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1、CH4:Discounted Cash Flow ValuationKey Concepts and SkillsvBe able to compute the future value and present value of a single cash flow or series of cash flowsvUnderstand NPV of an investmentvKnow APR and EARvUnderstand annuities and perpetuities Chapter Outline4.1 Valuation:The One-Period Case4.2 The
2、 Multiperiod Case4.3 Compounding Periods4.4 Simplifications4.5 What Is a Firm Worth?vDon is trying to sell a piece of land in Alaska.Yesterday,he was offered$10,000 for the property.He was about ready to accept the offer when another individual offered him$11,424.However,the second offer was to be p
3、aid a year from now.Don has satisfied himself that both buyers are honest and financially solvent,so he has no fear that the offer he selects will fall through.Which offer should Don choose?vMike,Dons financial advisor,points out that if Don takes the first offer,he could invest the$10,000 in the ba
4、nk at an insured rate of 12 percent.4.1 The One-Period CaseqIf 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=$1
5、0,000(1.05)qThe total amount due at the end of the investment is called the Future Value(FV).Future ValuevIn the one-period case,the formula for FV can be written as:FV=C0(1+r)Where C0 is cash flow today(time zero),and r is the appropriate interest rate.Present ValuevIf you were to be promised$10,00
6、0 due in one year when interest rates are 5-percent,your investment would be worth$9,523.81 in todays dollars.Note that$10,000=$9,523.81(1.05)vThe amount that a borrower would need to set aside today to be able to meet the promised payment of$10,000 in one year is called the Present Value(PV).vIn th
7、e 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.Net Present ValuevThe Net Present Value(NPV)of an investment is the present value of the expected cash flows,less the cost of the investment.vSuppose an investment that promi
8、ses to pay$10,000 in one year is offered for sale for$9,500.Your interest rate is 5%.Should you buy?The present value of the cash inflow is greater than the cost.In other words,the Net Present Value is positive,so the investment should be purchased.In the one-period case,the formula for NPV can be w
9、ritten as:NPV=Cost+PVvSuppose you has put$500 in a savings account at the bank.The account earns 7%,compounded annually.vHow much will you have at the end of 3 years?vHow much will you have at the end of 3 years if simple interest is used?500+5007%3=605500(1+7%)3=612.524.2 The Multiperiod CasevThe g
10、eneral formula for the future value of an investment over many periods can be written as:FV=C0(1+r)TWhere C0 is cash flow at date 0,r is the appropriate interest rate,and T is the number of periods over which the cash is invested.Future Value and CompoundingPresent Value and DiscountingvHow much wou
11、ld an investor have to set aside today in order to have$20,000 five years from now if the current rate is 15%?012345$20,000PVvIn the multiperiod case,the formula for the present can be written as:How Long is the Wait?If we deposit$5,000 today in an account paying 10%,how long does it take to grow to
12、$10,000?What Rate Is Enough?Assume the total cost of a college education will be$50,000 when a child enters college in 12 years.His/Her parents have$5,000 to invest today.What rate of interest must his/her parents earn on their investment to cover the cost of the childs education?About 21.15%At 9 pe
13、rcent interest,how long does it take to double your money?To quadruple it?Have a try!Multiple Cash FlowsvConsider an investment that pays$200 one year from now,with cash flows increasing by$200 per year through year 4.If the interest rate is 12%,what is the present value of this stream of cash flows
14、?vIf the issuer offers this investment for$1,500,should you purchase it?01234200400600800178.57318.88427.07508.411,432.93Present Value Cost Do Not PurchaseThe present value of the following cash flow stream is$6,453 when discounted at 10 percent annually.What is the value of the missing cash flow?Ye
