## T5

This last result we will call the basic present value equation. We will use it throughout the text. There are a number of variations that come up, but this simple equation underlies many of the most important ideas in corporate finance.

### Evaluating Investments

To give you an idea of how we will be using present and future values, consider the following simple investment. Your company proposes to buy an asset for \$335. This investment is very safe. You would sell off the asset in three years for \$400. You know you could invest the \$335 elsewhere at 10 percent with very little risk. What do you think of the proposed investment?

This is not a good investment. Why not? Because you can invest the \$335 elsewhere at 10 percent. If you do, after three years it will grow to:

\$335 X (1 + r)t = \$335 X 1.13 = \$335 X 1.331 = \$445.89

Because the proposed investment only pays out \$400, it is not as good as other alternatives we have. Another way of seeing the same thing is to notice that the present value of \$400 in three years at 10 percent is:

CHAPTER 5 Introduction to Valuation: The Time Value of Money 143

\$400 X [1/(1 + r)t] = \$400/1.13 = \$400/1.331 = \$300.53

This tells us that we only have to invest about \$300 to get \$400 in three years, not \$335. We will return to this type of analysis later on.

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