## Determining the Discount Rate

It will turn out that we will frequently need to determine what discount rate is implicit in an investment. We can do this by looking at the basic present value equation:

There are only four parts to this equation: the present value (PV), the future value (FVt), the discount rate (r), and the life of the investment ('). Given any three of these, we can always find the fourth.

Finding rfor a Single-Period Investment

You are considering a one-year investment. If you put up $1,250, you will get back $1,350. What rate is this investment paying?

First, in this single-period case, the answer is fairly obvious. You are getting a total of $100 in addition to your $1,250. The implicit rate on this investment is thus $100/1,250 = 8 percent.

More formally, from the basic present value equation, the present value (the amount you must put up today) is $1,250. The future value (what the present value grows to) is $1,350. The time involved is one period, so we have:

$1,250 = $1,350/(1 + r)1 1 + r = $1,350/1,250 = 1.08 r = 8%

In this simple case, of course, there was no need to go through this calculation, but, as we describe next, it gets a little harder when there is more than one period.

To illustrate what happens with multiple periods, let's say that we are offered an investment that costs us $100 and will double our money in eight years. To compare this to other investments, we would like to know what discount rate is implicit in these numbers. This discount rate is called the rate of return, or sometimes just return, on the investment. In this case, we have a present value of $100, a future value of $200 (double our money), and an eight-year life. To calculate the return, we can write the basic present value equation as:

It could also be written as:

We now need to solve for r. There are three ways we could do it:

### 1. Use a financial calculator.

2. Solve the equation for 1 + r by taking the eighth root of both sides. Because this is the same thing as raising both sides to the power of % or .125, this is actually easy

For a downloadable, Windows-based financial calculator, go to www.calculator.org..

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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PART THREE Valuation of Future Cash Flows

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