Corporate Finance: The Core (Berk/DeMarzo) Chapter 3 – Arbitrage and Financial Decision Making 7) You have an investment opportunity in Germany that requires an investment of $250,000 today and will produce a cash flow of €208,650 in one year with no risk. Suppose the risk-free rate of interest in Germany is 6% and the current competitive exchange rate is €0. 78 to $1. 00. What is the NPV of this project? Would you take the project? A) NPV = 0; No B) NPV = 2,358; No C) NPV = 2,358; Yes D) NPV = 13,650; Yes Answer: C Explanation: A) B) C) NPV = -250,000 + (€208,650 / 1. 06) ? $1. 00 / €0. 8 = 2358, so since NPV > 0, accept D) Diff: 3 Topic: 3. 3 Present Value and the NPV Decision Rule Skill: Analytical Use the table for the question(s) below. Project| Cash flow today| Cash flow in one year| “eenie”| -10| 15| “meenie”| 10| -8| “minie”| -15| 20| “moe”| 10| -15| 10) If the risk-free interest rate is 10%, then of the four projects listed, if you could only invest in one project, which on e would you select? A) Eenie B) Meenie C) Minie D) Moe Answer: A Explanation: A) Eenie has highest NPV NPV Eenie = -10 + 15 / 1. 1 = 3. 64 NPV Meenie = 10 – 8 / 1. 1 = 2. 73 NPV Minie = -15 + 20 / 1. = 3. 18 NPV moe = 10 – 15 / 1. 1 = -3. 64 B) C) D) Diff: 2 Topic: 3. 3 Present Value and the NPV Decision Rule Skill: Analytical 11) If the risk-free interest rate is 10%, then of the four projects listed, which project would you never want to invest in? A) Eenie B) Meenie C) Minie D) Moe Answer: D Explanation: A) B) C) D) Moe has negative NPV NPV Eenie = -10 + 15 / 1. 1 = 3. 64 NPV Meenie = 10 – 8/1. 1 = 2. 73 NPV Minie = -15 + 20 / 1. 1 = 3. 18 NPV moe = 10 – 15 / 1. 1 = -3. 64 Diff: 2 Topic: 3. 3 Present Value and the NPV Decision Rule Skill: Analytical 3. 4 Arbitrage and the Law of One Price ) Which of the following statements regarding the Law of One Price is incorrect? A) At any point in time, the price of two equivalent goods trading in different competitive markets will be the same. B) One useful consequence of the Law of One Price is that when evaluating costs and benefits to compute a net present value, we can use any competitive price to determine a cash value, without checking the price in all possible markets. C) If equivalent goods or securities trade simultaneously in different competitive markets, then they will trade for the same price in both markets. D)

An important property of the Law of One Price is that it holds even in markets where arbitrage is not possible. Answer: D Explanation: A) B) C) D) Diff: 2 Topic: 3. 4 Arbitrage and the Law of One Price Skill: Conceptual Use the table for the question(s) below. Consider the following prices from a McDonald’s Restaurant: Big Mac Sandwich| $2. 99| Large Coke| $1. 39| Large Fry| $1. 09| 4) A McDonald’s Big Mac value meal consists of a Big Mac Sandwich, Large Coke, and a Large Fry. Assume that there is a competitive market for McDonald’s food items and that McDonalds sells the Big Mac value meal for $4. 9. Does an arbitrage opportunity exists and if so how would you exploit it and how much would you make on one extra value meal? A) Yes, buy extra value meal and then sell Big Mac, Coke, and Fries to make arbitrage profit of $0. 68 B) No, no arbitrage opportunity exists C) Yes, buy Big Mac, Coke, and Fries then sell value meal to make arbitrage profit of $1. 09 D) Yes, buy Big Mac, Coke, and Fries then sell value meal to make arbitrage profit of $0. 68 Answer: A Explanation: A) Buy value meal and sell Big Mac, Coke and Fries -4. 79 + 2. 99 + 1. 39 + 1. 09 = 0. 68 (so arbitrage exists) B) C)

D) Diff: 2 Topic: 3. 4 Arbitrage and the Law of One Price Skill: Analytical 5) Walgreen Company (NYSE: WAG) is currently trading at $48. 75 on the NYSE. Walgreen Company is also listed on NASDAQ and assume it is currently trading on NASDAQ at $48. 50. Does an arbitrage opportunity exists and if so how would you exploit it and how much would you make on a block trade of 100 shares? A) No, no arbitrage opportunity exists B) Yes, buy on NASDAQ and sell on NYSE, make $25 C) Yes, buy on NYSE and sell on NASDAQ, make $25 D) Yes, buy on NASDAQ and sell on NYSE, make $250 Answer: B Explanation: A) B)

Yes, buy 100 shares ? 48. 50 and sell 100 shares ? 48. 75 = $25. 00 C) D) Diff: 2 Topic: 3. 4 Arbitrage and the Law of One Price Skill: Analytical 7) Advanced Micro Devices (NYSE: AMD) is currently trading at $20. 75 on the NYSE. Advanced Micro Devices is also listed on NASDAQ and assume it is currently trading on NASDAQ at $20. 50. Does an arbitrage opportunity exists and if so how would you exploit it and how much would you make on a block trade of 1000 shares? Answer: Yes, buy 1000 shares ? 20. 50 and sell 1000 shares ? 20. 75 = $250. 00 Diff: 1 Topic: 3. 4 Arbitrage and the Law of One Price

