公司理财讲义（3）--巫和懋

1、Corporate Finance3-0 Professor Ho-Mou Wu 3.1 Valuation of Bonds 3.2 The Term Structure of Interest Rates 3.3 Alternative Investment Rules (1) The Payback Period Rule (2) The Average Accounting Return (3) The Internal Rate of Return (4) The Profitability Index 3.4 Why Use Net Present Value? (RWJ Ch.5

2、,6) 3-1 Professor Ho-Mou WuCorporate Finance 3.1 Valuation of Bonds Example 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 = 926 2 year zero: Pric

3、e = 842 3 year zero: Price = 758 4 year zero: Price = 683 1 year bond 2 year bond 3 year bond 4 year bond y1 y2 y3 y4 i1i2?i4?i3? (maturity date) 3-2 Professor Ho-Mou WuCorporate Finance The Present Value Formulas for Bonds Pure Discount Bonds Level Coupon Bonds Consols for T-maturity bonds with fac

4、e value F. TT y F y C y C y C 1 1 1 1 PVP 2 B , 1 PVPB T T y F Such 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. y C PVPB (3.1) (3.2) (3.3) 3-3 Professor Ho-Mou WuCorporate Finance

5、 Yield to Maturity Example 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 maturity (n) ” yield curve” to summarize information about bond prices (diagram 1). n y )1

6、 ( 1000 926 1 y 2 2) 1 ( 1000 842 y 3 3) 1 ( 1000 758 y 4 4) 1 ( 1000 683 y )(%8 111 yiy %9 2 y %66. 9 3 y %10 4 y 3-4 Professor Ho-Mou WuCorporate Finance 3.2 The Term Structure of Interest Rates From bond prices, we can compute yields , plot the “yield curve”, and compute the implied forward rates

7、, . n y n f Yield Curve Maturity % 10 8 6 4 2 2 1 3 4 implied “forward rates” yield curve or “spot rates” 3-5 Professor Ho-Mou WuCorporate Finance Forward 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

8、bond in year n. For example, , (geometric mean) or , soas an approximation (arithmetic mean). Similarly, n f . 1 1 1 , 1 1 1 , 1 1 1 4 44 3 3 3 33 2 2 2 221 yfy yfy yfy 1 . 1 )08. 1 ( )09. 1 ( 1 2 2 f%10 2 f %10 2 f 212 2 1 fyy .%11 so ),( 3 1 33213 fffyy .%11 so ),( 3 1 443214 ffffyy 3-6 Professor

9、Ho-Mou WuCorporate Finance Forecast of Future Interest Can we use forward rates fn to forecast 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-ye

10、ar 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 1st year.) 842 ? 1000 926 1000 (A) (B) i2=? )1 ( 1000 2 i P B 3-7 Professor Ho-Mou WuCorporate Finance Pure Expectation Hypothesis Expected return of (A

11、) 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 in (A) and (B)： and we know So , hence The forward rates are market expectations of future short-term interest rates . This is called the Pure E

12、xpectations Hypothesis： . . .(3.4) 111 1or 1 1 926 1000 iyyEE 2 2 2 2 2 2 i1 1 1 1 1 842 1 1000 2 Ey i y E i E 2 2 21 1 1 1 1 i Eyy 2 1 2 2 1 1 1 f y y 22 1 1 1 1 i E f )( 2 or 1 1 2 22 iEfiEf n i nn iEf 3-8 Professor Ho-Mou WuCorporate Finance Liquidity Preference Hypothesis Assume investors are Ri

13、sk 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: + risk premium = f2 . In general, fn - risk premium = .(3.5) )1 ( 1 1 )1 ( 1 2 2 2 y i Ey

14、)(2 1 1 1 1 2 22 iEf i E f 2 iE n iE 3-9 Professor Ho-Mou WuCorporate Finance 3.3 Alternative Investment Rules How long does it take the project to “pay back” its initial investment? Payback Period = number of years to recover initial costs Minimum Acceptance Criteria: set by management Ranking Crit

15、eria: set by management (1) The Payback Period Rule 3-10 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 against long-term projects Requires an arbitrary acceptance criteria

16、 A project accepted based on the payback criteria may not have a positive NPV Advantages: Easy to understand Biased toward liquidity 3-11 Professor Ho-Mou WuCorporate Finance The Discounted Payback Period Rule How long does it take the project to “pay back” its initial investment taking the time val

17、ue 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. Ranking Criteria and Minimum Acceptance Criteria set by mana

18、gement 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 calculate Investent of ValueBook Average IncomeNet Average AAR 3-13 Professor Ho-Mo

19、u 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 Reinvestment assumption: All future cash flows assumed reinve

20、sted 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 communicate 3-14 Professor Ho-Mou WuCorporate Finance (3) The Internal Rate of Return:

21、Example Example 3 Consider the following project: 0123 $50$100$150 -$200 The internal rate of return for this project is 19.44% 32 )1 ( 150$ )1 ( 100$ )1 ( 50$ 0 IRRIRRIRR NPV 3-15 Professor Ho-Mou WuCorporate Finance The NPV Payoff Profile for This Example Discount RateNPV 0%$100.00 4%$71.04 8%$47.

22、32 12%$27.79 16%$11.65 20%($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 rate NPV 3

23、-16 Professor Ho-Mou WuCorporate Finance Problems with the IRR Approach Multiple IRRs. Are We Borrowing or Lending? The Scale Problem. The Timing Problem. 3-17 Professor Ho-Mou WuCorporate Finance Multiple IRRs Example 4: There are two IRRs for this project: 0 1 2 3 $200 $800 -$200 - $800 ($150.00)

24、($100.00) ($50.00) $0.00 $50.00 $100.00 -50%0%50%100%150%200% Discount rate NPV 100% = IRR2 0% = IRR1 Which one should we use? 3-18 Professor Ho-Mou WuCorporate Finance The Scale Problem Would you rather make 100% or 50% on your investments? What if the 100% return is on a $1 investment while the 50

25、% return is on a $1,000 investment? 3-19 Professor Ho-Mou WuCorporate Finance The Timing Problem 0 1 2 3 $10,000 $1,000$1,000 -$10,000 Project A 0 1 2 3 $1,000 $1,000 $12,000 -$10,000 Project B The preferred project in this case depends on the discount rate, not the IRR. Example 5: 3-20 Professor Ho

26、-Mou WuCorporate Finance The 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 $5,000.00 0%10%20%30%40% Discount rate NPV Project A Project B 10.55% = crossover rate 12.94% = IRRB16.04% = IRRA Example 5: 3-21 Professor Ho-Mou WuCorporate Fin

27、ance Calculating the Crossover Rate Compute the 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$0 1$10,000$1,000$9,000($9,000) 2$1,000$1,000$0$0 3$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

28、 $3,000.00 0%5%10%15%20% Discount rate NPV A-B B-A 10.55% = IRR Example 5: 3-22 Professor Ho-Mou WuCorporate Finance Mutually Exclusive vs. Independent Project Mutually Exclusive Projects: only ONE of several potential projects can be chosen, e.g. acquiring an accounting system. RANK all alternative

29、s 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 criteria. 3-23 Professor Ho-Mou WuCorporate Finance (4) The Profitability Index (PI) Rule Minimum Acceptance Criteria: Accept if PI

30、 1 Ranking Criteria: Select alternative with highest PI Disadvantages: 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 projects Investent Initial FlowsCash Future of PV Total PI 3-24 Professor Ho-Mou WuCorporate Finance 3.4 Why Use Net Present Value? A