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Chap006

# Chap006 - Chapter 6 Discounted Cash Flow Valuation Key...

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Chapter 6 Discounted Cash Flow Valuation

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Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute loan payments Be able to find the interest rate on a loan Understand how interest rates are quoted Understand how loans are amortized or paid off 6F-2
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 and Loan Amortization 6F-3

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Multiple Cash Flows –Future Value Example 6.1 Find the value at year 3 of each cash flow and add them together 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 value in 3 years = 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 6F-4
Multiple Cash Flows – FV Example 2 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 = 500(1.09) 2 + 600(1.09) = 1,248.05 6F-5

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Multiple Cash Flows – Example 2 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 6F-6
Multiple Cash Flows – FV Example 3 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 6F-7

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Multiple Cash Flows – Present Value Example 6.3 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 6F-8
Example 6.3 Timeline 0 1 2 3 4 200 400 600 800 178.57 318.88 427.07 508.41 1,432.93 6F-9

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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 6F-10
Multiple Cash Flows – PV 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? PV = 1000 / (1.1) 1 = 909.09 PV = 2000 / (1.1) 2 = 1,652.89 PV = 3000 / (1.1) 3 = 2,253.94 PV = 909.09 + 1,652.89 + 2,253.94 = 4,815.92 6F-11

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Multiple Uneven Cash Flows – Using the Calculator Another way to use the financial calculator for uneven cash flows is to use the cash flow keys Press CF and enter the cash flows beginning with year 0. You have to press the “Enter” key for each cash flow Use the down arrow key to move to the next cash flow The “F” is the number of times a given cash flow occurs in consecutive periods Use the NPV key to compute the present value by entering the interest rate for I, pressing the down arrow and then compute Clear the cash flow keys by pressing CF and then CLR Work 6F-12
Decisions, Decisions

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