Introduction to Corporate Finance

3: The Time Value of Money

arguments ‘pmt’ and ‘type’ still do not apply, so enter 0). For Excel to solve this problem, the values you

enter for present value and future value must have opposite signs (it doesn’t matter which is positive

and which is negative). Therefore, in Excel you could enter =nper(0.08,0,1000,-3000,0), and Excel

would provide the answer, 14.3 years. Alternatively, you could use a financial calculator, inputting the

keystrokes shown in Figure 3.5 to obtain the same answer.

Another common type of business problem requires analysts to determine the rate of return on a

particular investment or to calculate the rate of growth over time in a company’s sales or profits.

Google, Inc., became a public company when it
conducted an initial public offering (IPO) of ordinary
shares in August 2004. Originally priced at $85
per share, Google equity soared after the IPO. By
August 2011, Google shares stood at $600. What
annual rate of return did the investors who bought
Google shares at the IPO and held them until August
2011 earn? Once again, start with Equation 3.1

FV = PV × (1 + r)n

In this case we know FV = $600, PV = $85, and

n = 7 years. Plug those values into Equation 3.1 and

solve for r.

$600 = $85(1 +r)^7

$600 ÷ $85 = (1 + r)^7

($600 ÷ $85)(1 ÷ 7) = (1 + r)

1.322 = 1 + r

r = 0.322 = 32.2%

example

FIGURE 3.6 USING A CALCULATOR TO FIND RATE OF RETURN ON INVESTMENT

Formula B5: =RATE(B3,0,B1,B2,0,B4)

Interest rate 32.2%

Number of years 7

–$600

$85

Future value

Present value

Input

85

–600

7

PV

FV

N

CPT

I

Solution 32.2

Function

Row

Column

Calculator Spreadsheet

1 2 3 4 5 6

A B

Guess 10%

Google investors earned more than

32% per year in the company’s first seven

years. Figure 3.6 illustrates how to solve this

problem using a calculator or a spreadsheet.

The Excel function that solves this type of

problem is the ‘rate’ function, and its syntax is

=rate(nper,pmt,pv,fv,type, guess). All but one of

the arguments of this function should be familiar

by now. The new argument is ‘guess’, which is

not a value that is part of the problem, but rather

a numerical value that you provide just to ‘get

Excel started’ as it tries to find the solution. By

default, Excel assumes a value of ‘guess’ of 0.10

or 10%. You can leave that argument blank, or

enter any interest rate that you like – the value of

‘guess’ that you submit rarely has any impact on

the solution that Excel obtains. To find the rate of

return on Google’s equity in its first seven years,

you could type into Excel =rate(5,0,85,-600,0.10),

and Excel would give you 32.2% as the answer. You

could also solve the problem using the calculator

keystrokes shown in Figure 3.6.