公司理财讲义3巫和懋

1、Corporate Finance3-0 Professor Ho-Mou Wu3.1 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)3-1 P

2、rofessor Ho-Mou WuCorporate Finance3.1 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 yea

3、r zero: Price = 7584 year zero: Price = 6831 year bond2 year bond3 year bond4 year bondy1y2y3y4i1i2?i4?i3?(maturity date)3-2 Professor Ho-Mou WuCorporate FinanceThe Present Value Formulas for BondsPure Discount BondsLevel Coupon BondsConsolsfor T-maturity bonds with face value F.TTyFyCyCyC1 1 1 1 PV

4、P2 B,1PVPBTTyFSuch a rate y is known as the yield to maturity (YTM). The yield to maturity is a complicated average of different rates of interest. It can be a useful summary measure. yC PVPB (3.1) (3.2) (3.3)3-3 Professor Ho-Mou WuCorporate FinanceYield to MaturityExample 1.(continued): we can conv

5、ert 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 maturity (n) ” yield curve” to summarize information about bond prices (diagram 1). ny)1 (10009261y22)1 (1000842y33)1 (1000758y44)1 (1000683y)(%

6、8111yiy%92y%66. 93y%104y3-4 Professor Ho-Mou WuCorporate Finance3.2 The Term Structure of Interest RatesFrom bond prices, we can compute yields , plot the “yield curve”, and compute the implied forward rates, . ny nf Yield Curve Maturity % 10 8 6 4 2 2 1 3 4 implied “forward rates”yield curve or “sp

7、ot rates”3-5 Professor Ho-Mou WuCorporate FinanceForward Rates is the “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).Similar

8、ly, nf. 1 1 1, 1 1 1, 1 1 144433333222221yfyyfyyfy1 . 1)08. 1 ()09. 1 (122 f%102f%102f21221fyy.%11 so ),(3133213fffyy.%11 so ),(31443214ffffyy3-6 Professor Ho-Mou WuCorporate FinanceForecast of Future InterestCan we use forward rates fn to forecast future short-term interest rates in, also called “s

9、hort 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 1st year (risky, subject to price risk at the end of

10、 1st year.)842 ? 1000 926 1000 (A) (B) i2=? )1 (10002iPB3-7 Professor Ho-Mou WuCorporate FinancePure 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

11、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) 1111or 1 1 9261000 iyyEE222222i11 1 11 84211000 2EyiyEiE222111 1 1 iEyy21221 11fyy2211 11iEf )( 2or 1 1 222iEfiEfni nniEf3-

12、8 Professor Ho-Mou WuCorporate FinanceLiquidity Preference Hypothesis Assume investors are Risk averse. Still with one-year investment horizon (preference for “liquidity”). Since (B) is riskier, (B) should have higher expected return to attract investors： .Hence . The Liquidity Preference Hypothesis

13、: + risk premium = f2 . In general, fn - risk premium = .(3.5) )1 (11)1 (1222yiEy)(21111222iEfiEf 2iE niE3-9 Professor Ho-Mou WuCorporate Finance3.3 Alternative Investment Rules How long does it take the project to “pay back” its initial investment? Payback Period = number of years to recover initia

14、l costs Minimum Acceptance Criteria: set by management Ranking Criteria: set by management(1) The Payback Period Rule3-10 Professor Ho-Mou WuCorporate Finance(1) The Payback Period Rule (continued) Disadvantages: Ignores the time value of money Ignores cash flows after the payback period Biased agai

15、nst long-term projects Requires an arbitrary acceptance criteria A project accepted based on the payback criteria may not have a positive NPV Advantages: Easy to understand Biased toward liquidity3-11 Professor Ho-Mou WuCorporate FinanceThe Discounted Payback Period Rule How long does it take the pr

16、oject to “pay back” its initial investment taking the time value of money into account? By the time you have discounted the cash flows, you might as well calculate the NPV.3-12 Professor Ho-Mou WuCorporate Finance(2) The Average Accounting Return Rule Another attractive but fatally flawed approach.

