide you with the same supply for 3 million Thai baht today. If the current competitive market exchange rates are 25.50 koruna per dollar and 41.25 baht per dollar, what is the value of this deal?

3. Suppose the current market price of corn is $3.75 per bushel. Your firm has a technology that can convert 1 bushel of corn to 3 gallons of ethanol. If the cost of conversion is $1.60 per bushel, at what market price of ethanol does conversion become attractive?

4.     Suppose your employer offers you a choice between a $5000 bonus and 100 shares of the company stock. Whichever one you choose will be awarded today. The stock is currently trading for $63 per share.

1. Suppose that if you receive the stock bonus, you are free to trade it. Which form of the bonus should you choose? What is its value?
2. Suppose that if you receive the stock bonus, you are required to hold it for at least one year. What can you say about the value of the stock bonus now? What will your decision depend on?

5.        You have decided to take your daughter skiing in Utah. The best price you have been able to find for a roundtrip air ticket is $359. You notice that you have 20,000 frequent flier miles that are about to expire, but you need 25,000 miles to get her a free ticket. The airline offers to sell you 5000 additional miles for $0.03 per mile.

1. Suppose that if you don’t use the miles for your daughter’s ticket they will become worthless. What should you do?
2. What additional information would your decision depend on if the miles were not expiring? Why?

6.            Suppose the risk-free interest rate is 4%.

       a.              Having $200 today is equivalent to having what amount in one year?

2. Having $200 in one year is equivalent to having what amount today?
3. Which would you prefer, $200 today or $200 in one year? Does your answer depend on when you need the money? Why or why not?

7. You have an investment opportunity in Japan. It requires an investment of $1 million today and will produce a cash flow of ¥ 114 million in one year with no risk. Suppose the risk-free interest rate in the United States is 4%, the risk-free interest rate in Japan is 2%, and the current competitive exchange rate is ¥ 110 per $1. What is the NPV of this investment? Is it a good opportunity?

8.            Your firm has a risk-free investment opportunity where it can invest $160,000 today and receive

$170,000 in one year. For what level of interest rates is this project attractive?

1. What is the NPV of this opportunity?
2. How can your firm turn this NPV into cash today?

10.          Your firm has identified three potential investment projects. The projects and their cash flows are

       shown here:

Suppose all cash flows are certain and the risk-free interest rate is 10%.

1. What is the NPV of each project?
2. If the firm can choose only one of these projects, which should it choose?
3. If the firm can choose any two of these projects, which should it choose?

11. Your computer manufacturing firm must purchase 10,000 keyboards from a supplier. One supplier demands a payment of $100,000 today plus $10 per keyboard payable in one year. Another supplier will charge $21 per keyboard, also payable in one year. The risk-free interest rate is 6%.

1. What is the difference in their offers in terms of dollars today? Which offer should your firm take?
2. Suppose your firm does not want to spend cash today. How can it take the first offer and not spend $100,000 of its own cash today?

12. Suppose Bank One offers a risk-free interest rate of 5.5% on both savings and loans, and Bank Enn offers a risk-free interest rate of 6% on both savings and loans.

1. What arbitrage opportunity is available?
2. Which bank would experience a surge in the demand for loans? Which bank would receive a surge in deposits?
3. What would you expect to happen to the interest rates the two banks are offering?

13.    Throughout the 1990s, interest rates in Japan were lower than interest rates in the United States. As a result, many Japanese investors were tempted to borrow in Japan and invest the proceeds in the United States. Explain why this strategy does not represent an arbitrage opportunity.

14. An American Depositary Receipt (ADR) is security issued by a U.S. bank and traded on a U.S. stock exchange that represents a specific number of shares of a foreign stock. For example, Nokia Corporation trades as an ADR with symbol NOK on the NYSE. Each ADR represents one share of Nokia Corporation stock, which trades with symbol NOK1V on the Helsinki stock exchange. If the

U.S. ADR for Nokia is trading for $17.96 per share, and Nokia stock is trading on the Helsinki exchange for 14.78 € per share, use the Law of One Price to determine the current $/€ exchange rate.

16.    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 Hewlett-Packard (HPQ), one share of Sears (SHLD), and three shares of General Electric (GE). Suppose the current stock prices of each individual stock are as shown here:

1. What is the price per share of the ETF in a normal market?
2. If the ETF currently trades for $120, what arbitrage opportunity is available? What trades would you make?
3. If the ETF currently trades for $150, what arbitrage opportunity is available? What trades would you make?

1. What is the no-arbitrage price of a security that pays cash flows of $100 in one year and $100 in two years?
2. What is the no-arbitrage price of a security that pays cash flows of $100 in one year and $500 in two years?
3. Suppose a security with cash flows of $50 in one year and $100 in two years is trading for a price of $130. What arbitrage opportunity is available?

18.          Suppose a security with a risk-free cash flow of $150 in one year trades for $140 today. If there are no arbitrage opportunities, what is the current risk-free interest rate?

Xia plans to invest any unused cash today at the risk-free interest rate of 10%. In one year, all cash will be paid to investors and the company will be shut down.

1. What is the NPV of each project? Which projects should Xia undertake and how much cash should it retain?
2. What is the total value of Xia’s assets (projects and cash) today?
3. What cash flows will the investors in Xia receive? Based on these cash flows, what is the value of Xia today?

4. Suppose Xia pays any unused cash to investors today, rather than investing it. What are the cash flows to the investors in this case? What is the value of Xia now?
5. Explain the relationship in your answers to parts (b), (c), and (d).

A-1.        The table here shows the no-arbitrage prices of securities A and B that we calculated.

1. What are the payoffs of a portfolio of one share of security A and one share of security B?
2. What is the market price of this portfolio? What expected return will you earn from holding this portfolio?

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A-2.        Suppose security C has a payoff of $600 when the economy is weak and $1800 when the economy is strong. The risk-free interest rate is 4%.

1. Security C has the same payoffs as what portfolio of the securities A and B in problem A.1?
2. What is the no-arbitrage price of security C?
3. What is the expected return of security C if both states are equally likely? What is its risk premium?
4. What is the difference between the return of security C when the economy is strong and when it is weak?
5. If security C had a risk premium of 10%, what arbitrage opportunity would be available?

A-3.     You work for Innovation Partners and are considering creating a new security. This security would pay out $1000 in one year if the last digit in the closing value of the Dow Jones Industrial index in one year is an even number and zero if it is odd. The one-year risk-free interest rate is 5%. Assume that all investors are averse to risk.

1. What can you say about the price of this security if it were traded today?
2. Say the security paid out $1000 if the last digit of the Dow is odd and zero otherwise. Would your answer to part (a) change?
3. Assume both securities (the one that paid out on even digits and the one that paid out on odd digits) trade in the market today. Would that affect your answers?

A-4.        Suppose a risky security pays an expected cash flow of $80 in one year. The risk-free rate is 4%, and the expected return on the market index is 10%.

1. If the returns of this security are high when the economy is strong and low when the economy is weak, but the returns vary by only half as much as the market index, what risk premium is appropriate for this security?
2. What is the security’s market price?

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