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1、Discounted Cash Flow ValuationChapter 4Copyright 2010 by the McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin4-2Key Concepts and SkillsoBe able to compute the future value and/or present value of a single cash flow or series of cash flowsoBe able to compute the return on an investme
2、ntoBe able to use a financial calculator and/or spreadsheet to solve time value problemsoUnderstand perpetuities and annuities4-3Chapter Outline4.1 Valuation: The One-Period Case 4.2 The Multiperiod Case 4.3 Compounding Periods 4.4 Simplifications 4.5 Loan Amortization 4.6 What Is a Firm Worth?4-44.
3、1 The One-Period CaseoIf 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 amoun
4、t due at the end of the investment is call the Future Value (FV). 4-5Future ValueoIn 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.4-6Present ValueoIf you were to be promised $10,000 due in one
5、 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).4-7Present
6、 ValueoIn 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.4-8Net Present ValueoThe Net Present Value (NPV) of an investment is the present value of the expected cash flows, less the cost of the investment.oSuppose an i
7、nvestment that promises to pay $10,000 in one year is offered for sale for $9,500. Your interest rate is 5%. Should you buy?4-9Net Present ValueThe 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.4-10
8、Net 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
9、 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.4-14Future Value and Compounding0123454-15Present Value and DiscountingoHow 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
10、%?012345$20,000PV4-164.5 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?4-17Assume 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
11、of interest must you earn on your investment to cover the cost of your childs education? What Rate Is Enough?About 21.15%.4-18Calculator KeysoTexas Instruments BA-II PlusnFV = future valuenPV = present valuenI/Y = periodic interest rateoP/Y must equal 1 for the I/Y to be the periodic rateoInterest i
12、s entered as a percent, not a decimalnN = number of periodsnRemember to clear the registers (CLR TVM) after each problemnOther calculators are similar in format4-19Multiple Cash FlowsoConsider an investment that pays $200 one year from now, with cash flows increasing by $200 per year through year 4.
13、 If the interest rate is 12%, what is the present value of this stream of cash flows?oIf the issuer offers this investment for $1,500, should you purchase it?4-20Multiple Cash Flows01234200400600800 178.57318.88427.07508.411,432.93 Present Value Cost Do Not Purchase4-21Valuing “Lumpy” Cash FlowsFirs
14、t, set your calculator to 1 payment per year. Then, use the cash flow menu:CF2CF1F2F1CF0120011,432.930400INPV12CF4CF3F4F3160018004-224.3 Compounding PeriodsCompounding an investment m times a year for T years provides for future value of wealth:4-23Compounding Periodsq For example, if you invest $50
15、 for 3 years at 12% compounded semi-annually, your investment will grow to4-24Effective 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
16、would give us the same end -of-investment wealth after 3 years:4-25Effective Annual Rates of InterestSo, investing at 12.36% compounded annually is the same as investing at 12% compounded semi-annually.4-26Effective Annual Rates of InterestoFind the Effective Annual Rate (EAR) of an 18% APR loan that is compounded monthly.oWhat we have is a loan with a monthly interest rate rate of 1%.oThis is equivalent to a loan with an annu
