乔纳森-伯克-公司理财--课件(3)

1、Chapter 3Arbitrage and Financial Decision MakingChapter 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 PricesLearning ObjectivesAssess the relative merits of two-

2、period projects using net present value.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.Explain why maximizing NPV is always the correct decision rule.Define

3、 arbitrage, and discuss its role in asset pricing. How does it relate to the Law of One Price?Calculate the no-arbitrage price of an investment opportunity.Learning Objectives (contd)Show how value additivity can be used to help managers maximize the value of the firm.Describe the Separation Princip

4、le.3.1 Valuing DecisionsIdentify Costs and BenefitsMay need help from other areas in identifying the relevant costs and benefitsMarketingEconomicsOrganizational BehaviorStrategyOperationsAnalyzing Costs and BenefitsSuppose a jewelry manufacturer has the opportunity to trade 10 ounces of platinum and

5、 receive 20 ounces of gold today. To compare the costs and benefits, we first need to convert them to a common unit.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 receive has a cash value of:(20 ounc

6、es of gold) X ($250/ounce) = $5000 todayAnalyzing 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) = $5500Analyzing Costs and Benefits (contd)Therefore

7、, 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 = $500Because it is negative, the costs exceed the benefits and the jeweler should reject the trade.Using Market Prices to Determine Cash ValuesCompetiti

8、ve MarketA 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 price was fair or whether the

9、jeweler would use the silver or gold.Textbook Example 3.1Textbook Example 3.1 (contd)Alternative Example 3.1ProblemYour 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 is either a new motorcycle, with a MSRP of $

10、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?Alternative Example 3.1 (contd)SolutionCompetitive markets, not your personal preferences (or the MSRP of the motorc

11、ycle), 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.Textbook Example 3.2Textbook Example 3.2 (contd)Alterna

12、tive Example 3.2ProblemYou 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 current exchange rate is $1.50 per . Sh

13、ould you take this opportunity? Would your decision change if you believed the value of the euro would rise over the next month?Alternative Example 3.2 (contd)SolutionThe costs and benefits must be converted to their cash values. Assuming competitive market prices:2,500 shares $9/share = $22,50010,0

14、00 $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 the value the decision

15、 today.3.2 Interest Rates and the Time Value of MoneyTime Value of MoneyConsider an investment opportunity with the following certain cash flows.Cost: $100,000 todayBenefit: $105,000 in one yearThe difference in value between money today and money in the future is due to the time value of money.The

16、Interest Rate: An Exchange Rate Across TimeThe 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 one year for each $1 today.Risk

17、Free Interest Rate (Discount Rate), rf: The interest rate at which money can be borrowed or lent without risk.Interest Rate Factor = 1 + rfDiscount Factor = 1 / (1 + rf)The Interest Rate: An Exchange Rate Across Time (contd)Value of Investment in One YearIf the interest rate is 7%, then we can expre

18、ss our costs as:Cost = ($100,000 today) (1.07 $ in one year/$ today)= $107,000 in one yearThe Interest Rate: An Exchange Rate Across Time (contd)Value of Investment in One YearBoth costs and benefits are now in terms of “dollars in one year,” so we can compare them and compute the investments net va

19、lue:$105,000 $107,000 = $2000 in one yearIn 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.The Interest Rate: An Exchange Rate Across Time (contd)Value of Investment TodayConsider the benefit o

20、f $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 todayThis is the amount the bank would lend to us today if we promised to repay $105,000 in one year.The Interest

21、 Rate: An Exchange Rate Across Time (contd)Value of Investment TodayNow we are ready to compute the net value of the investment:$98,130.84 $100,000 = $1869.16 todayOnce again, the negative result indicates that we should reject the investment. The Interest Rate: An Exchange Rate Across Time (contd)P

22、resent Versus Future ValueThis 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

23、 results are equivalent, but expressed as values at different points in time.The Interest Rate: An Exchange Rate Across Time (contd)Present Versus Future ValueWhen 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 dollar