15、ar 1 Cash flow$1,200Year 2 Cash flow?Year 3 Cash flow$2,400Year 4 Cash flow$2,600Have a try!4.3 Compounding PeriodsCompounding an investment m times a year for T years provides for future value of wealth:qFor example,if you invest$50 for 3 years at 12%compounded semi-annually,your investment will gr
16、ow toEffective Annual Rates of InterestA reasonable question to ask in the above example is“what is the effective annual rate of interest on that investment?”The Effective Annual Rate(EAR)of interest is the annual rate that would give us the same end-of-investment wealth after 3 years:So,investing a
17、t 12.36%compounded annually is the same as investing at 12%compounded semi-annually.vFind the Effective Annual Rate(EAR)of an 18%APR loan that is compounded monthly.vWhat we have is a loan with a monthly interest rate of 1.5%.vThis is equivalent to a loan with an annual interest rate of 19.56%.APR a
18、nd EAR4.4 SimplificationsvAnnuity(年金年金)A stream of constant cash flows that lasts for a fixed number of periodsvGrowing annuity(增长年金增长年金)A stream of cash flows that grows at a constant rate for a fixed number of periodsvPerpetuity(永续年金永续年金)A constant stream of cash flows that lasts forevervGrowing p
19、erpetuity(永续增长年金永续增长年金)A stream of cash flows that grows at a constant rate foreverAnnuityA constant stream of cash flows with a fixed maturity01C2C3CTC01C2C3CTCAnnuity: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$40
20、03$40036$400What is the present value of a four-year annuity of$100 per year that makes its first payment two years from today if the discount rate is 9%?0 1 2 3 4 5$100$100$100$100$323.97$297.22What is the present and future value of a four-year annuity of$100 per year if the first payment occurs i
21、mmediately?(the discount rate is 9%)Have a try!Growing AnnuityA growing stream of cash flows with a fixed maturity01C2C(1+g)3C(1+g)2T C(1+g)T-1Growing Annuity:ExampleA defined-benefit retirement plan offers to pay$20,000 per year for 40 years and increase the annual payment by 3%each year.What is th
22、e present value at retirement if the discount rate is 10%?01$20,0002$20,000(1.03)40$20,000(1.03)39You are evaluating an income generating property.Net rent is received at the end of each year.The first years rent is expected to be$8,500,and rent is expected to increase 7%each year.What is the presen
23、t value of the estimated income stream over the first 5 years if the discount rate is 12%?0 1 2 3 4 5$34,706.28PerpetuityA constant stream of cash flows that lasts forever01C2C3CPerpetuity:ExamplenWhat is the value of a British consol that promises to pay 15 every year for ever?nThe interest rate is
24、 10-percent.0115215315Growing PerpetuityA growing stream of cash flows that lasts forever01C2C(1+g)3C(1+g)2Growing Perpetuity:ExamplenThe expected dividend next year is$1.30,and dividends are expected to grow at 5%forever.nIf the discount rate is 10%,what is the value of this promised dividend strea
25、m?01$1.302$1.30(1.05)3$1.30(1.05)24.5 What Is a Firm Worth?vConceptually,a firm should be worth the present value of the firms cash flows.vThe tricky part is determining the size,timing,and risk of those cash flows.Quick QuizvWhat is PVIF,FVIF,PVIFA and FVIFA?vWhat is the Net Present Value of an inv
26、estment?vWhat is an EAR,and how is it computed from APR?vWhat is a perpetuity?An annuity?1、每一个成功者都有一个开始。勇于开始，才能找到成功的路。11月-2211月-22Tuesday,November 8,20222、成功源于不懈的努力，人生最大的敌人是自己怯懦。07:41:0407:41:0407:4111/8/2022 7:41:04 AM3、每天只看目标，别老想障碍。11月-2207:41:0407:41Nov-2208-Nov-224、宁愿辛苦一阵子，不要辛苦一辈子。07:41:0407:41:
27、0407:41Tuesday,November 8,20225、积极向上的心态，是成功者的最基本要素。11月-2211月-2207:41:0407:41:04November 8,20226、生活总会给你另一个机会，这个机会叫明天。08十一月20227:41:04上午07:41:0411月-227、人生就像骑单车，想保持平衡就得往前走。十一月227:41上午11月-2207:41November 8,20228、业余生活要有意义，不要越轨。2022/11/87:41:0407:41:0408 November 20229、我们必须在失败中寻找胜利，在绝望中寻求希望。7:41:04上午7:41上午07:41:0411月-2210、一个人的梦想也许不值钱，但一个人的努力很值钱。11/8/2022 7:41:04 AM07:41:0408-11月-2211、在真实的生命里，每桩伟业都由信心开始，并由信心跨出第一步。11/8/2022 7:41 AM11/8/2022 7:41 AM11月-2211月-22谢谢大家谢谢大家