1、Chapter 3Arbitrage and Financial Decision Making3-2 Chapter Outline3.1 Valuing Decisions3.2 Interest Rates and the Time Value of Money3.3 Present Value and the NPV Decision Rule3.4 Arbitrage and the Law of One Price3.5 No-Arbitrage and Security Prices3-3 Learning Objectives1.Assess the relative meri
2、ts of two-period projects using net present value.2.Define the term“competitive market,”give examples of markets that are competitive and some that arent,and discuss the importance of a competitive market in determining the value of a good.3.Explain why maximizing NPV is always the correct decision
3、rule.4.Define arbitrage,and discuss its role in asset pricing.How does it relate to the Law of One Price?5.Calculate the no-arbitrage price of an investment opportunity.3-4 Learning Objectives(contd)6.Show how value additivity can be used to help managers maximize the value of the firm.7.Describe th
4、e Separation Principle.3-5 3.1 Valuing Decisions Identify Costs and Benefits May need help from other areas in identifying the relevant costs and benefits Marketing Economics Organizational Behavior Strategy Operations3-6 Analyzing Costs and Benefits Suppose a jewelry manufacturer has the opportunit
5、y to trade 10 ounces of platinum and receive 20 ounces of gold today.To compare the costs and benefits,we first need to convert them to a common unit.3-7 Analyzing Costs and Benefits(contd)Suppose gold can be bought and sold for a current market price of$250 per ounce.Then the 20 ounces of gold we r
6、eceive has a cash value of:(20 ounces of gold)X ($250/ounce)=$5000 today3-8 Analyzing Costs and Benefits(contd)Similarly,if the current market price for platinum is$550 per ounce,then the 10 ounces of platinum we give up has a cash value of:(10 ounces of platinum)X ($550/ounce)=$55003-9 Analyzing Co
7、sts and Benefits(contd)Therefore,the jewelers opportunity has a benefit of$5000 today and a cost of$5500 today.In this case,the net value of the project today is:$5000$5500=$500 Because it is negative,the costs exceed the benefits and the jeweler should reject the trade.3-10 Using Market Prices to D
8、etermine Cash Values Competitive Market A market in which goods can be bought and sold at the same price.In evaluating the jewelers decision,we used the current market price to convert from ounces of platinum or gold to dollars.We did not concern ourselves with whether the jeweler thought that the p
9、rice was fair or whether the jeweler would use the silver or gold.3-11 Textbook Example 3.13-12 Textbook Example 3.1(contd)3-13 Alternative Example 3.1 Problem Your car recently broke down and it needs$2,000 in repairs.But today is your lucky day because you have just won a contest where the prize i
10、s either a new motorcycle,with a MSRP of$15,000,or$10,000 in cash.You do not have a motorcycle license,nor do you plan on getting one.You estimate you could sell the motorcycle for$12,000.Which prize should you choose?3-14 Alternative Example 3.1(contd)Solution Competitive markets,not your personal
11、preferences(or the MSRP of the motorcycle),are relevant here:One Motorcycle with a market value of$12,000 or$10,000 cash.Instead of taking the cash,you should accept the motorcycle,sell it for$12,000,use$2,000 to pay for your car repairs,and still have$10,000 left over.3-15 Textbook Example 3.23-16
12、Textbook Example 3.2(contd)3-17 Alternative Example 3.2 Problem You are offered the following investment opportunity:In exchange for$27,000 today,you will receive 2,500 shares of stock in the Ford Motor Company and 10,000 euros today.The current market price for Ford stock is$9 per share and the cur
13、rent exchange rate is$1.50 per.Should you take this opportunity?Would your decision change if you believed the value of the euro would rise over the next month?3-18 Alternative Example 3.2(contd)Solution The costs and benefits must be converted to their cash values.Assuming competitive market prices
14、:2,500 shares$9/share=$22,50010,000$1.50/=$15,000 The net value of the opportunity is$22,500+$15,000-$40,000=-$2,500,we should not take it.This value depends only on the current market prices for Ford and the euro.Our personal opinion about the future prospects of the euro and Ford does not alter th
15、e value the decision today.3-19 3.2 Interest Rates and the Time Value of Money Time Value of Money Consider an investment opportunity with the following certain cash flows.Cost:$100,000 today Benefit:$105,000 in one year The difference in value between money today and money in the future is due to t
16、he time value of money.3-20 The Interest Rate:An Exchange Rate Across Time The rate at which we can exchange money today for money in the future is determined by the current interest rate.Suppose the current annual interest rate is 7%.By investing or borrowing at this rate,we can exchange$1.07 in on
17、e year for each$1 today.RiskFree Interest Rate(Discount Rate),rf:The interest rate at which money can be borrowed or lent without risk.Interest Rate Factor=1+rf Discount Factor=1/(1+rf)3-21 The Interest Rate:An Exchange Rate Across Time(contd)Value of Investment in One Year If the interest rate is 7
