We need to calculate the future value of $10,000 at 6 percent for five years. The future value factor is:

The future value is thus $10,000 X 1.3382 = $13,382.26.

We need the present value of $150,000 to be paid in 11 years at 9 percent. The discount factor is:

The present value is thus about $58,130.

Suppose you invest, say, $1,000. You will have $2,000 in 10 years with this investment. So, $1,000 is the amount you have today, or the present value, and $2,000 is the amount you will have in 10 years, or the future value. From the basic present value equation, we have:

From here, we need to solve for r, the unknown rate. As shown in the chapter, there are several different ways to do this. We will take the 10th root of 2 (by raising 2 to the power of 1/10):

Using the Rule of 72, we have 72/t = r%, or 72/10 = 7.2%, so our answer looks good (remember that the Rule of 72 is only an approximation). The basic equation is:

If we solve for t, we get that t = 8.04 years. Using the Rule of 72, we get 72/9 = 8 years, so, once again, our answer looks good. To get $45,000, verify for yourself that you will have to wait 12.75 years.

Ross et al.: Fundamentals of Corporate Finance, Sixth Edition, Alternate Edition

III. Valuation of Future Cash Flows

5. Introduction to Valuation: The Time Value of Money

© The McGraw-Hill Companies, 2002

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