Chapter 4 DISCOUNTED CASH FLOW VALUATION Copyright 2014 McGraw Hill Education All rights reserved No reproduction or distribution without the prior written consent of McGraw Hill Education KEY CONCEPTS AND SKILLS Appreciate the significance of compound vs simple interest Describe and compute the future value and or present value of a single cash flow or series of cash flows Define and calculate the return on an investment Recognize and compute the impact of compounding periods on the true return of stated interest rates Develop facility with a financial calculator and or spreadsheet to solve time value problems Comprehend and calculate time value metrics for perpetuities and annuities Familiarization with loan types and amortization 4 2 CHAPTER OUTLINE 4 1 4 2 4 3 4 4 4 5 4 6 Valuation The One Period Case The Multiperiod Case Compounding Periods Simplifications Loan Types and Loan Amortization What Is a Firm Worth 4 3 THE ESSENTIAL PREMISE A dollar today is more valuable than a dollar to be received in the future Why A dollar today is more valuable because It can be invested to make more dollars It can be immediately consumed There is no doubt about its receipt 4 4 AN IMPORTANT COROLLARY If you know your required rate of return and the length of time before cash is harvested you can calculate some critical metrics The value today of a payment to be received in the future This measure is called a Present Value The value in the future of a sum invested today This measure is called a Future Value Present and Future Values can be calculated over single and multiple periods 4 5 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 4 6 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 4 7 PRESENT VALUE Present Value is today s value of a sum to be received in the future given a specific rate of interest and time horizon Suppose you were promised 10 000 due in one year when interest rates are 5 percent Your investment 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 the Present Value PV Note that 10 000 9 523 81 1 05 4 8 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 4 9 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 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 4 10 NET PRESENT VALUE 10 000 NPV 9 500 1 05 NPV 9 500 9 523 81 NPV 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 4 11 NET PRESENT VALUE In the one period case the formula for NPV can be written as NPV Cost PV 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 4 12 4 2 THE MULTIPERIOD CASE The previous examples considered only one period of time It is possible to compute PV FV for multiple periods of time Doing so requires discrimination between simple and compound interest 4 13 SIMPLE INTEREST Suppose an investor has 1 000 to invest at an interest rate of 9 In one year they will have earned 90 1000 x 1 09 If they take the 90 earned out of the capital market and reinvest the 1 000 capital at 9 they will again earn 90 in a year s time This process could continue ad infinitum with the annual earnings never contributing further to the investor s wealth With simple interest therefore valuing future or present values never has to extend beyond the single period case 4 14 COMPOUND INTEREST Suppose an investor has 1 000 to invest at an interest rate of 9 In one year they will have earned 90 1000 x 09 Now suppose that the investor reinvests both the original 1 000 capital AND 90 earnings for another year at 9 In one year they will have earned 98 10 an amount 8 10 greater than the previous year In this example the interest in the second year is higher than the first because it is paid on the initial capital AND prior earnings In other words the earnings also earn interest or are compounded Compounding may not seem very compelling the early years of an investment But we will see that it is a very powerful long term force 4 15 MULTIPERIOD FUTURE VALUE 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 4 16 EXAMPLE MULTIPERIOD 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 4 17 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 40 percent on the original 1 10 dividend 5 92 1 10 5 1 10 40 3 30 This is due to compounding 4 18 FUTURE VALUE AND COMPOUNDING 1 10 1 40 5 4 1 10 1 40 1 10 1 40 2 1 10 1 40 1 10 1 40 1 10 0 3 1 54 2 16 1 2 3 02 4 23 5 92 3 4 5 4 19 MULTIPERIOD PRESENT VALUE The general formula for the present value of an investment over many periods can be written as PV CT 1 r T Where CT is cash flow at date …