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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

CHAPTER 5 Introduction to Valuation: The Time Value of Money

Your \$325 original principal earns \$325 x .14 = \$45.50 in interest each year, for a two-year total of \$91 in simple interest. The remaining \$97.37 - 91 = \$6.37 results from compounding. You can check this by noting that the interest earned in the first year is \$45.50. The interest on interest earned in the second year thus amounts to \$45.50 x .14 = \$6.37, as we calculated.

We now take a closer look at how we calculated the \$121 future value. We multiplied \$110 by 1.1 to get \$121. The \$110, however, was \$100 also multiplied by 1.1. In other words:

= (\$100 X 1.1) X 1.1 = \$100 X (1.1 X 1.1) = \$100 X 1.12 = \$100 X 1.21

At the risk of belaboring the obvious, let's ask: How much would our \$100 grow to after three years? Once again, in two years, we'll be investing \$121 for one period at 10 percent. We'll end up with \$1.10 for every dollar we invest, or \$121 X 1.1 = \$133.10 total. This \$133.10 is thus:

= (\$110 X 1.1) X 1.1 = (\$100 X 1.1) X 1.1 X 1.1 = \$100 X (1.1 X 1.1 X 1.1) = \$100 X 1.13 = \$100 X 1.331

You're probably noticing a pattern to these calculations, so we can now go ahead and state the general result. As our examples suggest, the future value of \$1 invested for t periods at a rate of r per period is:

simple interest

Interest earned only on the original principal amount invested.

For a discussion of time value concepts (and lots more) see www.financeprofessor.com..

The expression (1 + r)t is sometimes called the future value interest factor (or just future value factor) for \$1 invested at r percent for t periods and can be abbreviated as FVIF(r,i).

In our example, what would your \$100 be worth after five years? We can first compute the relevant future value factor as:

(1 + r)t = (1 + .10)5 = 1.15 = 1.6105 Your \$100 will thus grow to:

The growth of your \$100 each year is illustrated in Table 5.1. As shown, the interest earned in each year is equal to the beginning amount multiplied by the interest rate of 10 percent.

In Table 5.1, notice the total interest you earn is \$61.05. Over the five-year span of this investment, the simple interest is \$100 X .10 = \$10 per year, so you accumulate \$50 this way. The other \$11.05 is from compounding.

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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

PART THREE Valuation of Future Cash Flows

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