CHAPTER 4 McGraw Hill Irwin Lecture Note 5 Discounted Cash Flow Valuation Copyright 2008 by The McGraw Hill Companies Inc All rights Slide 2 Key Concepts and Skills compute the future value and or present value of series of cash flows compute the return on an investment use a spreadsheet to solve time value problems Understand perpetuities and annuities McGraw Hill Irwin Copyright 2008 by The McGraw Hill Companies Inc All rights Slide 3 4 1 The One Period Case If 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 McGraw Hill Irwin Copyright 2008 by The McGraw Hill Companies Inc All rights Slide 4 Future Value In 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 McGraw Hill Irwin Copyright 2008 by The McGraw Hill Companies Inc All rights Slide 5 Present Value If 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 today s dollars 10 000 9 523 81 1 05 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 McGraw Hill Irwin Copyright 2008 by The McGraw Hill Companies Inc All rights Slide 6 Present Value In the one period case the formula for PV can be written as C1 PV 1 r Where C1 is cash flow at date 1 and r is the appropriate interest rate McGraw Hill Irwin Copyright 2008 by The McGraw Hill Companies Inc All rights Slide 7 Net Present Value The Net Present Value NPV of an investment is the present value of the expected cash flows less the cost of the investment NPV Cost PV 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 10 000 NPV 9 500 1 05 McGraw Hill Irwin Copyright 2008 by The McGraw Hill Companies Inc All rights Net Present Value Slide 8 NPV 9 500 9 523 81 23 81 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 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 worse off in FV terms 9 500 1 05 9 975 10 000 McGraw Hill Irwin Copyright 2008 by The McGraw Hill Companies Inc All rights Slide 9 4 2 The Multiperiod Case The general formula for the future value of an investment over many periods can be written as FV C0 1 r T Where 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 I e C2 C0 1 r 2 where McGraw Hill Irwin 1 r 2 1 2r r2 Copyright 2008 by The McGraw Hill Companies Inc All rights Slide 10 Future Value Suppose a stock currently pays a dividend of 1 10 which is expected to grow at 40 per year for the next five years What will the dividend be in five years FV C0 1 r T 5 92 1 10 1 40 5 McGraw Hill Irwin Copyright 2008 by The McGraw Hill Companies Inc All rights Slide 11 Future Value and Compounding Notice that the dividend in year five 5 92 is considerably higher than the sum of the original dividend plus five increases of 40percent on the original 1 10 dividend 5 92 1 10 5 1 10 40 3 30 This is due to compounding McGraw Hill Irwin Copyright 2008 by The McGraw Hill Companies Inc All rights Slide 12 Present Value and Discounting The PV of a cash payment in period T discounted at interest rate r CT PV T 1 r McGraw Hill Irwin Copyright 2008 by The McGraw Hill Companies Inc All rights Slide 13 Present Value and Discounting How 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 PV 0 20 000 1 2 3 4 5 20 000 9 943 53 1 15 5 McGraw Hill Irwin Copyright 2008 by The McGraw Hill Companies Inc All rights Slide 14 How Long is the Wait If we deposit 5 000 today in an account paying 10 how long does it take to grow to 10 000 FV C0 1 r T 10 000 5 000 1 10 T 10 000 1 10 2 5 000 T ln 1 10 T ln 2 ln 2 0 6931 T 7 27 years ln 1 10 0 0953 McGraw Hill Irwin Copyright 2008 by The McGraw Hill Companies Inc All rights What Rate Is Enough Slide 15 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 child s education FV C0 1 r T 50 000 5 000 1 r 12 50 000 1 r 10 5 000 12 1 12 r 10 1 12 1 r 10 1 1 2115 1 2115 About 21 15 McGraw Hill Irwin Copyright 2008 by The McGraw Hill Companies Inc All rights Slide 16 Multiple Cash Flows Consider 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 McGraw Hill Irwin Copyright 2008 by The McGraw Hill Companies Inc All rights Slide 17 Multiple Cash Flows 0 1 200 2 3 4 400 600 800 178 57 318 88 427 07 508 41 1 432 93 Present Value Cost Do Not Purchase McGraw Hill Irwin Copyright 2008 by The McGraw Hill Companies Inc All rights Slide 18 Multiple Cash Flows The PV of a set of cash flows in different periods is the sum of their present value C3 C1 C2 CT PV 2 3 1 r 1 r 1 r 1 r T T Ci i i 1 1 r McGraw Hill Irwin Copyright 2008 by The McGraw Hill Companies Inc All …