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Unformatted text preview: 6 Discounted Cash Flow Valuation Slide 6  1 Chapter Outline ¡ Future and Present Values of Multiple Cash Flows ¡ Valuing Level Cash Flows: Annuities and Perpetuities ¡ Comparing Rates: The Effect of Compounding ¡ Loan Types Slide 6  2 ¡ Future Value of Multiple Cash Flows ● We have discussed: for a single cash flow: FV = PV (1+r) t Where, PV = Value of original investment FV = Future value of investment t = Number of periods r = Interest rate per period ● FV for Multiple Cash Flows W e convert multiple cash flows to the same time point. Then, the future value of a stream of cash flows is the sum of the FV of each cash flow. Multiple Cash Flows: FV Slide 6  3 ¡ Future Value: Example Consider the following uneven cash flow stream with r = 10%: Find FV at year 3 of each cash flow and add them together. (PV is to be discussed) t=0 1 2 3 $700 (PV) $400 $400 $400 FV? Multiple Cash Flows: FV Slide 6  4 ● Value at year 3 Year 0 (today): FV = 700(1.08) 3 = 881.80 Year 1: FV = 400(1.08) 2 = 466.56 Year 2: FV = 400(1.08) = 432.00 Year 3: Value = 400 Total FV = 881.80 + 466.56 + 432 + 400 = 2,180.36 ● Further, what will be the value at year 4? 2,180.36(1.08) = 2,354.79 Multiple Cash Flows: FV Slide 6  5 ¡ Another Example Suppose you invest $500 in a mutual fund today and further invest $600 in one year. The fund pays 9% annually. ● How much will you have in two years? FV = 500(1.09) 2 + 600(1.09) = 1248.05 ● 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 = 1616.26 Second way: Use year2 value: FV=1248.05(1.09) 3 = 1616.26 Multiple Cash Flows: FV Slide 6  6 Multiple Cash Flows: PV ¡ Present Value of Multiple Cash Flows We first calculate the PV for each cash flow, then add them together. ¡ The Link between PV and FV If we want to find the FV at time t for the same stream of cash flows, we can use the basic formula after finding PV. t r PV FV ) 1 ( + = ( ) ( ) ( ) t t r C r C r C PV + + + + + + = 1 ... 1 1 2 2 1 1 Slide 6  7 ¡ Example Find PV of each of the following cash flows and then add them together: $200 in one year, $400 in two years, $600 in three years, and $800 in four years. 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 Multiple Cash Flows: PV Slide 6  8 ¡ Another Example You are considering an investment that will pay you $1,000 in one year, $2,000 in two years and $3000 in three years. If you want to earn 10% on your money, how much would you be willing to pay? Year 1 CF: PV = 1000 / (1.1) 1 = 909.09 Year 2 CF: PV = 2000 / (1.1) 2 = 1,652.89 Year 3 CF: PV = 3000 / (1.1) 3 = 2,253.94 Total PV = 909.09 + 1,652.89 + 2,253.94 = 4,815.92 Total FV in three years: 4,815.92(1.1) 3 = 6,409.99 Multiple Cash Flows: PV Slide 6  9 Multiple Cash Flows: Use the Calculator ¡ Use N, I/Y, PV, and FV for each cash flow then add up...
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This note was uploaded on 07/30/2011 for the course STAT 3801 taught by Professor Kc during the Fall '11 term at HKU.
 Fall '11
 KC

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