24、s in the future, we call it the future value of the investment.The Interest Rate: An Exchange Rate Across Time (contd)Discount Factors and RateWe can interpretas 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 as the disco

25、unt rate for a risk-free investment.Textbook Example 3.3Textbook Example 3.3 (contd)Alternative Example 3.3ProblemThe 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 the interest rate was 4%,

26、what was the cost of a delay in terms of dollars in 2009?Alternative Example 3.3SolutionIf the project were delayed, its cost in 2010 would be:$100 million (1.085) = $108.5 millionCompare this amount to the cost of $100 million in 2009 using the interest rate of 4%:$108.5 million 1.04 = $104.33 mill

27、ion in 2009 dollars.The cost of a delay of one year would be:$104.33 million $100 million = $4.33 million in 2009 dollars.Figure 3.1 Converting Between Dollars Today and Gold, Euros, or Dollars in the Future 3.3 Present Value and the NPV Decision RuleThe net present value (NPV) of a project or inves

28、tment is the difference between the present value of its benefits and the present value of its costs.Net Present Value The NPV Decision RuleWhen making an investment decision, take the alternative with the highest NPV. Choosing this alternative is equivalent to receiving its NPV in cash today.The NP

29、V Decision Rule (contd)Accepting or Rejecting a ProjectAccept those projects with positive NPV because accepting them is equivalent to receiving their NPV in cash today.Reject those projects with negative NPV because accepting them would reduce the wealth of investors.Textbook Example 3.4Textbook Ex

30、ample 3.4 (contd)Choosing Among AlternativesWe 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. This alternative is the one which will lead to the largest increase in the value of the fir

31、m.Textbook Example 3.5Textbook Example 3.5 (contd)Choosing Among Alternatives (contd)Table 3.1 Cash Flows and NPVs for Web Site Business AlternativesNPV and Cash NeedsRegardless of our preferences for cash today versus cash in the future, we should always maximize NPV first. We can then borrow or le

32、nd to shift cash flows through time and find our most preferred pattern of cash flows.NPV and Cash Needs (contd)Table 3.2 Cash Flows of Hiring and Borrowing Versus Selling and Investing3.4 Arbitrage and the Law of One PriceArbitrageThe practice of buying and selling equivalent goods in different mar

33、kets 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 MarketA competitive market in which there are no arbitrage opportunities.3.4 Arbitrage and the Law of One Price (contd)Law of One

34、 PriceIf equivalent investment opportunities trade simultaneously in different competitive markets, then they must trade for the same price in both markets.3.5 No-Arbitrage and Security PricesValuing a Security with the Law of One PriceAssume a security promises a risk-free payment of $1000 in one y

35、ear. If the risk-free interest rate is 5%, what can we conclude about the price of this bond in a normal market?Price(Bond) = $952.38Identifying Arbitrage Opportunities with SecuritiesWhat if the price of the bond is not $952.38?Assume the price is $940.The opportunity for arbitrage will force the p

36、rice of the bond to rise until it is equal to $952.38.Table 3.3 Net Cash Flows from Buying the Bond and BorrowingIdentifying Arbitrage Opportunities with SecuritiesWhat 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

37、fall until it is equal to $952.38.Table 3.4 Net Cash Flows from Selling the Bond and InvestingDetermining the No-Arbitrage PriceUnless the price of the security equals the present value of the securitys cash flows, an arbitrage opportunity will appear.No Arbitrage Price of a SecurityTextbook Example

38、 3.6Textbook Example 3.6 (contd)Determining the Interest Rate From Bond PricesIf 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.Determining the Interest Rate From Bond Prices (contd)Suppose a risk-free b

39、ond 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.Determining the Interest Rate From Bond Prices (contd)The risk-free interest rate must be 7.55%.The NPV of Trading Se

40、curities and Firm Decision MakingIn a normal market, the NPV of buying or selling a security is zero.The NPV of Trading Securities and Firm Decision Making (contd)Separation PrincipleWe can evaluate the NPV of an investment decision separately from the decision the firm makes regarding how to financ

