McGraw-Hill/Irwin Corporate Finance, 7/e 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.CHAPTER4Net Present Value1McGraw-Hill/Irwin Corporate Finance, 7/e 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.Chapter Outline4.1 The One-Period Case 4.2 The Multiperiod Case 4.3 Compounding Periods 4.4 Simplifications 4.5 What Is a Firm Worth? 4.6 Summary and Conclusions2McGraw-Hill/Irwin Corporate Finance, 7/e 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.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 = $10,000(1.05).The total amount due at the end of the investment is call the Future Value (FV). 3McGraw-Hill/Irwin Corporate Finance, 7/e 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.4.1 The One-Period Case: Future ValueIn the one-period case, the formula for FV can be written as: FV = C0(1 + r)TWhere C0 is cash flow today (time zero) and r is the appropriate interest rate.4McGraw-Hill/Irwin Corporate Finance, 7/e 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.4.1 The One-Period Case: Present 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 (PV) of $10,000. Note that $10,000 = $9,523.81(1.05).5McGraw-Hill/Irwin Corporate Finance, 7/e 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.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.6McGraw-Hill/Irwin Corporate Finance, 7/e 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.4.1 The One-Period Case: Net 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?Yes!7McGraw-Hill/Irwin Corporate Finance, 7/e 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.4.1 The One-Period Case: 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 would be unambiguously worse off in FV terms as well: $9,500(1.05) = $9,975 $1.10 + 5$1.10.40 = $3.30This is due to compounding.11McGraw-Hill/Irwin Corporate Finance, 7/e 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.Future Value and Compounding01234512McGraw-Hill/Irwin Corporate Finance, 7/e 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.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$20,000PV13McGraw-Hill/Irwin Corporate Finance, 7/e 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.If we deposit $5,000 today in an account paying 10%, how long does it take to grow to $10,000?How Long is the Wait?14McGraw-Hill/Irwin Corporate Finance, 7/e 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.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%.What Rate Is Enough?15McGraw-Hill/Irwin Corporate Finance, 7/e 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.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 to16McGraw-Hill/Irwin Corporate Finance, 7/e 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.Effective Annual Interest RatesA 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:17McGraw-Hill/Irwin Corporate Finance, 7/e 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.Effective Annual Interest Rates (continued)So, investing at 12.36% compounded annually is the same as investing at 12% compounded semiannually.18McGraw-Hill/Irwin Corporate Finance, 7/e 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.Effe