Chapter 4 Introduction To Valuation: The Time Value Of Money PDF

Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.  Chapter Outline 4.1 Future Value and Compounding 4.2 Present Value and Discounting 4.3 More o...

Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.  Chapter Outline 4.1 Future Value and Compounding 4.2 Present Value and Discounting 4.3 More on Present and Future Values Solving for: Implied interest rate Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-2  Basic Definitions Present Value (PV) – The current value of future cash flows discounted at the appropriate discount rate – Value at t=0 on a time line Future Value (FV) – The amount an investment is worth after one or more periods. – “Later” money on a time line Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-3  Basic Definitions Interest rate (r) – Discount rate – Cost of capital – Opportunity cost of capital – Required return – Terminology depends on usage Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-4  Time Line of Cash Flows Tick marks at ends of periods Time 0 is today; Time 1 is the end of Period 1 0 1 2 3 r% CF0 CF1 CF2 CF3 +CF = Cash INFLOW -CF = Cash OUTFLOW PMT = Constant CF Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-5 Time Line for a $100 Lump Sum due at the End of Year 2 0 1 2 Year r% 100 Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-6  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 Note: “yx” key on your calculator 4-7 Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Future Values: Example 1 Suppose you invest $100 for one year at 10% per year. What is the future value in one year? Suppose you leave the money in for another year. How much will you have two years from now? Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-8 Future Values: Example 1 Suppose you invest $100 for one year at 10% per year. What is the future value in one year? – Interest = 100(.10) = 10 – Value in one year = Principal + interest = 100 + 10 = 110 – Future Value (FV) = 100(1 +.10) = 110 Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-9  Effects of Compounding Simple interest – Interest earned only on the original principal Compound interest – Interest earned on principal and on interest received – “Interest on interest” – interest earned on reinvestment of previous interest payments Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-10  Effects of Compounding Consider the previous example – FV w/simple interest = 100 + 10 + 10 = 120 – FV w/compound interest =100(1.10)2 = 121.00 – The extra 1.00 comes from the interest of.10(10) = 1.00 earned on the first interest payment Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-11 Future Values: Example 2 Suppose you invest the $100 from the previous example for 5 years. How much would you have? Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-12  Table 4.1 Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-13  Figure 4.1 Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-14  Excel Spreadsheet Functions Excel TVM functions: =FV(rate,nper,pmt,pv) =PV(rate,nper,pmt,fv) =RATE(nper,pmt,pv,fv) =NPER(rate,pmt,pv,fv) Use the formula icon (ƒx) when you can’t remember the exact formula Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-15  Future Value: General Growth Formula Suppose your company expects to increase unit sales of widgets by 15% per year for the next 5 years. If you currently sell 3 million widgets in one year, how many widgets do you expect to sell in 5 years? Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-16  Future Value: Important Relationship I For a given interest rate: – The longer the time period, – The higher the future value FV = PV(1 + r)t For a given r, as t increases, FV increases Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-17  Future Value: Important Relationship II For a given time period: – The higher the interest rate, – The larger the future value FV = PV(1 + r)t For a given t, as r increases, FV increases Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-18  Figure 4.2 Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-19  Quick Quiz: Part 1 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? Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-20  Present Values The current value of future cash flows discounted at the appropriate discount rate Value at t=0 on a time line Answers the questions: – How much do I have to invest today to have some amount in the future? – What is the current value of an amount to be received in the future? Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-21  Present Values Present Value = the current value of an amount to be received in the future Why is it worth less than face value? – Opportunity cost – Risk & Uncertainty Discount Rate = ƒ (time, risk) Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-22  Time Line of Cash Flows Tick marks at ends of periods Time 0 is today; Time 1 is the end of Period 1 0 1 2 3 r% CF0 CF1 CF2 CF3 +CF = Cash INFLOW -CF = Cash OUTFLOW PMT = Constant CF Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-23  Present Values FV = PV(1 + r)t Rearrange to solve for PV PV = FV / (1+r)t PV = FV(1+r)-t “Discounting” = finding the present value of one or more future amounts. Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-24 What’s the PV of $100 due in 3 FindingYears if r = 10%? PVs is discounting, and it’s the reverse of compounding. 0 1 2 3 10% PV = ? 100 Formula: PV = FV(1+r)-t = 100(1.10)-3 = $75.13 Excel: =PV(.10,3,0,100) = -75.13 Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-25  Present Values: Example 2 Multi-Periods 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? Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-26  Present Value: Important Relationship I For a given interest rate: – The longer the time period, – The lower the present value FV PV  t (1  r ) For a given r, as t increases, PV decreases Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-27  Present Value: Important Relationship I What is the present value of $500 to be received in 5 years? 10 years? The discount rate is 10% 0 r=10% 5 10 -310.46 PV? 500 -192.77 PV? 500 5 yrs: PV = 500/(1.10)5 = -310.46 (1.10)5 =1.6105 10 yrs: PV = 500/(1.10)10= -192.77 (1.10)10 = 2.5937 Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-28  Present Value: Important Relationship II For a given time period: – The higher the interest rate, – The smaller the present value FV PV  t (1  r ) For a given t, as r increases, PV decreases Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-29  Present Value: Important Relationship II What is the present value of $500 received in 5 years if the interest rate is Rate 10%? 15%? = 10% Rate = 15% PV = 500/(1.10)5 PV = 500/(1.15)5 = 310.46 = 248.59 Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-30  Figure 4.3 Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-31  The Basic PV Equation— Refresher PV = FV / (1 + r)t There are four parts to this equation – PV, FV, r and t – Know any three, solve for the fourth Be sure and remember the sign convention +CF = Cash INFLOW -CF = Cash OUTFLOW Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-32  Discount Rate To find the implied interest rate, rearrange the basic PV equation and solve for r: FV = PV(1 + r)t r = (FV / PV)1/t – 1 If using formulas with a calculator, make use of both the yx and the 1/x keys Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-33  Discount Rate: Example 1 You are looking at an investment that will pay $1200 in 5 years if you invest $1000 today. What is the implied rate of interest? Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-34  Quick Quiz: Part 3 What are some situations in which you might want to compute the implied interest rate? Suppose you are offered the following investment choices: – 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% annually. – What is the implied interest rate for the first choice and which investment should you choose? 4-35 Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.  Finding the Number of Periods Start with basic equation and solve for t: FV = PV(1 + r)t  FV  ln    PV  t ln(1  r ) Calculator: CPT N Excel: =NPER(Rate, Pmt, PV, FV) Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-36  Number of Periods: Example 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? Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-37  Table 4.4 Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-38  Chapter 4 END Copyright ©2020 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-39