corporate-finance4(ppt文档).ppt

4-0Discounted Cash Flow ValuationChapter 4Copyright 2010 by the McGraw-Hill Companies,Inc.All rights reserved.McGraw-Hill/Irwin4-1Chapter Outline4.1 Valuation:The One-Period Case4.2 The Multiperiod Case4.3 Compounding Periods4.4 Simplifications4.5 Loan Amortization4.6 What Is a Firm Worth?4-24.1 The One-Period CaseIf 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=$10,000(1.05)qThe total amount due at the end of the investment is call the Future Value(FV).4-3Future ValueIn 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.4-4Present ValueIf you were to be promised$10,000 due in one year when interest rates are 5-percent,your investment would be worth$9,523.81 in todays dollars.The 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).Note that$10,000=$9,523.81(1.05).4-5Present 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.4-6Net Present ValueThe Net Present Value(NPV)of an investment 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?4-7Net Present ValueThe present value of the cash inflow is greaterthan the cost.In other words,the Net PresentValue is positive,so the investment should be purchased.4-8Net Present ValueIn the one-period case,the formula for NPV can be written as:NPV=Cost+PVIf 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 worse off in FV terms:$9,500(1.05)=$9,975$1.10+5$1.10.40=3.30This is due to compounding.4-12Future Value and Compounding0123454-13Present Value and DiscountingHow 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$20,000PV4-144.5 Finding the Number of PeriodsIf we deposit$5,000 today in an account paying 10%,how long does it take to grow to$10,000?4-15What Rate Is Enough?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 childs education?About 21.15%.4-16Calculator KeysTexas Instruments BA-II PlusFV=future valuePV=present valueI/Y=periodic interest rateP/Y must equal 1 for the I/Y to be the periodic rateInterest is entered as a percent,not a decimalN=number of periodsRemember to clear the registers(CLR TVM)after each problemOther calculators are similar in format4-17Multiple Cash FlowsConsider 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?If the issuer offers this investment for$1,500,should you purchase it?4-18Multiple Cash Flows01234200400600800178.57318.88427.07508.411,432.93Present Value Cost Do Not Purchase4-194.3 Compounding PeriodsCompounding an investment m times a year for T years provides for future value of wealth:4-20Compounding PeriodsqFor example,if you invest$50 for 3 years at 12%compounded semi-annually,your investment will grow to4-21Effective 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:4-22Effective Annual Rates of InterestSo,investing at 12.36%compounded annually is the same as investing at 12%compounded semi-annually.4-23Effective Annual Rates of InterestFind the Effective Annual Rate(EAR)of an 18%APR loan that is compounded monthly.What we have is a loan with a monthly interest rate rate of 1%.This is equivalent to a loan with an annual interest rate of 19.56%.4-24Continuous CompoundingThe 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 annual interest rate,T is the number of years,ande is a transcendental number approximately equal to 2.718.ex is a key on your calculator.4-254.4 SimplificationsPerpetuityA constant stream of cash flows that lasts foreverGrowing perpetuityA stream of cash flows that grows at a constant rate foreverAnnuityA stream of constant cash flows that lasts for a fixed number of periodsGrowing annuityA stream of cash flows that grows at a constant rate for a fixed number of periods4-26PerpetuityA constant stream of cash flows that lasts forever01C2C3C4-27Perpetuity:ExampleWhat is the value of a British consol that promises to pay 15 every year for ever?The interest rate is 10-percent.01152153154-28Growing PerpetuityA growing stream of cash flows that lasts forever01C2C(1+g)3C(1+g)24-29Growing 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$1.30(1.05)3$1.30(1.05)24-30AnnuityA constant stream of cash flows with a fixed maturity01C2C3CTC4-31Annuity: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$4004-32 What 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$297.222-324-33Growing AnnuityA growing stream of cash flows with a fixed maturity01C2C(1+g)3C(1+g)2T C(1+g)T-14-34Growing 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 the present value at retirement if the discount rate is 10%?01$20,0002$20,000(1.03)40$20,000(1.03)394-35Growing Annuity:ExampleYou 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 present value of the estimated income stream over the first 5 years if the discount rate is 12%?0 1 2 3 4 5$34,706.264-364.5 Loan AmortizationPure Discount Loans are the simplest form of loan.The borrower receives money today and repays a single lump sum(principal and interest)at a future time.Interest-Only Loans require an interest payment each period,with full principal due at maturity.Amortized Loans require repayment of principal over time,in addition to required interest.4-37Pure Discount LoansTreasury bills are excellent examples of pure discount loans.The principal amount is repaid at some future date,without any periodic interest payments.If a T-bill promises to repay$10,000 in 12 months and the market interest rate is 7 percent,how much will the bill sell for in the market?PV=10,000/1.07=9,345.794-38Interest-Only LoanConsider a 5-year,interest-only loan with a 7%interest rate.The principal amount is$10,000Interest is paid annually.What would the stream of cash flows be?Years 1 4:Interest payments of.07(10,000)=700Year 5:Interest+principal=10,700This cash flow stream is similar to the cash flows on corporate bonds,and we will talk about them in greater detail later.4-39Amortized Loan with Fixed Principal PaymentConsider a$50,000,10 year loan at 8%interest.The loan agreement requires the firm to pay$5,000 in principal each year plus interest for that year.4-40Amortized Loan with Fixed PaymentEach payment covers the interest expense plus reduces principalConsider a 4 year loan with annual payments.The interest rate is 8%,and the principal amount is$5,000.4-414.6 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.