10066CalculatorsDiscounted Cash Flow ValuationDiscounted Cash Flow Valuation11Key Concepts and SkillsKey Concepts and Skills¾¾Be able to compute the future value of multiple Be able to compute the future value of multiple cash flowscash flows¾¾Be able to compute the present value of multiple Be able to compute the present value of multiple cash flowscash flows¾¾Be able to compute loan paymentsBe able to compute loan payments¾¾Be able to find the interest rate on a loanBe able to find the interest rate on a loan¾¾Understand how interest rates are quotedUnderstand how interest rates are quoted¾¾Understand how loans are amortized or paid offUnderstand how loans are amortized or paid off22Chapter OutlineChapter Outline¾¾Future and Present Values of Multiple Future and Present Values of Multiple Cash FlowsCash Flows¾¾Valuing Level Cash Flows: Annuities and Valuing Level Cash Flows: Annuities and PerpetuitiesPerpetuities¾¾Comparing Rates: The Effect of Comparing Rates: The Effect of CompoundingCompounding¾¾Loan Types and Loan AmortizationLoan Types and Loan Amortization33Multiple Cash Flows Multiple Cash Flows ––Future Future Value Example 6.1Value Example 6.1¾¾Find the value at year 3 of each cash flow and add Find the value at year 3 of each cash flow and add them together.them together.zzTodayToday’’s (year 0) CF: 3 N; 8 I/Y; s (year 0) CF: 3 N; 8 I/Y; --7,000 PV; CPT FV = 8817.987,000 PV; CPT FV = 8817.98zzYear 1 CF: 2 N; 8 I/Y; Year 1 CF: 2 N; 8 I/Y; --4,000 PV; CPT FV = 4,665.604,000 PV; CPT FV = 4,665.60zzYear 2 CF: 1 N; 8 I/Y; Year 2 CF: 1 N; 8 I/Y; --4,000 PV; CPT FV = 4,3204,000 PV; CPT FV = 4,320zzYear 3 CF: value = 4,000Year 3 CF: value = 4,000zzTotal value in 3 years = 8,817.98 + 4,665.60 + 4,320 + 4,000 = Total value in 3 years = 8,817.98 + 4,665.60 + 4,320 + 4,000 = 21,803.5821,803.58¾¾Value at year 4: 1 N; 8 I/Y; Value at year 4: 1 N; 8 I/Y; --21,803.58 PV; CPT FV = 21,803.58 PV; CPT FV = 23,547.8723,547.8744Multiple Cash Flows Multiple Cash Flows ––FV FV Example 2Example 2¾¾Suppose you invest $500 in a mutual fund Suppose you invest $500 in a mutual fund today and $600 in one year. If the fund pays today and $600 in one year. If the fund pays 9% annually, how much will you have in two 9% annually, how much will you have in two years?years?zzYear 0 CF: 2 N; Year 0 CF: 2 N; --500 PV; 9 I/Y; CPT FV = 594.05500 PV; 9 I/Y; CPT FV = 594.05zzYear 1 CF: 1 N; Year 1 CF: 1 N; --600 PV; 9 I/Y; CPT FV = 654.00600 PV; 9 I/Y; CPT FV = 654.00zzTotal FV = 594.05 + 654.00 = 1,248.05Total FV = 594.05 + 654.00 = 1,248.0555Multiple Cash Flows Multiple Cash Flows ––Example 2 Example 2 ContinuedContinued¾¾How much will you have in 5 years if you make no How much will you have in 5 years if you make no further deposits?further deposits?