企業(yè)凈現(xiàn)值全面概述英文版

1、企業(yè)凈現(xiàn)值全面概述英文版4.1 The One-Period Case: Future ValueIf you were to invest $10,000 at 5-percent interest for one year, your investment would grow to $10,500 $500 would be interest ($10,000 .05)$10,000 is the principal repayment ($10,000 1)$10,500 is the total due. It can be calculated as:$10,500 = $10,0

2、00(1.05).The total amount due at the end of the investment is call the Future Value (FV). 4.1 The One-Period Case: Future ValueIn the one-period case, the formula for FV can be written as:FV = C1(1 + r)Where C1 is cash flow at date 1 and r is the appropriate interest rate.4.1 The One-Period Case: Pr

3、esent ValueIf 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. 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

4、(PV) of $10,000.Note that $10,000 = $9,523.81(1.05).4.1 The One-Period Case: Present ValueIn the one-period case, the formula for PV can be written as:Where C1 is cash flow at date 1 and r is the appropriate interest rate.4.1 The One-Period Case: Net Present ValueThe Net Present Value (NPV) of an in

5、vestment is the present value of the expected cash flows, less the cost of the investment.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?Yes!4.1 The One-Period Case: Net Present ValueIn the one-period case, the

6、formula for NPV can be written as:If 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 the investment promised and we would be unambiguously worse off in FV terms as well:$9,500(1

7、.05) = $9,975 $1.10 + 5$1.10.40 = $3.30This is due to compounding.Future Value and Compounding012345Present 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$20,000PVHow Long is the Wait?If we deposi

8、t $5,000 today in an account paying 10%, how long does it take to grow to $10,000?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 invest today. What rate of interest must you earn on your investment to cover the cost of your

9、 childs education? About 21.15%. What Rate Is Enough?4.3 Compounding PeriodsCompounding an investment m times a year for T years provides for future value of wealth:For example, if you invest $50 for 3 years at 12% compounded semi-annually, your investment will grow toEffective Annual Interest Rates

10、A reasonable question to ask in the above example is what is the effective annual rate of interest on that investment?The Effective Annual Interest Rate (EAR) is the annual rate that would give us the same end-of-investment wealth after 3 years:Effective Annual Interest Rates (continued)So, investin

11、g at 12.36% compounded annually is the same as investing at 12% compounded semiannually.Continuous Compounding (Advanced)The general formula for the future value of an investment compounded continuously over many periods can be written as:FV = C0erTWhere C0 is cash flow at date 0,r is the stated ann

12、ual interest rate, T is the number of periods over which the cash is invested, ande is a transcendental number approximately equal to 2.718. ex is a key on your calculator.4.4 SimplificationsPerpetuityA constant stream of cash flows that lasts forever.Growing perpetuityA stream of cash flows that gr

13、ows 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.PerpetuityA constant stream of cash flows that lasts forever.01C2C3CThe formula for the pre

14、sent value of a perpetuity is:Perpetuity: ExampleWhat is the value of a British consol that promises to pay 15 each year, every year until the sun turns into a red giant and burns the planet to a crisp? The interest rate is 10-percent.0115215315Growing PerpetuityA growing stream of cash flows that l

15、asts forever.01C2C(1+g)3C (1+g)2The formula for the present value of a growing perpetuity is:Growing Perpetuity: ExampleThe expected dividend next year is $1.30 and dividends are expected to grow at 5% forever. If the discount rate is 10%, what is the value of this promised dividend stream?01$1.302$

16、1.30(1.05)3$1.30 (1.05)2AnnuityA constant stream of cash flows with a fixed maturity.01C2C3CThe formula for the present value of an annuity is:TCAnnuity: ExampleIf you can afford a $400 monthly car payment, how much car can you afford if interest rates are 7% on 36-month loans?01$4002$4003$40036$400

17、Growing 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-1Growing AnnuityA defined-benefit retirement plan offers to pay $20,000 per year for 40 years and increase the annual payment by 3-percent each year

18、. What is the present value at retirement if the discount rate is 10-percent?01$20,0002$20,000(1.03)40 $20,000(1.03)394.5 What 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.4.6 Summary and ConclusionsTwo basic concepts, future value and present value are introduced in this chapter.Interest rates are commonly expressed on an annual basis, but semi-annual, quarterly, monthly and even continuously compoun