Chapter 6

# Chapter 6 - Chapter Six Discounted Cash Flow Valuation 6.2...

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Discounted Cash Flow Valuation Chapter Six

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6.2 Learning Objectives of Chapter Six Be able to compute the future value of multiple cash flows – both annuity and uneven cash flows Be able to compute the present value of multiple cash flows – both annuity and uneven cash flows Be able to compute the payment of an annuity Be able to find the interest rate on annuity cash flows Be able to explain how interest rates are quoted Be able to calculate the effective annual rate (EAR) and the annual percentage rate (APR), and to explain the difference between them Be able to describe the payment patterns of
6.3 Future Value of Multiple Cash Flows(Fig. 6-3) In the examples that follow, cash flows are assumed to occur at the end of the relevant period. Thus a year 1 cash flow occurs at the end of year 1, a year 2 cash flow occurs at the end of year 2, etc. Cash flows that occur at the end of the period are called ordinary cash flows. This is the normal assumption for most (but not all) finance problems.

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6.4 Future Value of Multiple Cash Flows(Fig. 6-3) The future value of a series of multiple cash flows can always be calculated by compounding each cash flow separately to the end of the investment holding period and then adding up the separate FVs, as shown below. r=10% Yr. 5 CF Yr. 4 CF Yr. 3 CF Yr. 2 CF Yr. 1 CF
6.5 Future Value of Multiple Cash Flows – Ex. 6.1 You plan to deposit \$4,000 at the end of each of the next three years in a bank account paying 8 percent interest. You also have \$7,000 in the account now. How much will you have at the end of year 3 (EOY3)? 0 1 2 3 7,000 4,000 4,000 4,000 FV at EOY3 = ? Find the FV of each cash flow at EOY3, and then sum up the FVs. FV Current deposit (year 0): = 7,000(1.08) 3 = \$ 8,817.98 FV Year 1 deposit: = 4,000(1.08) 2 = 4,665.60 FV Year 2 deposit: = 4,000(1.08) 1 = 4,320.00 FV Year 3 deposit: value = 4,000(1.08) 0 = 4,000.00

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6.6 Future Value Example 6.1 (Continued) By calculator: 1) Compute the future value at the end of 3 years (at EOY3) of each cash flow, then sum the future values: Year 0 CF: 3 N; 8 I/Y; -7000 PV; CPT FV = 8817.98 Year 1 CF: 2 N; 8 I/Y; - 4000 PV; CPT FV = 4665.60 Year 2 CF: 1 N; 8 I/Y; - 4000 PV; CPT FV = 4320 Year 3 CF: value = 4,000 Total value in 3 years = \$8,817.98 + 4,665.60 + 4,320 + 4,000 = \$21,803.58
6.7 FV of Multiple Cash Flows–Example 2 Suppose you invest \$500 in a mutual fund today (t =0) and then \$600 in one year. If the fund pays 9% annually, how much money will you have two years from now? FV = \$500(1.09) 2 + \$600(1.09) = \$1,248.05 Calculator keystrokes: Year 0 CF: -500 PV; 9 I/Y; 2 N; CPT FV = \$594.05 Year 1 CF: -600 PV; 9 I/Y; 1 N; CPT FV = \$654.00 Total FV = \$594.05 + \$654.00 = \$1,248.05 Another way: -500 PV; -600 PMT; 9 I/Y; 2 N; CPT FV = \$1,848.05 – 600 = \$1,248.05 (Get it?)

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6.8 FV of Multiple Cash Flows – Example 2 (Cont.) If the money remains invested, how much will you
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## This note was uploaded on 04/30/2010 for the course FRL 300 taught by Professor Lentz during the Spring '08 term at Cal Poly Pomona.

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Chapter 6 - Chapter Six Discounted Cash Flow Valuation 6.2...

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