公司理财课件英文版(ppt 25).pptx

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1、Corporate Finance2-0 Professor Ho-Mou Wu2.1 Net Present Value2.2 Project Valuation in a Riskless World Fishers Principle2.3 Present Value and Compounding2.4 Present Value with Special Cash Flows (RWJ Ch 3, 4)Corporate Finance2-1 Professor Ho-Mou WuInvestment DecisionExample 1: Suppose an investment

2、that promises to pay $10,000 in one year is offered for sale for $9,500. Your interest rate is 5%. Should you buy? If you were to be promised $10,000 due in one year when interest rates are at 5-percent, your investment be worth $9,523.81 in todays dollars. 05. 1000,10$81.523, 9$Corporate Finance2-2

3、 Professor Ho-Mou Wu2.1 Net Present Value : FV and PV The amount that a borrower would need to set aside today to to able to meet the promised payment of $10,000 in one year is call the Present Value (PV) of $10,000.Note that $10,000 = $9,523.81(1.05). If you were to invest $10,000 at 5-percent inte

4、rest for one year, your investment would grow to $10,500 : $10,500 = $10,000(1.05).The total amount due at the end of the investment is call the Future Value (FV). Corporate Finance2-3 Professor Ho-Mou WuNet Present Value The Net Present Value (NPV) of an investment is the present value of the expec

5、ted cash flows, less the cost of the investment. 81.523, 9$500, 9$05. 1000,10$500, 9$NPVNPV: So you should Invest.81.23$NPVBack to Example 1:Corporate Finance2-4 Professor Ho-Mou WuNet Present Value as the Investment CriterionIn the one-period case, the formula for NPV can be written as:PVCostNPVIf

6、we had not undertaken the positive NPV project considered on the last slide, and instead invested our $9,500 elsewhere at 5-percent, our FV would be less than the $10,000 that investment promised and we would be unambiguously worse off in FV terms as well:$9,500(1.05) = $9,975 $10,000.rCFPV11,where

7、is cash flow at date 11CFCorporate Finance2-5 Professor Ho-Mou Wu2.2 Project Evaluation in a Riskless WorldC0 C0 C1 C1 Y1=1.2m Y0=1m Saver (lending) B Spender (borrowing) A Y ) r1 (YY)Y(PV101 1+r slope = -(1+r) Why do we use NPV as the investment criterion ?Assume Perfect Capital Market and Two Peri

8、odCorporate Finance2-6 Professor Ho-Mou Wu(I) Saving (Financing) Decision Income Y： ， Consumption C： Is C(C0, C1) feasible? There is only one interest rate in the perfect capital market. Saver (C01m)：C1 1.2(1C0)(1r) Spender (C01m)：C1 1.2(C01)(1r) Same equation C1 Y1(Y0C0)(1r) m2 . 1Ym1Y10.,) r1 (YY)

9、 r1 (CC or 1010feasible is C then PV(Y),PV(C) Ifm325. 1Cm9 . 0C10Corporate Finance2-7 Professor Ho-Mou WuUse PV to Check Feasibility of Consumption planExample 2: Is the consumption plan C00.9m and C11.325m feasible?Use the PV formula to evaluate it.If r10%, 0.9 2.105PV(C)1 2.091PV(Y) : not feasible

10、If r20%, 0.9 2.004PV(C)1 2.000PV(Y) : not feasibleIf r30%, 0.9 1.919PV(C)1 1.923PV(Y) : feasible!1 . 1325. 12 . 1325. 13 . 1325. 11 . 12 . 12 . 12 . 13 . 12 . 1Corporate Finance2-8 Professor Ho-Mou Wu() Investment Opportunities Real Investment opportunities transform input into output： Consider a fa

11、rmer with wheat (endowment) E that can be used either for consumption or as input to produce output next period. The spender and saver will not agree on the choice of the best investment plan (AB). Both consume what they produce (Y0,Y1), where EY0input and Y1output. C 1 B Saver Spender A Y0 E input

12、output Y1 Corporate Finance2-9 Professor Ho-Mou WuCorporate Investment DecisionMakingConsumption at t+1Positive NPV projects shift the shareholders opportunity set out, which is unambiguously good.All shareholders agree on their preference for positive NPV projects, whether they are borrowers or len

13、ders.Corporate Finance2-10 Professor Ho-Mou Wu() Investment Opportunities with Financial MarketsFinancial markets present saving/borrowing opportunities, as represented by the dotted straight line. Suppose the company (farm) chooses D, its owners can then use financial markets for saving or borrowin

14、g. Both investors are happier than in (), but D is not the optimal investment plan yet.C0BADEC1slope = -(1+r)PV(D)Corporate Finance2-11 Professor Ho-Mou WuProject Valuation in a Riskless WorldC0ADEslope = -(1+r)PV(Y)C1BY*Y1Y0Y* is the optimal investment plan, which is the one that maximizes NPV(Y)PV

