# Chapter 3 - Math 3650 Practice Problems Chapter 3 1 How...

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Math 3650 – Practice Problems – Chapter 3 1. How should the costs and benefits of a project be compared? In particular, what decision rule should financial managers use to compare costs and benefits? 2. Your firm needs to buy a new \$4500 printer. The manufacturer has offered that you can pay \$5000 in one year versus cash today as a promotional event. Suppose that the risk- free rate is 10%. Is this a good deal? 3. What is the Fischer Separation Theory? 4. What is arbitrage? What arbitrage opportunities exist in an efficient market? 5. Assume the risk free rate is 4% compounded annually. Now assume a U.S. Treasury one year zero coupon bond is trading in the marketplace. What should the price of that bond be? If the bond is selling for \$950, what arbitrage opportunity would exist? What arbitrage opportunity would exist if it were selling for \$975? In each of these 2 cases, what would happen very quickly in the marketplace to eliminate the arbitrage opportunity? 6. What is the risk free rate? What is commonly used as the risk free rate in the U.S.? 7. What is the risk premium? How is it determined? What factor determines the size of the risk premium (i.e when is the risk premium larger?) 8. An investment of \$1000 has a 10% chance of returning \$900, a 25% chance of returning \$950, a 30% chance of returning \$1135 and a 35% chance of returning \$1235. If the risk free rate is 4%, determine the risk premium. Also, determine the standard deviation of the returns. 9. What is a replicating portfolio? How it is used in pricing securities, for example to price derivatives contracts? 10. In addition, you should do problems 10, 14, 16 and 17 in the book.

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Math 3650 – Practice Problems – Chapter 3 Answers 1. Answer: Costs and benefits must be compared on the same terms; we must express them in the same currency and at the same time. Financial managers use the Net Present Value decision rule. Costs and benefits are both expressed in dollars today by calculating their respective present values. The net present value is the present value of the benefits minus the present value of the costs.
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• Spring '14
• Trimble,J

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