Introduction to Corporate Finance

3: The Time Value of Money

In practice, when analysts solve problems like these, they don’t solve for the future value algebraically.

Instead, they use a financial calculator or a spreadsheet program such as Excel to do the calculations.

Figure 3.1 illustrates how to solve the previous example using a financial calculator and Excel. With a

calculator, you enter the value –$100 and press the PV key. Next, enter the number of periods, 5, and

press the N key. Then enter the interest rate, 6, and press the I key. Now you are ready to calculate the

answer. Instruct the calculator to compute (press CPT) the future value (press FV), and you will have

the same answer we reached before, $133.82.

If you are using Excel rather than a calculator to solve this problem, you will make use of the FV

(future value) function. The format of that function is = fv(rate,nper,pmt,pv,type). In this function, the

symbols ‘pmt’ and ‘type’ refer to inputs that you need when solving problems involving multiple cash flows

over time. Because the problem you are solving involves a single, up-front investment, you can enter

the value zero for both ‘pmt’ and ‘type’. The only other inputs required are the interest rate, the number

of periods and the present value (that is, the initial investment). Therefore, in Excel, you could type =

fv(0.06,5,0,-100,0), and when you enter this formula, Excel will produce the answer you seek, $133.82.

Notice that, whether you use a financial calculator or Excel, you enter the initial $100 investment

as a negative number. You can interpret this as taking money out of your wallet or pay cheque to put it

into the bank savings account. Five years later, you receive the future value, $133.82, which appears as

a positive number.

Suppose the interest rate on a bank savings account
is only 2%, one-third of the rate in our earlier
example. How much money will be in the account in
five years, and how much growth does that represent
on the initial investment?
By using a spreadsheet or a financial calculator
to solve Equation 3.1 using the inputs given here, we
can quickly determine that the future value of a $100
investment for five years is $110.41.

Eq. 3.1 FV = $100 × (1 + 0.02)^5 = $110.41

In this case, the investment grew by $10.41.

Notice that, while the interest rate used in this

calculation was one-third of the rate we used

before (2% rather than 6%), the growth in the

account’s value was less than one-third of what it

was before ($10.41 versus $33.82). This is the effect

of compound interest. When the interest rate on an

investment increases, the value of the investment

rises at an increasing rate; and a reduction of the

interest rate will still see the value of the investment

grow, but at a decreasing rate.

example

3-2c A GRAPHIC VIEW OF FUTURE VALUE

Remember that we measure future value at the end of the given period. Figure 3.2 shows how quickly

a $1.00 investment grows over time at various annual interest rates. The figure shows that: (1) the higher

the interest rate, the higher the future value; and (2) the longer the period of time, the higher the future

value. Note that for an interest rate of 0%, the future value always equals the present value ($1), but for

any interest rate greater than zero, the future value is greater than $1.