15、(Y)E or PV(Y). Perfect capital market (borrowing ratelending rate) is assumed.Corporate Finance2-12 Professor Ho-Mou WuCorporate Investment DecisionMaking In reality, shareholders do not vote on every investment decision faced by a firm and the managers of firms need decision rules to operate by. Al

16、l shareholders of a firm will be made better off if managers follow the NPV ruleundertake positive NPV projects and reject negative NPV projects. Corporate Finance2-13 Professor Ho-Mou WuOptimal Investment PlanNet Present Value NPV PV(Y)ETherefore, the best investment plan is the one that maximizes

17、NPV(Y); and the best investment plan is independent of investors preferences.E)r1YY(r1Y101input)YE(0PVNPV 33221)1 ()1 (1rCFrCFrCF 332210)1 ()1 (1rCFrCFrCFCFPVCF 0Corporate Finance2-14 Professor Ho-Mou WuFishers Separation PrincipleGiven perfect capital market and certainty, the optimal investment pl

18、an is the one that maximizes the net present value of available production plans, without regard to the individuals subjective preferences that enter into their consumption/saving decisions. (Irving Fisher) This is the basis for using the present value as the evaluation criterion.Separation of inves

19、tment and financing decisionsSeparation of ownership and management.Corporate Finance2-15 Professor Ho-Mou WuWhy do we use NPV or PV as investment criterionExample 3. A project which requires $650m investment will have payoffs $300m and $400m in the next two years. Is it a good investment project wh

20、en r6%? Example 4. Consider a two-period world with an interest rate of 25%. Suppose you have a fund of $100m and can choose one from the following three projects. What is not invested will be consumed. Which is the best project? Investment Payoffs next period 1 25m 30m 2 50m 100m 3 100m 160m Corpor

21、ate Finance2-16 Professor Ho-Mou WuNPV as Investment CriterionExample 3(continued): NPV Example 4(continued): Y0 Y1 PV(Y) NPV PVE -CF0 1 75 30 7530/1.2599 -1 -2530/1.25 2 50 100 50100/1.25130* 30* -50100/1.25 3 0 160 0160/1.25128 28 -100160/1.25 r1CF106. 140006. 1300650011356283650Corporate Finance2

22、-17 Professor Ho-Mou Wu2.3 Present Value and Compounding How much would an investor have to set aside today in order to have $20,000 five years from now if the current rate is 15%?012345$20,000PV5)15. 1 (000,20$53.943, 9$Corporate Finance2-18 Professor Ho-Mou WuHow Long is the Wait?Example 5: If we

23、deposit $5,000 today in an account paying 10%, how long does it take to grow to $10,000?TrCFFV)1 (0T)10. 1 (000, 5$000,10$2000, 5$000,10$)10. 1 (T2ln)10. 1ln(Tyears 27. 70953. 06931. 0)10. 1ln(2lnTCorporate Finance2-19 Professor Ho-Mou WuExample 6: Assume the total cost of a college education will b

24、e $50,000 when your child enters college in 12 years. You have $5,000 to invest today. What rate of interest must you earn on your investment to cover the cost of your childs education?What Rate Is Enough?TrCFFV)1 (012)1 (000, 5$000,50$r10000, 5$000,50$)1 (12r12110)1 (r2115.12115. 1110121rCorporate

25、Finance2-20 Professor Ho-Mou Wu2.4 PV with Special Cash Flows Perpetuity A constant stream of cash flows that lasts forever. Growing perpetuity A stream of cash flows that grows at a constant rate forever. Annuity A stream of constant cash flows that lasts for a fixed number of periods. Growing annu

26、ity A stream of cash flows that grows at a constant rate for a fixed number of periods.Corporate Finance2-21 Professor Ho-Mou WuPerpetuityA constant stream of cash flows that lasts forever.01C2C3CThe formula for the present value of a perpetuity is:32)1 ()1 ()1 (rCrCrCPVrCPV Corporate Finance2-22 Pr

27、ofessor Ho-Mou WuGrowing PerpetuityA growing stream of cash flows that lasts forever.01C2C(1+g)3C (1+g)2The formula for the present value of a growing perpetuity is:322)1 ()1 ()1 ()1 ()1 (rgCrgCrCPVgrCPVCorporate Finance2-23 Professor Ho-Mou WuAnnuityA constant stream of cash flows with a fixed matu

28、rity.01C2C3CThe formula for the present value of an annuity is:TrCrCrCrCPV)1 ()1 ()1 ()1 (32TrrCPV)1 (11TCCorporate Finance2-24 Professor Ho-Mou WuGrowing AnnuityA growing stream of cash flows with a fixed maturity.01CThe formula for the present value of a growing annuity:TTrgCrgCrCPV)1 ()1 ()1 ()1

29、()1 (12TrggrCPV)1 (112C(1+g)3C (1+g)2T C(1+g)T-1Corporate Finance2-25 Professor Ho-Mou WuWhat Is a Firm Worth? Conceptually, a firm should be worth the present value of the firms cash flows. The tricky part is determining the size, timing and “risk” of those cash flows : we will probe further in later class.