Skill: Analytical 3. 5 No-Arbitrage and Security Prices 1) Which of the following statements regarding arbitrage and security prices is incorrect? A) We call the price of a security in a normal market the no-arbitrage price for the security. B) In financial markets it is possible to sell a security you do not own by doing a short sale. C) When a bond is underpriced, the arbitrage strategy involves selling the bond and investing some of the proceeds. D) The general formula for the no-arbitrage price of a security is Price(security) = PV(All cash flows paid by the security). Answer: C Explanation: A) B)

C) D) Diff: 2 Topic: 3. 5 No-Arbitrage and Security Prices Skill: Conceptual Use the information for the question(s) below. An independent film maker is considering producing a new movie. The initial cost for making this movie will be $20 million today. Once the movie is completed, in one year, the movie will be sold to a major studio for $25 million. Rather than paying for the $20 million investment entirely using its own cash, the film maker is considering raising additional funds by issuing a security that will pay investors $11 million in one year. Suppose the risk-free rate of interest is 10%. ) Without issuing the new security, the npv for this project is closest to what amount? Should the film maker make the investment? A) $1. 7 million; Yes B) $1. 7 million; No C) $2. 7 million; Yes D) $2. 7 million; No Answer: C Explanation: A) B) C) NPV = -20 + 25 / 1. 10 = $2. 7 million, since NPV ; 0 take the investment D) Diff: 2 Topic: 3. 5 No-Arbitrage and Security Prices Skill: Analytical 8) What is the NPV of this project if the film maker does not issue the new security? What is the NPV if the film maker issues the new security? A) $1. 7 million; $1. 7 million B) $1. 7 million; $2. million C) $2. 7 million; $1. 7 million D) $2. 7 million; $2. 7 million Answer: D Explanation: A) B) C) D) NPV (no security) = -20 + 25 / 1. 1 = $2. 7 NPV(w/ security) = -10 + (25 – 11) / 1. 10 = $2. 7 million Diff: 2 Topic: 3. 5 No-Arbitrage and Security Prices Skill: Analytical Use the table for the question(s) below. Security| Cash flowtoday| Cash flowin one year| A| 0| 100| B| 100| 0| C| 100| 100| 9) If the risk-free rate of interest is 7. 5%, then the value of security “A” is closest to: A) $91. 00 B) $92. 50 C) $93. 00 D) $100. 00 Answer: C Explanation: A) B) C) = 100 / 1. 075 = 93. 2 which is approximately $93. 00 D) Diff: 2 Topic: 3. 5 No-Arbitrage and Security Prices Skill: Analytical 11) If the value of security “C” is $180, then what must be the value of security “A”? A) $80 B) $90 C) $100 D) Unable to determine without the risk-free rate. Answer: A Explanation: A) The cash flows from C are simply a combination of A ; B, so price(C) = price(A) + price(B) Since B is already in todays dollars, price(B) must = 100, so price A = 180 – 100 = $80. B) C) D) Diff: 3 Topic: 3. 5 No-Arbitrage and Security Prices Skill: Analytical Use the information for the question(s) below.

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 below: Stock| Current Price| IBM| $79. 50| MRK| $40. 00| C| $48. 50| 13) Suppose that the ETF is trading for $424. 50; you should A) sell the EFT and buy 2 shares of IBM, 3 shares of MRK, and 3 shares of C. B) sell the EFT and buy 3 shares of IBM, 2 shares of MRK, and 3 shares of C.

C) buy the EFT and sell 2 shares of IBM, 3 shares of MRK, and 3 shares of C. D) do nothing, no arbitrage opportunity exists. Answer: D Explanation: A) B) C) D) Value of ETF = 2 ? 79. 50 + 3 ? 40. 00 + 3 ? 48. 50 = $424. 50, so no arbitrage opportunity exists Diff: 3 Topic: 3. 5 No-Arbitrage and Security Prices Skill: Analytical 14) Suppose a security with a risk-free cash flow of $1000 in one year trades for $909 today. If there are no arbitrage opportunities, then the current risk-free interest rate is closest to: A) 8% B) 10% C) 11% D) 12% Answer: B Explanation: A) B)

PV = FV / (1 + i) ==;;; (1 + i) = FV / PV = $1000 / $909 = 1. 10 so i = 10% C) D) Diff: 3 Topic: 3. 5 No-Arbitrage and Security Prices Skill: Analytical Use the information for the question(s) below. 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 below: Stock| Current Price| IBM| $79. 50| MRK| $40. 00|

C| $48. 50| 15) Assume that the ETF is trading for $426. 00, what (if any) arbitrage opportunity exists? What (if any) trades would you make? Answer: Value of ETF = 2 ? 79. 50 + 3 ? 40. 00 + 3 ? 48. 50 = $424. 50, so an arbitrage opportunity exists. You should sell the EFT for $426. 00 and buy 2 shares of IBM, 3 shares of MRK, and 3 shares of C. Diff: 3 Topic: 3. 5 No-Arbitrage and Security Prices Skill: Analytical 3. 6 The Price of Risk 1) Which one of the following statements is false? A) When we compute the return of a security based on the average payoff we expect to receive, we call it the expected return.