18、%,then we can express our costs as:Cost=($100,000 today)(1.07$in one year/$today)=$107,000 in one year3-22 The Interest Rate:An Exchange Rate Across Time(contd)Value of Investment in One Year Both costs and benefits are now in terms of“dollars in one year,”so we can compare them and compute the inve
19、stments net value:$105,000$107,000=$2000 in one year In other words,we could earn$2000 more in one year by putting our$100,000 in the bank rather than making this investment.We should reject the investment.3-23 The Interest Rate:An Exchange Rate Across Time(contd)Value of Investment Today Consider t
20、he benefit of$105,000 in one year.What is the equivalent amount in terms of dollars today?Benefit=($105,000 in one year)(1.07$in one year/$today)=($105,000 in one year)1/1.07=$98,130.84 today This is the amount the bank would lend to us today if we promised to repay$105,000 in one year.3-24 The Inte
21、rest Rate:An Exchange Rate Across Time(contd)Value of Investment Today Now we are ready to compute the net value of the investment:$98,130.84$100,000=$1869.16 today Once again,the negative result indicates that we should reject the investment.3-25 The Interest Rate:An Exchange Rate Across Time(contd
22、)Present Versus Future Value This demonstrates that our decision is the same whether we express the value of the investment in terms of dollars in one year or dollars today.If we convert from dollars today to dollars in one year,($1869.16 today)(1.07$in one year/$today)=$2000 in one year.The two res
23、ults are equivalent,but expressed as values at different points in time.3-26 The Interest Rate:An Exchange Rate Across Time(contd)Present Versus Future Value When we express the value in terms of dollars today,we call it the present value(PV)of the investment.If we express it in terms of dollars in
24、the future,we call it the future value of the investment.3-27 The Interest Rate:An Exchange Rate Across Time(contd)Discount Factors and Rate We can interpret110.9345811.07r11ras the price today of$1 in one year.The amount is called the one-year discount factor.The risk-free rate is also referred to
25、as the discount rate for a risk-free investment.3-28 Textbook Example 3.33-29 Textbook Example 3.3(contd)3-30 Alternative Example 3.3 Problem The cost of replacing a fleet of company trucks with more energy efficient vehicles was$100 million in 2009.The cost is estimated to rise by 8.5%in 2010.If th
26、e interest rate was 4%,what was the cost of a delay in terms of dollars in 2009?3-31 Alternative Example 3.3 Solution If the project were delayed,its cost in 2010 would be:$100 million (1.085)=$108.5 million Compare this amount to the cost of$100 million in 2009 using the interest rate of 4%:$108.5
27、million 1.04=$104.33 million in 2009 dollars.The cost of a delay of one year would be:$104.33 million$100 million=$4.33 million in 2009 dollars.3-32 Figure 3.1 Converting Between Dollars Today and Gold,Euros,or Dollars in the Future 3-33 3.3 Present Value and the NPV Decision Rule The net present va
28、lue(NPV)of a project or investment is the difference between the present value of its benefits and the present value of its costs.Net Present Value(Benefits)(Costs)(All project cash flows)3-34 The NPV Decision Rule When making an investment decision,take the alternative with the highest NPV.Choosing
29、 this alternative is equivalent to receiving its NPV in cash today.3-35 The NPV Decision Rule(contd)Accepting or Rejecting a Project Accept those projects with positive NPV because accepting them is equivalent to receiving their NPV in cash today.Reject those projects with negative NPV because accep
30、ting them would reduce the wealth of investors.3-36 Textbook Example 3.43-37 Textbook Example 3.4(contd)3-38 Choosing Among Alternatives We can also use the NPV decision rule to choose among projects.To do so,we must compute the NPV of each alternative,and then select the one with the highest NPV.Th
31、is alternative is the one which will lead to the largest increase in the value of the firm.3-39 Textbook Example 3.53-40 Textbook Example 3.5(contd)3-41 Choosing Among Alternatives(contd)Table 3.1 Cash Flows and NPVs for Web Site Business Alternatives3-42 NPV and Cash Needs Regardless of our prefere
32、nces for cash today versus cash in the future,we should always maximize NPV first.We can then borrow or lend to shift cash flows through time and find our most preferred pattern of cash flows.3-43 NPV and Cash Needs(contd)Table 3.2 Cash Flows of Hiring and Borrowing Versus Selling and Investing3-44
33、3.4 Arbitrage and the Law of One Price Arbitrage The practice of buying and selling equivalent goods in different markets to take advantage of a price difference.An arbitrage opportunity occurs when it is possible to make a profit without taking any risk or making any investment.Normal Market A comp
