Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Principles of Corporate Finance Chapter 3 How To Calculate Present Values Ninth Edition Slides by Matthew Will McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 2 Topics Covered Valuing Long-Lived Assets Looking for Shortcuts – Perpetuities and Annuities More Shortcuts – Growing Perpetuities and Annuities Compound Interest & Present Values McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 3 Present Values C1 PV DF C1 1 r1 DF 1 (1 r ) t Discount Factors can be used to compute the present value of any cash flow. McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 4 Present Values Example You just bought a new computer for $3,000. The payment terms are 2 years same as cash. If you can earn 8% on your money, how much money should you set aside today in order to make the payment when due in two years? PV McGraw Hill/Irwin 3000 (1.08)2 $2,572 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 5 Present Values Example You have the opportunity to purchase the baseball hit by Barry Bonds to break Hank Arron’s home run record (home run # 756). You estimate this baseball will be worth $2,000,000 when you retire at the end of twenty years. If you expect a 12% return on your investment, how much will you pay for the baseball ? PV McGraw Hill/Irwin 2 , 000, 000 (1.12) 20 $207,334 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 6 Present Values Ct PV DF Ct t (1 r ) Replacing “1” with “t” allows the formula to be used for cash flows that exist at any point in time McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 7 Present Values Example You will receive $200 risk free in two years. If the annual rate of interest on a two year treasury note is 7.7%, what is the present value of the $200? PV (1.200 2 $172.42 077) McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 8 Present Values PVs can be added together to evaluate multiple cash flows. PV McGraw Hill/Irwin C1 (1 r ) (1r )2 .... C2 1 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 9 Present Values PVs can be added together to evaluate multiple cash flows. PV McGraw Hill/Irwin 100 (1.07)1 (1200 2 265.88 077) Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 10 Present Values $200 $100 Present Value Year 0 Year 0 1 100/1.07 = $93.46 200/1.0772 = $172.42 Total = $265.88 McGraw Hill/Irwin 2 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 11 Present Values Given two dollars, one received a year from now and the other two years from now, the value of each is commonly called the Discount Factor. Assume r1 = 20% and r2 = 7%. McGraw Hill/Irwin DF1 1.00 (1.20)1 .83 DF2 1.00 (1.07 ) 2 .87 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 12 Present Values Example Assume that the cash flows from the construction and sale of an office building is as follows. Given a 5% required rate of return, create a present value worksheet and show the net present value. Year 0 Year 1 Year 2 170,000 100,000 320,000 McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 13 Present Values Example - continued Assume that the cash flows from the construction and sale of an office building is as follows. Given a 5% required rate of return, create a present value worksheet and show the net present value. Period Discount 0 Factor 1.0 1 1 1.05 2 1 1.052 McGraw Hill/Irwin .952 .907 Cash Present Flow 170,000 Value 170,000 100,000 95,238 320,000 290,249 NPV Total $25,011 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 14 Present Values Example - continued Assume that the cash flows from the construction and sale of an office building is as follows. Given a 5% required rate of return, create a present value worksheet and show the net present value. +$320,000 -$100,000 -$170,000 Present Value Year 0 -170,000 Year 0 1 2 = -$170,000 -100,000/1.05 = $95,238 320,000/1.052 = $290,249 Total = NPV = $25,011 McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 15 Short Cuts Sometimes there are shortcuts that make it very easy to calculate the present value of an asset that pays off in different periods. These tools allow us to cut through the calculations quickly. McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 16 Short Cuts Perpetuity - Financial concept in which a cash flow is theoretically received forever. cash flow Return present va lue C r PV McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 17 Short Cuts Perpetuity - Financial concept in which a cash flow is theoretically received forever. cash flow PV of Cash Flow discount rate C1 PV0 r McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 18 Present Values Example What is the present value of $1 billion every year, for all eternity, if you estimate the perpetual discount rate to be 10%?? PV McGraw Hill/Irwin $1 bil 0.10 $10 billion Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 19 Short Cuts Annuity - An asset that pays a fixed sum each year for a specified number of years. Asset Perpetuity (first payment in year 1) Year of Payment 1 2…..t t+1 Present Value C r Perpetuity (first payment in year t + 1) C 1 t r (1 r ) Annuity from year 1 to year t C C 1 t r r (1 r ) McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 20 Present Values Example Tiburon Autos offers you “easy payments” of $5,000 per year, at the end of each year for 5 years. If interest rates are 7%, per year, what is the cost of the car? 5,000 Present Value at 0 year 0 5,000 5,000 5,000 5,000 Year 1 2 3 4 5 5,000 / 1.07 4,673 5,000 / 1.07 4,367 2 5,000 / 1.07 4,081 3 5,000 / 1.07 3,814 4 5,000 / 1.07 3,565 5 Total NPV 20,501 McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 21 Short Cuts Annuity - An asset that pays a fixed sum each year for a specified number of years. 