41、e the investment or any other security transactions the firm is considering.Textbook Example 3.7 Textbook Example 3.7 (contd)Valuing a PortfolioThe 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

42、 as A and B combined. In this case, security C is equivalent to a portfolio, or combination, of the securities A and B.Value AdditivityTextbook Example 3.8 Textbook Example 3.8 (contd)Alternative Example 3.8ProblemMoon Holdings is a publicly traded company with only three assets:It owns 50% of Due B

43、everage 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 million.What is the market value of the

44、Oxford Bears?Alternative Example 3.8 (contd)SolutionThink of Moon as a portfolio consisting of a:50% stake in Due Beverage50% $75 million = $37.5 million70% stake in Mountain Industries70% $100 million = $70 million100% stake in Oxford BearsUnder the Value Added Method, the sum of the value of the s

45、takes 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 millionChapter QuizIf gasoline trades in a competitive market, would a transportation company that has a use for the gasoline value it differ

46、ently than another investor?How do you compare benefits at different points in time?If interest rates fall, what happens to the value today of a promise of money in one year?What is the NPV decision rule?Chapter Quiz (contd)Does the NPV decision rule depend on the investors preferences?What is the L

47、aw of One Price?What is Arbitrage?If a firm makes an investment that has a negative NPV, how does the value of the firm change?What is the Separation Principle?Chapter 3 AppendixLearning ObjectivesCalculate the value of a risky asset, using the Law of One Price.Describe the relationship between a se

48、curitys risk premium and its correlation with returns of other securities.Describe the effect of transactions costs on arbitrage and the Law of One Price.Appendix: The Price of RiskRisky Versus Risk-free Cash FlowsAssume there is an equal probability of either a weak economy or strong economy.Table

49、3A.1 Cash Flows and Market Prices (in $) of a Risk-FreeBond and an Investment in the Market PortfolioAppendix: The Price of Risk (contd)Risky Versus Risk-free Cash Flows (contd)Expected Cash Flow (Market Index) ($800) + ($1400) = $1100 Although both investments have the same expected value, the mark

50、et index has a lower value since it has a greater amount of risk.Risk Aversion and the Risk PremiumRisk AversionInvestors prefer to have a safe income rather than a risky one of the same average amount.Risk PremiumThe additional return that investors expect to earn to compensate them for a securitys

51、 risk.When a cash flow is risky, to compute its present value we must discount the cash flow we expect on average at a rate that equals the risk-free interest rate plus an appropriate risk premium.Risk Aversion and the Risk Premium (contd)Market return if the economy is strong(1400 1000) / 1000 = 40

52、%Market return if the economy is weak(800 1000) / 1000 = 20%Expected market return (40%) + (20%) = 10%The No-Arbitrage Price of a Risky SecurityIf we combine security A with a risk-free bond that pays $800 in one year, the cash flows of the portfolio in one year are identical to the cash flows of th

53、e market index.By the Law of One Price, the total market value of the bond and security A must equal $1000, the value of the market index. Table 3A.2 Determining the Market Price of Security A (cash flows in $)The No-Arbitrage Price of a Risky Security (contd)Given a risk-free interest rate of 4%, t

54、he market price of the bond is:($800 in one year) / (1.04 $ in one year/$ today) = $769 todayTherefore, the initial market price of security A is $1000 $769 = $231.Risk Premiums Depend on RiskIf an investment has much more variable returns, it must pay investors a higher risk premium.Risk Is Relativ

55、e to the Overall MarketThe risk of a security must be evaluated in relation to the fluctuations of other investments in the economy. A securitys risk premium will be higher the more its returns tend to vary with the overall economy and the market index. If the securitys returns vary in the opposite direction of the market index, it offers insurance and will have a negative risk premium.Risk Is Relative to the Overall Market (contd)Table 3A.3 Risk and Risk Premiums for Different SecuritiesTextbook Example 3.A.1Textbook Example 3A.1 (con