34、etitive market in which there are no arbitrage opportunities.3-45 3.4 Arbitrage and the Law of One Price(contd)Law of One Price If equivalent investment opportunities trade simultaneously in different competitive markets,then they must trade for the same price in both markets.3-46 3.5 No-Arbitrage a
35、nd Security Prices Valuing a Security with the Law of One Price Assume a security promises a risk-free payment of$1000 in one year.If the risk-free interest rate is 5%,what can we conclude about the price of this bond in a normal market?Price(Bond)=$952.38($1000 in one year)($1000 in one year)(1.05$
36、in one year/$today)$952.38 today3-47 Identifying Arbitrage Opportunities with Securities What if the price of the bond is not$952.38?Assume the price is$940.The opportunity for arbitrage will force the price of the bond to rise until it is equal to$952.38.Table 3.3 Net Cash Flows from Buying the Bon
37、d and Borrowing3-48 Identifying Arbitrage Opportunities with Securities What if the price of the bond is not$952.38?Assume the price is$960.The opportunity for arbitrage will force the price of the bond to fall until it is equal to$952.38.Table 3.4 Net Cash Flows from Selling the Bond and Investing3
38、-49 Determining the No-Arbitrage Price Unless the price of the security equals the present value of the securitys cash flows,an arbitrage opportunity will appear.No Arbitrage Price of a SecurityPrice(Security)(All cash flows paid by the security)3-50 Textbook Example 3.63-51 Textbook Example 3.6(con
39、td)3-52 Determining the Interest Rate From Bond Prices If we know the price of a risk-free bond,we can use to determine what the risk-free interest rate must be if there are no arbitrage opportunities.Price(Security)(All cash flows paid by the security)3-53 Determining the Interest Rate From Bond Pr
40、ices(contd)Suppose a risk-free bond that pays$1000 in one year is currently trading with a competitive market price of$929.80 today.The bonds price must equal the present value of the$1000 cash flow it will pay.3-54 Determining the Interest Rate From Bond Prices(contd)The risk-free interest rate mus
41、t be 7.55%.$929.80 today ($1000 in one year)(1$in one year/$today)$1000 in one year1 1.0755$in one year/$today$929.80 today3-55 The NPV of Trading Securities and Firm Decision Making In a normal market,the NPV of buying or selling a security is zero.(Buy security)(All cash flows paid by the security
42、)Price(Security)0(Sell security)Price(Security)(All cash flows paid by the security)03-56 The NPV of Trading Securities and Firm Decision Making(contd)Separation Principle We can evaluate the NPV of an investment decision separately from the decision the firm makes regarding how to finance the inves
43、tment or any other security transactions the firm is considering.3-57 Textbook Example 3.7 3-58 Textbook Example 3.7(contd)3-59 Valuing a Portfolio The Law of One Price also has implications for packages of securities.Consider two securities,A and B.Suppose a third security,C,has the same cash flows
44、 as A and B combined.In this case,security C is equivalent to a portfolio,or combination,of the securities A and B.Value AdditivityPrice(C)Price(A B)Price(A)Price(B)3-60 Textbook Example 3.8 3-61 Textbook Example 3.8(contd)3-62 Alternative Example 3.8 Problem Moon Holdings is a publicly traded compa
45、ny with only three assets:It owns 50%of Due Beverage Co.,70%of Mountain Industries,and 100%of the Oxford Bears,a football team.The total market value of Moon Holdings is$200 million,the total market value of Due Beverage Co.is$75 million and the total market value of Mountain Industries is$100 milli
46、on.What is the market value of the Oxford Bears?3-63 Alternative Example 3.8(contd)Solution Think of Moon as a portfolio consisting of a:50%stake in Due Beverage 50%$75 million=$37.5 million 70%stake in Mountain Industries 70%$100 million=$70 million 100%stake in Oxford Bears Under the Value Added M
47、ethod,the sum of the value of the stakes in all three investments must equal the$200 million market value of Moon.The Oxford Bears must be worth:$200 million$37.5 million$70 million=$92.5 million3-64 Chapter Quiz1.If gasoline trades in a competitive market,would a transportation company that has a u
48、se for the gasoline value it differently than another investor?2.How do you compare benefits at different points in time?3.If interest rates fall,what happens to the value today of a promise of money in one year?4.What is the NPV decision rule?3-65 Chapter Quiz(contd)5.Does the NPV decision rule dep
49、end on the investors preferences?6.What is the Law of One Price?7.What is Arbitrage?8.If a firm makes an investment that has a negative NPV,how does the value of the firm change?9.What is the Separation Principle?Chapter 3 Appendix3-67 Learning Objectives1.Calculate the value of a risky asset,using
50、the Law of One Price.2.Describe the relationship between a securitys risk premium and its correlation with returns of other securities.3.Describe the effect of transactions costs on arbitrage and the Law of One Price.3-68 Appendix:The Price of Risk Risky Versus Risk-free Cash Flows Assume there is a