¾¾First way:First way:zzYear 0 CF: 5 N; Year 0 CF: 5 N; --500 PV; 9 I/Y; CPT FV = 769.31500 PV; 9 I/Y; CPT FV = 769.31zzYear 1 CF: 4 N; Year 1 CF: 4 N; --600 PV; 9 I/Y; CPT FV = 846.95600 PV; 9 I/Y; CPT FV = 846.95zzTotal FV = 769.31 + 846.95 = 1,616.26Total FV = 769.31 + 846.95 = 1,616.26¾¾Second way Second way ––use value at year 2:use value at year 2:zz3 N; 3 N; --1,248.05 PV; 9 I/Y; CPT FV = 1,616.261,248.05 PV; 9 I/Y; CPT FV = 1,616.26266Multiple Cash Flows Multiple Cash Flows ––FV FV Example 3Example 3¾¾Suppose you plan to deposit $100 into an Suppose you plan to deposit $100 into an account in one year and $300 into the account account in one year and $300 into the account in three years. How much will be in the in three years. How much will be in the account in five years if the interest rate is 8%?account in five years if the interest rate is 8%?zzYear 1 CF: 4 N; Year 1 CF: 4 N; --100 PV; 8 I/Y; CPT FV = 136.05100 PV; 8 I/Y; CPT FV = 136.05zzYear 3 CF: 2 N; Year 3 CF: 2 N; --300 PV; 8 I/Y; CPT FV = 349.92300 PV; 8 I/Y; CPT FV = 349.92zzTotal FV = 136.05 + 349.92 = 485.97Total FV = 136.05 + 349.92 = 485.9777Multiple Cash Flows Multiple Cash Flows ––Present Present Value Example 6.3Value Example 6.3¾¾Find the PV of each cash flows and add themFind the PV of each cash flows and add themzzYear 1 CF: N = 1; I/Y = 12; FV = 200; CPT PV = Year 1 CF: N = 1; I/Y = 12; FV = 200; CPT PV = --178.57178.57zzYear 2 CF: N = 2; I/Y = 12; FV = 400; CPT PV = Year 2 CF: N = 2; I/Y = 12; FV = 400; CPT PV = --318.88318.88zzYear 3 CF: N = 3; I/Y = 12; FV = 600; CPT PV = Year 3 CF: N = 3; I/Y = 12; FV = 600; CPT PV = --427.07427.07zzYear 4 CF: N = 4; I/Y = 12; FV = 800; CPT PV = Year 4 CF: N = 4; I/Y = 12; FV = 800; CPT PV = --508.41508.41zzTotal PV = 178.57 + 318.88 + 427.07 + 508.41 = 1,432.93Total PV = 178.57 + 318.88 + 427.07 + 508.41 = 1,432.9388Example 6.3 TimelineExample 6.3 Timeline01234200 400 600 800178.57318.88427.07508.411,432.9399Multiple Cash Flows Using a Multiple Cash Flows Using a SpreadsheetSpreadsheet¾¾You can use the PV or FV functions in Excel to You can use the PV or FV functions in Excel to find the present value or future value of a set of find the present value or future value of a set of cash flowscash flows¾¾Setting the data up is half the battle Setting the data up is half the battle ––if it is set if it is set up properly, then you can just copy the up properly, then you can just copy the formulasformulas¾¾Click on the Excel icon for an exampleClick on the Excel icon for an example1010Multiple Cash Flows Multiple Cash Flows ––PV PV Another ExampleAnother Example¾¾You are considering an investment that will pay You are considering an investment that will pay you $1,000 in one year, $2,000 in two years you $1,000 in one year, $2,000 in two years and $3,000 in three years. If you want to earn and $3,000 in three years. If you want to earn 10% on your money, how much would you be 10% on your money, how much would you be willing to pay?willing to pay?zzN = 1; I/Y = 10; FV = 1,000; CPT PV = N = 1; I/Y = 10; FV = 1,000; CPT PV = --909.09909.09zzN = 2; I/Y = 10; FV = 2,000; CPT PV = N = 2; I/Y = 10; FV = 2,000; CPT PV = --1,652.891,652.89zzN = 3; I/Y = 10; FV = 3,000; CPT PV = N = 3; I/Y = 10; FV = 3,000; CPT PV = --2,253.942,253.94zzPV = 909.09 + 1,652.89 + 2,253.94 = 4,815.93PV = 909.09 + 1,652.89 + 2,253.94 = 4,815.931111Multiple Uneven Cash Flows Multiple Uneven Cash Flows ––Using the CalculatorUsing the Calculator¾¾Another …