1、Bond Market and Alternative Investment Rules3.1 Valuation of Bonds3.2 The Term Structure of Interest Rates3.3 Alternative Investment Rules(1) The Payback Period Rule(2) The Average Accounting Return(3) The Internal Rate of Return(4) The Profitability Index3.4 Why Use Net Present Value? (RWJ Ch.5,6)3

2、.1 Valuation of BondsExample 1： Suppose we observe the following bond prices for default-free zero coupon bonds (pure discount bond, with face value $1,000)： How are the bond prices related with interest rates? 1 year zero: Price = 9262 year zero: Price = 8423 year zero: Price = 7584 year zero: Pric

3、e = 6831 year bond2 year bond3 year bond4 year bondy1y2y3y4i1i2?i4?i3?(maturity date)The Present Value Formulas for BondsPure Discount BondsLevel Coupon BondsConsolsfor T-maturity bonds with face value F.Such a rate y is known as the yield to maturity (YTM). The yield to maturity is a complicated av

4、erage of different rates of interest. It can be a useful summary measure. (3.1) (3.2) (3.3)Yield to MaturityExample 1.(continued): we can convert bond prices into “yield to maturity” ( )hence, yn= yield of bonds with n periods as time to maturity, also called “spot rates.” Plot yn against time to ma

5、turity (n) ” yield curve” to summarize information about bond prices (diagram 1). 3.2 The Term Structure of Interest RatesFrom bond prices, we can compute yields , plot the “yield curve”, and compute the implied forward rates, . implied “forward rates”yield curve or “spot rates”Forward Rates is the

6、“break-even” interest rate that equates the returns on a n-period bond to that of a (n 1) period bond rolled over into a one-year bond in year n. For example, , (geometric mean) or , soas an approximation (arithmetic mean).Similarly, Forecast of Future InterestCan we use forward rates fn to forecast

7、 future short-term interest rates in, also called “short rates”？ Assume that the investment horizon is one year, and investors are risk neutral. Example 2: Consider two investment alternatives： (A) buy 1-year zero-coupon bond (safe, no risk).(B) buy 2-year zero-coupon bond and sell it at the end of

8、1st year (risky, subject to price risk at the end of 1st year.)842 ? 1000 926 1000 (A) (B) i2=? Pure Expectation HypothesisExpected return of (A) Expected return of (B) Assume that investors are risk-neutral. These two expected returns should be the same (do not worry about different risks involved

9、in (A) and (B)： and we knowSo , henceThe forward rates are market expectations of future short-term interest rates . This is called the Pure Expectations Hypothesis： . . .(3.4) Liquidity Preference Hypothesis Assume investors are Risk averse. Still with one-year investment horizon (preference for “l(fā)

10、iquidity”). Since (B) is riskier, (B) should have higher expected return to attract investors： .Hence . The Liquidity Preference Hypothesis: + risk premium = f2 . In general, fn - risk premium = .(3.5) 3.3 Alternative Investment RulesHow long does it take the project to “pay back” its initial invest

11、ment?Payback Period = number of years to recover initial costsMinimum Acceptance Criteria: set by managementRanking Criteria: set by management(1) The Payback Period Rule(1) The Payback Period Rule (continued)Disadvantages:Ignores the time value of moneyIgnores cash flows after the payback periodBia

12、sed against long-term projectsRequires an arbitrary acceptance criteriaA project accepted based on the payback criteria may not have a positive NPVAdvantages:Easy to understandBiased toward liquidityThe Discounted Payback Period RuleHow long does it take the project to “pay back” its initial investm

13、ent taking the time value of money into account?By the time you have discounted the cash flows, you might as well calculate the NPV.(2) The Average Accounting Return RuleAnother attractive but fatally flawed approach.Ranking Criteria and Minimum Acceptance Criteria set by managementDisadvantages:Ign

14、ores the time value of moneyUses an arbitrary benchmark cutoff rateBased on book values, not cash flows and market valuesAdvantages:The accounting information is usually availableEasy to calculate (3) The Internal Rate of Return (IRR) RuleIRR: the discount that sets NPV to zero Minimum Acceptance Cr

15、iteria: Accept if the IRR exceeds the required return.Ranking Criteria: Select alternative with the highest IRRReinvestment assumption: All future cash flows assumed reinvested at the IRR.Disadvantages:Does not distinguish between investing and borrowing.IRR may not exist or there may be multiple IR

16、R Problems with mutually exclusive investmentsAdvantages:Easy to understand and communicate(3) The Internal Rate of Return: ExampleExample 3Consider the following project:0123$50$100$150-$200The internal rate of return for this project is 19.44%The NPV Payoff Pro This ExampleIf we graph NPV versus d

17、iscount rate, we can see the IRR as the x-axis intercept.IRR = 19.44%Problems with the IRR ApproachMultiple IRRs.Are We Borrowing or Lending?The Scale Problem.The Timing Problem.Multiple IRRsExample 4: There are two IRRs for this project: 0 1 2 3$200 $800-$200- $800100% = IRR20% = IRR1Which one shou

18、ld we use? The Scale ProblemWould you rather make 100% or 50% on your investments?What if the 100% return is on a $1 investment while the 50% return is on a $1,000 investment?The Timing Problem0 1 2 3$10,000 $1,000$1,000-$10,000Project A0 1 2 3$1,000 $1,000 $12,000-$10,000Project BThe preferred proj

19、ect in this case depends on the discount rate, not the IRR. Example 5:The Timing Problem10.55% = crossover rate12.94% = IRRB16.04% = IRRAExample 5:Calculating the Crossover RateCompute the IRR for either project “A-B” or “B-A”10.55% = IRRExample 5:Mutually Exclusive vs. Independent ProjectMutually E

20、xclusive Projects: only ONE of several potential projects can be chosen, e.g. acquiring an accounting system. RANK all alternatives and select the best one.Independent Projects: accepting or rejecting one project does not affect the decision of the other projects.Must exceed a MINIMUM acceptance cri

21、teria.(4) The Profitability Index (PI) RuleMinimum Acceptance Criteria: Accept if PI 1Ranking Criteria: Select alternative with highest PIDisadvantages:Problems with mutually exclusive investmentsAdvantages:May be useful when available investment funds are limitedEasy to understand and communicateCorrect decision when evaluating independent projects3.4 Why Use Net Present Value?Accepting positive NPV projects benefits shareholders.NPV uses cash flowsNPV uses all the cash flows of the projectNPV discounts the cash fl