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# Chapter 6 - Discounted Cash Flow Valuation Chapter Six...

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Discounted Cash Flow Valuation Chapter Six

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2 Chapter Outline Future and Present Values of Multiple Cash Flows Valuing Level Cash Flows: Annuities and Perpetuities Loan Types and Loan Amortization
3 Multiple CFs – FV Example 1 Suppose you deposit \$7000 today in an account paying 8%. You will deposit \$4000 in one year, \$5000 in two years and \$2000 in three years. How much you will have in three years? Find the value at year 3 of each cash flow and add them together. FV = 7000(1.08) 3 + 4,000(1.08) 2 + 5,000(1.08)+2,000 = 20,883.58 Total value in 3 years 20,883.58

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4 Multiple CFs – FV Example 2 Suppose you invest \$500 in a mutual fund today and \$600 in one year, and \$700 in three years. If the fund pays 9% annually, how much will you have in four years? FV = 500(1.09) 4 + 600(1.09) 3 + 700(1.09) = 2,245.81
5 Multiple CFs – FV Example 2 How much will you have in 40 years (from today) if you make no further deposits? FV = 2,245.81(1.09) 36 = 49,972.02

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6 Multiple CFs – PV Example 1 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 up. PV = 200 / (1.12) 1 + 400 / (1.12) 2 + 600 / (1.12) 3 + 800 / (1.12) 4 = 1432.93
7 Multiple CFs – PV Example 2 You are offered an investment that costs \$5000. It will pay you \$1000 in one year, \$2000 in two years and \$3000 in three years. If you want to earn 10% on your money should you do it? PV = 1000 / (1.1) 1 + 2000 / (1.1) 2 + 3000 / (1.1) 3 = 4815.93

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8 Annuities Defined Annuity – finite series of equal payments that occur at regular intervals If the first payment occurs at the end of the period, it is called an ordinary annuity If the first payment occurs at the beginning of the period, it is called an annuity due
9 Ordinary Annuity 0 1 2 3 4 5 0 1 2 3 4 5 |----------|----------|----------|----------|----------| 200 200 200 200 200 PV FV

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10 Annuity Due 0 1 2 3 4 5 0 1 2 3 4 5 |--------|--------|--------|--------|--------| 200 200 200 200 200 PV FV
11 Ordinary Annuity Basic Formulas Annuities: 0 1 1 (1 ) (1 ) 1 t t t r PV C r r FV C r - + = + - =

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12 Annuity Due Basic Formulas The relationship between the value of an annuity due and an ordinary annuity is: This works for both present and future values Calculating the value of an annuity due calculate the PV or FV as if it were an ordinary annuity multiply the answer by (1+r) Annuity due value Ordinary Annuity value (1+r) = ×
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Chapter 6 - Discounted Cash Flow Valuation Chapter Six...

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