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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