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Slide+6 - Lecture 6 Discounted Cash Flow Valuation by Diep...

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Lecture 6 Discounted Cash Flow Valuation by Diep Duong

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Outline Future and Present Values of Multiple Cash Flows Valuing Level Cash Flows: Annuities and Perpetuities Comparing Rates: The Effect of Compounding Loan Types and Loan Amortization
FV of Multiple Cash Flows FV of Multiple Cash Flows = Sum of all Future Values of Single Cash Flows You invest in period t1, t2,…,tn, and you want to know your future value at time T Firstly calculate future value for single cash flow at each period (for t1, t2,….) Note that this this future value at time T Sum all the future values, you get the FV of all your cash flows at time T

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FV of Multiple Cash Flows - Example You think you will be able to deposit \$4,000 at the end of each of the next three years in a bank account paying 8 percent interest. You currently have \$7,000 in the account. How much will you have in 3 years? In 4 years? - Today (year 0): FV = 7000(1.08)3 = 8,817.98 Year 1: FV = 4,000(1.08) 2 = 4,665.60 Year 2: FV = 4,000(1.08) = 4,320 Year 3: value = 4,000 Total FV = 8,817.98 + 4,665.60 + 4,320 + 4,000 = 21,803.58 Value at year 4 = 21,803.58(1.08) = 23,547.87
FV of Multiple Cash Flows Example Suppose you invest \$500 in a mutual fund today and \$600 in one year. If the fund pays 9% annually, how much will you have in two years? FV of your today money (Year 0) = 500(1.09) 2 FV of your money next year (Year 1) = 600(1.09) In two years what you have is : 500(1.09)^2+ 600(1.09)

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Multiple Cash Flows – Example (Continued) How much will you have in 5 years if you make no further deposits? First way: FV = 500(1.09) 5 + 600(1.09) 4 = 1,616.26 Second way – use value at year 2: FV = 1,248.05(1.09) 3 = 1,616.26
Multiple Cash Flows – FV Example Suppose you plan to deposit \$100 into an account in one year and \$300 into the account in three years. How much will be in the account in five years if the interest rate is 8%? FV = 100(1.08) 4 + 300(1.08) 2 = 136.05 + 349.92 = 485.97

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Multiple Cash Flows – Present Value PV of Multiple Cash Flows = Sum of all Present Values of Single Future Cash Flows You receive future payments in period t1, t2,…,tn, and you want to know your present value at time t Firstly calculate present value for single cash flow at each period (for t1, t2,….) Note that this this present value at time t Sum all the present values, you get the PV at time t of all your future cash flows
Multiple Cash Flows – Present Value You are offered an investment that will pay you \$200 in one year, \$400 the next year, \$600 the next year and \$800 at the end of the next year. You can earn 12 percent on very similar investments. What is the most you should pay for this one? Find the PV of each cash flows and add them Year 1 CF: 200 / (1.12) 1 = 178.57 Year 2 CF: 400 / (1.12) 2 = 318.88 Year 3 CF: 600 / (1.12) 3 = 427.07 Year 4 CF: 800 / (1.12) 4 = 508.41 Total PV = 178.57 + 318.88 + 427.07 + 508.41 = 1,432.93

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Example - Timeline 0 1 2 3 4 200 400 600 800 178.57 318.88 427.07 508.41 1,432.93 6F-10
Multiple Cash Flows Using a Spreadsheet You can use the PV or FV functions in Excel to find the present value or future value of a set of cash flows Setting the data up is half the battle – if it is set up properly, then you can just copy the formulas Click on the Excel icon for an example

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