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# Chapter%204 - FIN3100 Chapter 4 Time Value of Money Part 2...

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FIN3100: Chapter 4 Time Value of Money Part 2

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Learning Objectives Compute the future value and present value of multiple cash flows. Determine the future value of an annuity. Determine the present value of an annuity. Adjust the annuity formula for present value and future value for an annuity due, and understand the concept of a perpetuity. Calculate payments and waiting time for an annuity. Distinguish between the different types of loan repayments: discount loans, interest-only loans, and amortized loans.
Multiple Payment Streams With unequal periodic cash flows, treat each of the cash flows as a lump sum and calculate its FV or PV over the relevant number of periods. Sum up the individual future values to get the value of the multiple payment streams.

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FV 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 = 500(1.09) 2 + 600(1.09) = 1,248.05
PV Example 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?

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PV continued Find the PV of each cash flow 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
PV Timeline 0 1 2 3 4 200 400 600 800 178.57 318.88 427.07 508.41 1,432.93

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Suppose you are looking at the following possible cash flows: Year 1 CF = \$100; Years 2 and 3 CFs = \$200; Years 4 and 5 CFs = \$300. The required discount rate is 7%.
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Chapter%204 - FIN3100 Chapter 4 Time Value of Money Part 2...

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