1 1 PV of annuity C t r r 1 r McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 22 Annuity Short Cut Example You agree to lease a car for 4 years at $300 per month. You are not required to pay any money up front or at the end of your agreement. If your opportunity cost of capital is 0.5% per month, what is the cost of the lease? McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 23 Annuity Short Cut Example - continued You agree to lease a car for 4 years at $300 per month. You are not required to pay any money up front or at the end of your agreement. If your opportunity cost of capital is 0.5% per month, what is the cost of the lease? 1 1 Lease Cost 300 48 .005 .0051 .005 Cost $12,774.10 McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 24 Annuity Short Cut Example The state lottery advertises a jackpot prize of $295.7 million, paid in 25 installments over 25 years of $11.828 million per year, at the end of each year. If interest rates are 5.9% what is the true value of the lottery prize? 1 1 Lottery Value 11.828 25 . 059 .0591 .059 Value $152,600,000 McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 25 FV Annuity Short Cut Future Value of an Annuity – The future value of an asset that pays a fixed sum each year for a specified number of years. 1 r 1 FV of annuity C r t McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 26 Annuity Short Cut Example What is the future value of $20,000 paid at the end of each of the following 5 years, assuming your investment returns 8% per year? 1 .085 1 FV 20,000 .08 $117,332 McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 27 Constant Growth Perpetuity C1 PV0 rg g = the annual growth rate of the cash flow McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 28 Constant Growth Perpetuity NOTE: This formula can be used to value a perpetuity at any point in time. C1 PV0 rg McGraw Hill/Irwin C t 1 PVt rg Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 29 Constant Growth Perpetuity Example What is the present value of $1 billion paid at the end of every year in perpetuity, assuming a rate of return of 10% and a constant growth rate of 4%? 1 PV0 .10 .04 $16.667 billion McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 30 Perpetuities A three-year stream of cash flows that grows at the rate g is equal to the difference between two growing perpetuities. McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 31 Compound Interest i ii Periods Interest per per year period iii APR (i x ii) iv Value after one year v Annually compounded interest rate 1 6% 6% 1.06 2 3 6 1.032 = 1.0609 6.090 4 1.5 6 1.0154 = 1.06136 6.136 12 .5 6 1.00512 = 1.06168 6.168 52 .1154 6 1.00115452 = 1.06180 6.180 365 .0164 6 1.000164365 = 1.06183 6.183 McGraw Hill/Irwin 6.000% Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 32 Simple and Compound Interest The value of a $100 investment earning 10% annually. McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 33 Compound Interest Compound interest versus simple interest. The top two ascending lines show the growth of $100 invested at simple and compound interest. The longer the funds are invested, the greater the advantage with compound interest. The bottom line shows that $38.55 must be invested now to obtain $100 after 10 periods. Conversely, the present value of $100 to be received after 10 years is $38.55. McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 34 Compound Interest The same story as the previous chart, except that the vertical scale is logarithmic. A constant compound rate of growth means a straight ascending line. This graph makes clear that the growth rate of funds invested at simple interest actually declines as time passes. McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 35 18 16 14 12 10 8 6 4 2 0 10% Simple 30 27 24 21 18 15 12 9 6 10% Compound 3 0 FV of $1 Compound Interest Number of Years McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 36 Compound Interest Example Suppose you are offered an automobile loan at an APR of 6% per year. What does that mean, and what is the true rate of interest, given monthly payments? McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 37 Compound Interest Example - continued Suppose you are offered an automobile loan at an APR of 6% per year. What does that mean, and what is the true rate of interest, given monthly payments? Assume $10,000 loan amount. Loan Pmt 10,000 (1.005) 12 10,616.78 APR 6.1678% McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 3- 38 Web Resources Click to access web sites Internet connection required www.bankrate.com www.money.cnn.com www.quicken.com www.smartmoney.com McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved