Chapter 5 CalculatorsCalculators Introduction to Valuation The Time Value of Money McGraw Hill Irwin Copyright 2013 by The McGraw Hill Companies Inc All rights reserved Key Concepts and Skills Be able to compute the future value of an investment made today Be able to compute the present value of cash to be received at some future date Be able to compute the return on an investment Be able to compute the number of periods that equates a present value and a future value given an interest rate Be able to use a financial calculator and a spreadsheet to solve time value of money problems 5C 2 Chapter Outline Future Value and Compounding Present Value and Discounting More about Present and Future Values 5C 3 Basic Definitions Present Value earlier money on a time line Future Value later money on a time line Interest rate exchange rate between earlier money and later money Discount rate Cost of capital Opportunity cost of capital Required return 5C 4 Future Values Suppose you invest 1 000 for one year at 5 per year What is the future value in one year Interest 1 000 05 50 Value in one year principal interest 1 000 50 1 050 Future Value FV 1 000 1 05 1 050 Suppose you leave the money in for another year How much will you have two years from now FV 1 000 1 05 1 05 1 000 1 05 2 1 102 50 5C 5 Future Values General Formula FV PV 1 r t FV future value PV present value r period interest rate expressed as a decimal t number of periods Future value interest factor 1 r t 5C 6 Effects of Compounding Simple interest Compound interest Consider the previous example FV with simple interest 1 000 50 50 1 100 FV with compound interest 1 102 50 The extra 2 50 comes from the interest of 05 50 2 50 earned on the first interest payment 5C 7 Calculator Keys Texas Instruments BA II Plus FV future value PV present value I Y period interest rate P Y must equal 1 for the I Y to be the period rate Interest is entered as a percent not a decimal N number of periods Remember to clear the registers CLR TVM after each problem Other calculators are similar in format 5C 8 Future Values Example 2 Suppose you invest the 1 000 from the previous example for 5 years How much would you have 5 N 5 I Y 1 000 PV CPT FV 1 276 28 The effect of compounding is small for a small number of periods but increases as the number of periods increases Simple interest would have a future value of 1 250 for a difference of 26 28 5C 9 Future Values Example 3 Suppose you had a relative deposit 10 at 5 5 interest 200 years ago How much would the investment be worth today 200 N 5 5 I Y 10 PV CPT FV 447 189 84 What is the effect of compounding Simple interest 10 200 10 055 120 00 Compounding added 447 069 84 to the value of the investment 5C 10 Future Value as a General Growth Formula Suppose your company expects to increase unit sales of widgets by 15 per year for the next 5 years If you sell 3 million widgets in the current year how many widgets do you expect to sell in the fifth year 5 N 15 I Y 3 000 000 PV CPT FV 6 034 072 units remember the sign convention 5C 11 Quick Quiz Part I What is the difference between simple interest and compound interest Suppose you have 500 to invest and you believe that you can earn 8 per year over the next 15 years How much would you have at the end of 15 years using compound interest How much would you have using simple interest 5C 12 Present Values How much do I have to invest today to have some amount in the future FV PV 1 r t Rearrange to solve for PV FV 1 r t When we talk about discounting we mean finding the present value of some future amount When we talk about the value of something we are talking about the present value unless we specifically indicate that we want the future value 5C 13 Present Value One Period Example Suppose you need 10 000 in one year for the down payment on a new car If you can earn 7 annually how much do you need to invest today PV 10 000 1 07 1 9 345 79 Calculator 1 N 7 I Y 10 000 FV CPT PV 9 345 79 5C 14 Present Values Example 2 You want to begin saving for your daughter s college education and you estimate that she will need 150 000 in 17 years If you feel confident that you can earn 8 per year how much do you need to invest today N 17 I Y 8 FV 150 000 CPT PV 40 540 34 remember the sign convention 5C 15 Present Values Example 3 Your parents set up a trust fund for you 10 years ago that is now worth 19 671 51 If the fund earned 7 per year how much did your parents invest N 10 I Y 7 FV 19 671 51 CPT PV 10 000 5C 16 Present Value Important Relationship I For a given interest rate the longer the time period the lower the present value What is the present value of 500 to be received in 5 years 10 years The discount rate is 10 5 years N 5 I Y 10 FV 500 CPT PV 310 46 10 years N 10 I Y 10 FV 500 CPT PV 192 77 5C 17 Present Value Important Relationship II For a given time period the higher the interest rate the smaller the present value What is the present value of 500 received in 5 years if the interest rate is 10