1、 INTRODUCTION TO VALUATION:THE TIME VALUE OF MONEY(CALCULATOR)CHAPTER 5Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.Determine the future value of an investment made today Determine the present valu
2、e of cash to be received at a future date Find the return on an investment Calculate how long it takes for an investment to reach a desired valueCopyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.Key Con
3、cepts and Skills Future Value and Compounding Present Value and Discounting More about Present and Future ValuesCopyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.Chapter Outline Present Value earlier mo
4、ney 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 returnCopyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the
5、prior written consent of McGraw-Hill Education.Basic Definitions 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
6、another year.How much will you have two years from now?FV=1,000(1.05)(1.05)=1,000(1.05)2=1,102.50Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.Future Value Example 1 FV=PV(1+r)t FV=future value PV=p
7、resent value r=period interest rate,expressed as a decimal t=number of periods Future value interest factor=(1+r)tCopyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.Future Value:General Formula Simple in
8、terest vs.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 paymentCopyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or
9、 distribution without the prior written consent of McGraw-Hill Education.Effects of Compounding 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
10、 Remember to clear the registers(CLR TVM)after each problem.Other calculators are similar in format.Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.Calculator Keys Suppose you invest the$1,000 from th
11、e 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.)Copyright 2019 M
12、cGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.Future Value Example 2 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,
13、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 investmentCopyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.Future Value
14、 Example 3 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)Copyri
15、ght 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.Future Value as a General Growth Formula What is the difference between simple interest and compound interest?Suppose you have$500 to invest and you believe t
16、hat 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?Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw
17、-Hill Education.Quick Quiz Part I 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
18、 the present value unless we specifically indicate that we want the future value.Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.Present Value Suppose you need$10,000 in one year for the down payment
19、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=-9,345.79Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.P
20、resent Value Example 1 You want to begin saving for your daughters 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)Co
21、pyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.Present Value Example 2 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
22、parents invest?N=10;I/Y=7;FV=19,671.51 CPT PV=-10,000Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.Present Value Example 3 For a given interest rate the longer the time period,the lower the present
23、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=500CPT PV=-310.46 10 years:N=10;I/Y=10;FV=500CPT PV=-192.77Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consen
24、t of McGraw-Hill Education.Present Value Important Relationship I 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%?15%?Rate=10%:N=5;I/Y=10;FV=500CPT PV=-310.46 Rate=15%;N=5;I/Y=15;FV=50
25、0CPT PV=-248.59Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.Present Value Important Relationship II What is the relationship between present value and future value?Suppose you need$15,000 in 3 year
26、s.If you can earn 6%annually,how much do you need to invest today?If you could invest the money at 8%,would you have to invest more or less than at 6%?How much?Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Ed
27、ucation.Quick Quiz Part II PV=FV/(1+r)t There are four parts to this equation:PV,FV,r and t If we know any three,we can solve for the fourth.If you are using a financial calculator,be sure to remember the sign convention or you will receive an error(or a nonsense answer)when solving for r or t.Copyr
28、ight 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.The Basic PV Equation-Refresher Often we will want to know what the implied interest rate is on an investment Rearrange the basic PV equation and solve for r
29、 FV=PV(1+r)t r=(FV/PV)1/t 1 If you are using formulas,you will want to make use of both the yx and the 1/x keysCopyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.Discount Rate You are looking at an inves
30、tment that will pay$1,200 in 5 years if you invest$1,000 today.What is the implied rate of interest?r=(1,200/1,000)1/5 1=.03714=3.714%Calculator the sign convention matters!N=5 PV=-1,000(you pay 1,000 today)FV=1,200(you receive 1,200 in 5 years)CPT I/Y=3.714%Copyright 2019 McGraw-Hill Education.All
31、rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.Discount Rate Example 1 Suppose you are offered an investment that will allow you to double your money in 6 years.You have$10,000 to invest.What is the implied rate of interest?N=6 PV=-10,000 F
32、V=20,000 CPT I/Y=12.25%Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.Discount Rate Example 2 Suppose you have a 1-year old son and you want to provide$75,000 in 17 years towards his college educatio
33、n.You currently have$5,000 to invest.What interest rate must you earn to have the$75,000 when you need it?N=17;PV=-5,000;FV=75,000 CPT I/Y=17.27%Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.Discoun
34、t Rate Example 3 What are some situations in which you might want to know the implied interest rate?You are offered the following investments:You can invest$500 today and receive$600 in 5 years.The investment is considered low risk.You can invest the$500 in a bank account paying 4%.What is the impli
35、ed interest rate for the first choice and which investment should you choose?Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.Quick Quiz Part III Start with the basic equation and solve for t(remember
36、your logs).FV=PV(1+r)t t=ln(FV/PV)/ln(1+r)You can use the financial keys on the calculator as well;just remember the sign convention.Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.Finding the Number
37、of Periods You want to purchase a new car,and you are willing to pay$20,000.If you can invest at 10%per year and you currently have$15,000,how long will it be before you have enough money to pay cash for the car?I/Y=10;PV=-15,000;FV=20,000 CPT N=3.02 yearsCopyright 2019 McGraw-Hill Education.All rig
38、hts reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.Number of Periods Example 1 Suppose you want to buy a new house.You currently have$15,000,and you figure you need to have a 10%down payment plus an additional 5%of the loan amount for closing cost
39、s.Assume the type of house you want will cost about$150,000 and you can earn 7.5%per year.How long will it be before you have enough money for the down payment and closing costs?Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent
40、 of McGraw-Hill Education.Number of Periods Example 2 How much do you need to have in the future?Down payment=.1(150,000)=15,000 Closing costs=.05(150,000 15,000)=6,750 Total needed=15,000+6,750=21,750 Compute the number of periods.Using a financial calculator:PV=-15,000;FV=21,750;I/Y=7.5 CPT N=5.14
41、 years Using the formula:t=ln(21,750/15,000)/ln(1.075)=5.14 yearsCopyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.Number of Periods Example 2(ctd.)When might you want to compute the number of periods?S
42、uppose you want to buy some new furniture for your family room.You currently have$500,and the furniture you want costs$600.If you can earn 6%,how long will you have to wait if you dont add any additional money?Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution w
43、ithout the prior written consent of McGraw-Hill Education.Quick Quiz Part IV Use the following formulas for TVM calculations FV(rate,nper,pmt,pv)PV(rate,nper,pmt,fv)RATE(nper,pmt,pv,fv)NPER(rate,pmt,pv,fv)The formula icon is very useful when you cant remember the exact formula.Click on the Excel ico
44、n to open a spreadsheet containing four different examples.Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.Spreadsheet Example Many financial calculators are available online.Go to Investopedias websi
45、te and work the following example:You need$50,000 in 10 years.If you can earn 6%interest,how much do you need to invest today?You should get$27,919.74Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.Wo
46、rk the Web ExampleCopyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.Table 5.4 You have$10,000 to invest for five years.How much additional interest will you earn if the investment provides a 5%annual re
47、turn,when compared to a 4.5%annual return?How long will it take your$10,000 to double in value if it earns 5%annually?What annual rate has been earned if$1,000 grows into$4,000 in 20 years?Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.Comprehensive ProblemEnd of Chapter Chapter 5-CalculatorCopyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.
