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1、Corporate Finance2-0 Professor Ho-Mou WuCapital Investment Decisions2.1 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 DecisionExampl
2、e 1:Suppose an investment 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.Corporate Finance2-2 Prof
3、essor 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 interest for one yea
4、r,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 ValueThe Net Present Value(NPV)of an investment is the present value of the expected cash flows,less the cos
5、t of the investment.:So you should Invest.Back 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:If we had not undertaken the positive NPV project considered on the last slide,and instead inv
6、ested 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.,where is cash flow at date 1Corporate Finance2-5 Professor Ho-Mou Wu2.2 Project Evaluation in a Riskless WorldW
7、hy do we use NPV as the investment criterion?Assume Perfect Capital Market and Two PeriodCorporate Finance2-6 Professor Ho-Mou Wu(I)Saving(Financing)Decision Corporate Finance2-7 Professor Ho-Mou WuUse PV to Check Feasibility of Consumption planExample 2:Is the consumption plan C00.9m and C11.325m f
8、easible?Use the PV formula to evaluate it.If r10%,0.9 2.105PV(C)1 2.091PV(Y):not feasibleIf r20%,0.9 2.004PV(C)1 2.000PV(Y):not feasibleIf r30%,0.9 1.919PV(C)1 1.923PV(Y):feasible!Corporate Finance2-8 Professor Ho-Mou Wu()Investment OpportunitiesCorporate Finance2-9 Professor Ho-Mou WuCorporate Inve
9、stment 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 lenders.Corporate Finance2-10 Professor Ho-Mou Wu()Investment Opportu
10、nities 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 borrowing.Both investors are happier than in(),but D is not the optimal investme
11、nt 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(Y)E or PV(Y).Perfect capital market(borrowing ratelending rate)is assumed.Corpor
12、ate Finance2-12 Professor Ho-Mou WuCorporate Investment DecisionMakingIn reality,shareholders do not vote on every investment decision faced by a firm and the managers of firms need decision rules to operate by.All shareholders of a firm will be made better off if managers follow the NPV ruleunderta
13、ke 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 NPV(Y);and the best investment plan is independent of investors preferences.PVNPV Corpora
14、te Finance2-14 Professor Ho-Mou WuFishers Separation PrincipleGiven perfect capital market and certainty,the optimal investment plan is the one that maximizes the net present value of available production plans,without regard to the individuals subjective preferences that enter into their consumptio
15、n/saving decisions.(Irving Fisher)This is the basis for using the present value as the evaluation criterion.Separation of investment and financing decisionsSeparation of ownership and management.Corporate Finance2-15 Professor Ho-Mou WuWhy do we use NPV or PV as investment criterionCorporate Finance
16、2-16 Professor Ho-Mou WuNPV as Investment CriterionCorporate Finance2-17 Professor Ho-Mou Wu2.3 Present Value and CompoundingHow 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$20,000PVCorporate Finance2-18 Professor Ho-Mou
17、 WuHow Long is the Wait?Example 5:If we deposit$5,000 today in an account paying 10%,how long does it take to grow to$10,000?Corporate Finance2-19 Professor Ho-Mou WuExample 6:Assume the total cost of a college education will be$50,000 when your child enters college in 12 years.You have$5,000 to inv
18、est today.What rate of interest must you earn on your investment to cover the cost of your childs education?What Rate Is Enough?Corporate Finance2-20 Professor Ho-Mou Wu2.4 PV with Special Cash FlowsPerpetuityA constant stream of cash flows that lasts forever.Growing perpetuityA stream of cash flows
19、 that grows at a constant rate forever.AnnuityA stream of constant cash flows that lasts for a fixed number of periods.Growing annuityA 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
20、that lasts forever.01C2C3CThe formula for the present value of a perpetuity is:Corporate Finance2-22 Professor 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:Corporate Finance2-23 Professor H
21、o-Mou WuAnnuityA constant stream of cash flows with a fixed maturity.01C2C3CThe formula for the present value of an annuity is:TCCorporate 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:2C(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.