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Chapter06

# Chapter06 - Outline L06-1 Chapter 6 Discounted Cash Flow...

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L06-1 Outline Chapter 6. Discounted Cash Flow Valuation Future and Present Values with Multiple Cash Flows Valuing Constant Cash Flows : Annuities and Perpetuities Comparing Rates: The Effect of Compounding Loan Types and Loan Amortization Summary and Conclusions

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L06-2 Future Value with Multiple Cash Flows How would you calculate the future value when there are multiple cash flows? Suppose you deposit \$100 today in an account paying 8 percent. In one year, you will deposit another \$100. How much will you have in two years? At the end of the first year, you will have \$108 plus the second \$100 you deposit, for a total of \$208. You leave this \$208 on deposit at 8 percent for another year. At the end of the second year, it should be worth \$208 x 1.08 = \$224.64 The figure 6.1 is a time line that helps us in calculating the future or present value.
L06-3 Future Value with Multiple Cash Flows We could calculate this in an another way. The first \$100 is on deposit for two years at 8 percent, so its future value is \$100 x 1.08 2 = \$100 x 1.1664 = \$116.64. The second \$100 is on deposit for one year at 8 percent, and its future value is \$100 x 1.08 = \$108. Thus, the total future value is equal to the sum of these two future values \$116.64 + 108 = \$224.64 Figure 6.1

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L06-4 Future Value with Multiple Cash Flows (continued) Based on this example, there are two ways to calculate the future value for multiple cash flows: 1. Compound the accumulated balance forward one year at a time 2. Calculate the future value of each cash flow first and then add them up. Example : Find the future value of \$2,000 invested at the end of each of the next five years. The current balance is zero, and the rate is 10%. Then, the time line can be drawn as in Figure 6.2. Figure 6.2 Nothing happens until the end of the first year, when we make the first \$2,000 investment. This first \$2,000 earns interest for the next four (not five) years. The last \$2,000 earns no interest.
L06-5 Future Value with multiple cash flows (continued) Figure 6.3 illustrates the calculations involved if we compound the investment one period at a time. Figure 6.3 Figure 6.4 illustrates the calculations involved if each cash flow is compounded separately. Figure 6.4

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L06-6 Future Value with Multiple Cash Flows (continued) Example 6.2: Saving up once again If you deposit \$100 in one year, \$200 in two years, and \$300 in three years, how much will you have in three years? How much of this is interest? How much will you have in five years if you don’t add additional amounts? Assume a 7 percent interest rate throughout. Let us calculate the future value of each amount in three years. Notice that the \$100 earns interest for two years, and the \$200 earns interest for one year. The final \$300 earns no interest. The future values are \$100 x 1.07 2 = \$114.49, \$200 x 1.07 = \$214.00, and \$300. Hence, Total future value = \$114.49 + \$214.00 + \$300 = \$628.49. Total interest is \$628.49 – (100 + 200 + 300) = \$28.49.
L06-7 Future Value with Multiple Cash Flows (continued) We could calculate this by calculating the future value of each amount separately.

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Chapter06 - Outline L06-1 Chapter 6 Discounted Cash Flow...

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