Problems Problem 3-4 Problem 3-6 Problem 3-7 Problem 3-12 Problem 3-14 Problem 3-16 Problem 3-4 Suppose the risk-free interest rate is 4%. a. Having $200 today is equivalent to having what amount in one year? Amount today $200.00 Interest rate 4.00% Value in 1 year $208.00 b. Having $200 in one year is equivalent to having what amount today? Amount in 1 year $200.00 Interest rate 4.00% Value today $192.31 c. Which would you prefer, $200 today or $200 in one year? $200 today Does your answer depend on when you need the money? Why or why not? The answer does not depend on when the money is needed. at amount in one year? ng what amount today? in one year? he money? Why or why not? ey is needed. Problem 3-6 You run a construction firm. You have just won a contract to build a government office building. Building it will require an investment of $10 million today and $5 million in one year. The government will pay you $20 million in one year upon the building’s completion. Suppose the cash flows and their times of payment are certain, and the risk- free interest rate is 10%. a. What is the NPV of this opportunity? Interest rate 10.00% Year 0 Investment ($10,000,000.00) Government payment Net cash flow (10,000,000.00) Value today (10,000,000.00) NPV 3,636,363.64 b. How can your firm turn this NPV into cash today? Borrow 13,636,363.64 Use (10,000,000.00) Pay back loan plus interest 15,000,000.00 a contract to build a government office f $10 million today and $5 million in one n one year upon the building’s es of payment are certain, and the risk- Year 1 ($5,000,000.00) $20,000,000.00 15,000,000.00 13,636,363.64 ash today? today today for investment with cash inflow in 1 year Problem 3-7 Your firm has identified three potential investment projects. The projects and their cash flows are shown here: Cash Flow Cash Flow Project Today ($) in One Year ($) A -10 20 B 5 5 C 20 -10 Suppose all cash flows are certain and the risk-free interest rate is 10%. a. What is the NPV of each project? Interest rate 10.00% Year 0 1 Project A Cash flows (10.00) 20.00 Value today (10.00) 18.18 NPV of A 8.18 Project B Cash flows 5.00 5.00 Value today 5.00 4.55 NPV of B 9.55 Project C Cash flows 20.00 (10.00) Value today 20.00 (9.09) NPV of C 10.91 Summary Project NPV Project A 8.18 Project B 9.55 Project C 10.91 b. If the firm can choose only one of these projects, which should it choose? Project C c. If the firm can choose any two of these projects, which should it choose? Projects B and C Problem 3-12 The promised cash flows of three securities are listed here. If the cash flows are risk-free, and the risk-free interest rate is 5%, determine the no-arbitrage price of each security before the first cash flow is paid. Cash Flow Cash Flow Security Today ($) in One Year ($) A 500 500 B 0 1000 C 1000 0 Interest rate 5.00% Cash flow Cash flow in No-arbitrage Security today one year price A 500.00 500.00 976.19 B 0.00 1000.00 952.38 C 1000.00 0.00 1,000.00 the cash flows are o-arbitrage price Problem 3-14 Consider two securities that pay risk-free cash flows over the next two years and that have the current market prices shown here: Cash Flow Cash Flow Security Price Today ($) in One Year ($) in Two Years ($) B1 94 100 0 B2 85 0 100 Cash flow Cash flow Security Price Today in one year in two years B1 (94.00) 100.00 0.00 B2 (85.00) 0.00 100.00 a. What is the no-arbitrage price of a security that pays cash flows of $100 in one year and $100 in two years? 179.00 since this is just like buying both B1 and B2 b. What is the no-arbitrage price of a security that pays cash flows of $100 in one year and $500 in two years? 519.00 since this is just like buying 1 B1 and 5 B2s c. 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? 130.00 is the price the security trades at. 132.00 is the correct price for the security. You could do arbitrage by buying the security. You could then either sell it after the price adjusts or just collect the cash flows at their alotted times. Either way, you'll receive more than you should. two years and flows of $100 in and B2 flows of $100 in 5 B2s d $100 in two unity is Problem 3-16 Xia Corporation is a company whose sole assets are $100,000 in cash and three projects th undertake. The projects are risk-free and have the following cash flows: Cash Flow Cash Flow Project Today ($) in One Year ($) A -20,000 30,000 B -10,000 25,000 C -60,000 80,000 Xia plans to invest any unused cash today at the risk-free interest rate of 10%. In one year, will be paid to investors and the company will be shut down. Interest rate 10.00% a. What is the NPV of each project? Which projects should Xia undertake and much cash should it retain? Cash flow Cash flow in Project today one year A (20000.00) 30000.00 B (10000.00) 25000.00 C (60000.00) 80000.00 Accept Projects A B b. What is the total value of Xia’s assets (projects and cash) today? Value of company is the sum of its projects' NPVs Plus its cash Total value of the company c. What cash flows will the investors in Xia receive? Based on these cash flow is the value of Xia today? They will receive the sum of the cash flows above plus the proceeds from the investment of $10,000 extra cash. Its value is They will receive the sum of the cash flows above plus the proceeds from the investment of $10,000 extra cash. Its value is d. Suppose Xia pays any unused cash to investors today, rather than investing are the cash flows to the investors in this case? What is the value of Xia no Xia's shareholders will get the same amount, regardless. If the company p excess cash now, shareholders will get $10,000 plus the present value of th flows Xia will get in one year. e. Explain the relationship in your answers to parts (b), (c), and (d). No matter how Xia's shareholders get their cash, they're entitled to the sam amount becaause in every case the values are discounted. 0,000 in cash and three projects that it will ing cash flows: Cash Flow in One Year ($) 30,000 25,000 80,000 e interest rate of 10%. In one year, all cash own. projects should Xia undertake and how NPV 7,272.73 12,727.27 12,727.27 and C rojects and cash) today? jects' NPVs 32,727.27 100,000.00 132,727.27 a receive? Based on these cash flows, what ws above plus the proceeds h. Its value is ws above plus the proceeds h. Its value is 132,727.27 vestors today, rather than investing it. What case? What is the value of Xia now? unt, regardless. If the company pays out 10,000 plus the present value of the cash to parts (b), (c), and (d). eir cash, they're entitled to the same s are discounted.
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