17、Ranking Criteria and Minimum Acceptance Criteria set by management Disadvantages: Ignores the time value of money Uses an arbitrary benchmark cutoff rate Based on book values, not cash flows and market values Advantages: The accounting information is usually available Easy to calculateInvestent of V

18、alueBook AverageIncomeNet AverageAAR 3-13 Professor Ho-Mou WuCorporate Finance (3) The Internal Rate of Return (IRR) Rule IRR: the discount that sets NPV to zero Minimum Acceptance Criteria: Accept if the IRR exceeds the required return. Ranking Criteria: Select alternative with the highest IRR Rein

19、vestment 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 IRR Problems with mutually exclusive investments Advantages: Easy to understand and communicate3-14 Professor Ho-M

20、ou WuCorporate Finance(3) The Internal Rate of Return: ExampleExample 3Consider the following project:0123$50$100$150-$200The internal rate of return for this project is 19.44%32)1 (150$)1 (100$)1 (50$0IRRIRRIRRNPV3-15 Professor Ho-Mou WuCorporate FinanceThe NPV Payoff Profile for This ExampleDiscou

21、nt RateNPV0%$100.004%$71.048%$47.3212%$27.7916%$11.6520%($1.74)24%($12.88)28%($22.17)32%($29.93)36%($36.43)40%($41.86)If we graph NPV versus discount rate, we can see the IRR as the x-axis intercept.IRR = 19.44%($60.00)($40.00)($20.00)$0.00$20.00$40.00$60.00$80.00$100.00$120.00-1%9%19%29%39%Discount

22、 rateNPV3-16 Professor Ho-Mou WuCorporate FinanceProblems with the IRR Approach Multiple IRRs. Are We Borrowing or Lending? The Scale Problem. The Timing Problem.3-17 Professor Ho-Mou WuCorporate FinanceMultiple IRRsExample 4: There are two IRRs for this project: 0 1 2 3$200 $800-$200- $800($150.00)

23、($100.00)($50.00)$0.00$50.00$100.00-50%0%50%100%150%200%Discount rateNPV100% = IRR20% = IRR1Which one should we use? 3-18 Professor Ho-Mou WuCorporate FinanceThe 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 o

24、n a $1,000 investment?3-19 Professor Ho-Mou WuCorporate FinanceThe 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 project in this case depends on the discount rate, not the IRR. Example 5:3-20 Professor Ho-Mou WuCorporate FinanceT

25、he Timing Problem($4,000.00)($3,000.00)($2,000.00)($1,000.00)$0.00$1,000.00$2,000.00$3,000.00$4,000.00$5,000.000%10%20%30%40%Discount rateNPVProject AProject B10.55% = crossover rate12.94% = IRRB16.04% = IRRAExample 5:3-21 Professor Ho-Mou WuCorporate FinanceCalculating the Crossover RateCompute the

26、 IRR for either project “A-B” or “B-A”Year Project A Project B Project A-B Project B-A 0 ($10,000) ($10,000)$0$01$10,000$1,000$9,000($9,000)2$1,000$1,000$0$03$1,000$12,000($11,000)$11,000($3,000.00)($2,000.00)($1,000.00)$0.00$1,000.00$2,000.00$3,000.000%5%10%15%20%Discount rateNPVA-BB-A10.55% = IRRE

27、xample 5:3-22 Professor Ho-Mou WuCorporate FinanceMutually Exclusive vs. Independent Project Mutually Exclusive 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 rejec

28、ting one project does not affect the decision of the other projects. Must exceed a MINIMUM acceptance criteria.3-23 Professor Ho-Mou WuCorporate Finance(4) The Profitability Index (PI) Rule Minimum Acceptance Criteria: Accept if PI 1 Ranking Criteria: Select alternative with highest PI Disadvantages

29、: Problems with mutually exclusive investments Advantages: May be useful when available investment funds are limited Easy to understand and communicate Correct decision when evaluating independent projectsInvestent InitialFlowsCash Future of PV TotalPI 3-24 Professor Ho-Mou WuCorporate Finance3.4 Why Use Net Present Value? Accepting positive NPV projec