B) The notion that investors prefer to have a safe income rather than a risky one of the same average amount is call risk aversion. C) Because investors are risk averse, the risk-free interest rate is not the right rate to use when converting risky cash flows across time. D) The more risk averse investors are, the higher the current price of a risky asset will be compared to a risk-free bond. Answer: D Explanation: A) B) C) D) Diff: 2 Topic: 3. 6 The Price of Risk Skill: Conceptual Use the table for the question(s) below. | Market Price| Cash Flow in One Year| Security| Today| Poor Economy| Good Economy|

A| 200| 840| 0| B| 600| 0| 840| C| ??? | 840| 4200| 2) Based upon the information provided about securities A, B, and C, the risk-free rate of interest is closest to: A) 4% B) 5% C) 8% D) 10% Answer: B Explanation: A) B) We can construct the risk-free asset by forming a portfolio of A and B. This portfolio has a certain payoff of $840. The price for this portfolio is $800. We know that $800 = $840 / (1 + i) ==; (1 + i) = 840 / 800 = 1. 05 ==; i = . 05 or 5%. C) D) Diff: 2 Topic: 3. 6 The Price of Risk Skill: Analytical 4) Suppose a risky security pays an average cash flow of $100 in one year.

The risk-free rate is 5%, and the expected return on the market index is 13%. If the returns on 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? A) 4% B) 6. 5% C) 9% D) 11% Answer: A Explanation: A) Since the security is half as risky as the market, then the risk-premium for the security should be half of the market risk premium. The market risk premium is 13% – 5% = 8%, so the risk premium on this security should be half of this or 4%. B) C) D) Diff: 2

Topic: 3. 6 The Price of Risk Skill: Analytical Use the table for the question(s) below. | Market Price| Cash Flow in One Year| Security| Today| Poor Economy| Good Economy| A| 200| 840| 0| B| 600| 0| 840| C| ??? | 840| 4200| 3. 7 Arbitrage with Transaction Costs 1) Which of the following statements is false? A) No arbitrage opportunities will exist until the underlying prices diverge by more than the amount of the transaction costs. B) Because you will generally pay a slightly lower price when you buy a security (the ask price) than you receive when you sell (the bid price) you will pay the bid-ask spread.

C) The price of a security should equal the present value of its cash flows, up to the transaction costs of trading the security and the cash flows. D) In most markets, you must pay transactions costs to trade securities. Answer: B Explanation: A) B) C) D) Diff: 3 Topic: 3. 7 Arbitrage with Transactions Costs Skill: Conceptual 2) Consider a bond that pays $1000 in one year. Suppose that the market interest rate for savings is 8%, but the interest rate for borrowing is 10%. The price range that this bond must trade in a normal market if no arbitrage opportunities exist is closest to: A) 909 to $917 B) $909 to $926 C) $917 to $926 D) $909 to $1000 Answer: B Explanation: A) B) VB @ 8% = 1000 / 1. 08 = $926 VB @ 10% = 1000 / 1. 10 = $909 so range is 909 to 926 C) D) Diff: 2 Topic: 3. 7 Arbitrage with Transactions Costs Skill: Analytical Use the table for the question(s) below. Security| Bid| Ask| IBM| 79. 45| 79. 50| MRK| 39. 95| 40. 05| C| 48. 50| 48. 55| 6) Consider an ETF that is made up of one share each of IBM, MRK, and C. The current quote for this ETF currently is $167. 75 (bid) $167. 85 (ask). What should you do? Answer:

There is an arbitrage opportunity. Buy the ETF at the ask of $167. 85 and sell the underlying securities at the bid prices. So we have +79. 45 + 39. 95 + 48. 50 – 167. 85 = . 05 arbitrage profit per share Diff: 2 Topic: 3. 7 Arbitrage with Transactions Costs Skill: Analytical 7) Consider an ETF that is made up of one share each of IBM, MRK, and C. The current quote for this ETF currently is $167. 85 (bid) $167. 95 (ask). What should you do? Answer: Nothing, there is no arbitrage opportunity here. The ask price must fall below $167. 90 or the bid price must be above $168. 0 for there to be an arbitrage. Diff: 2 Topic: 3. 7 Arbitrage with Transactions Costs Skill: Analytical 8) Consider an ETF that is made up of one share each of IBM, MRK, and C. The current quote for this ETF currently is $168. 15 (bid) $168. 20 (ask). What should you do? Answer: There is an arbitrage opportunity. Sell the ETF at the bid of $168. 15 and buy the underlying securities at the ask prices. So we have + 168. 15 – 79. 50 – 40. 05 – 48. 55 = . 05 arbitrage profit per share Diff: 2 Topic: 3. 7 Arbitrage with Transactions Costs Skill: Analytical