128 Part 2 Fundamental Concepts in Financial Management

As noted in our example, you! rst enter the known values (N, I/YR, PMT, and

PV) and then press the FV key to get the answer, 115.76. Again, note that if you

enter the PV as 100 without a minus sign, the FV will be given as a negative. The

calculator assumes that either the PV or the FV is negative. This should not be con-

fusing if you think about what you are doing.

5-2d Spreadsheets^3

Students generally use calculators for homework and exam problems; but in busi-

ness, people generally use spreadsheets for problems that involve the time value

of money (TVM). Spreadsheets show in detail what is happening, and they help

reduce both conceptual and data-entry errors. The spreadsheet discussion can be

skipped without loss of continuity; but if you understand the basics of Excel and

have access to a computer, we recommend that you read through this section.

Even if you aren’t familiar with spreadsheets, the discussion will still give you an

idea of how they operate.

We used Excel to create Table 5-1, which summarizes the four methods of

! nding the FV and shows the spreadsheet formulas toward the bottom. Note that

spreadsheets can be used to do calculations; but they can also be used like a word

processor to create exhibits like Table 5-1, which includes text, drawings, and cal-

culations. The letters across the top designate columns, the numbers to the left

designate rows, and the rows and columns jointly designate cells. Thus, C14 is the

cell in which we specify the $$100 investment, C15 shows the interest rate, and

C16 shows the number of periods. We then created a time line on Rows 17 to 19;

and on Row 21, we have Excel go through the step-by-step calculations, multiply-

ing the beginning-of-year values by (1 # I) to! nd the compounded value at the

end of each period. Cell G21 shows the! nal result. Then on Row 23, we illustrate

the formula approach, using Excel to solve Equation 5-1, and! nd the FV, $115.76.

Next, on Rows 25 to 27, we show a picture of the calculator solution. Finally, on

Rows 29 and 30, we use Excel’s built-in FV function to! nd the answers given in

Cells G29 and G30. The G29 answer is based on! xed inputs, while the G30 an-

swer is based on cell references, which makes it easy to change inputs and see the

effects on the output.

Table 5-1 demonstrates that all four methods get the same result, but they use

different calculating procedures. It also shows that with Excel, all inputs are shown

(^3) If you have never worked with spreadsheets, you may choose to skip this section. However, you might want to
read through it and refer to this chapter’s Excel model to get an idea of how spreadsheets work.
N! Number of periods. Some calculators use n rather than N.
I/YR! Interest rate per period. Some calculators use i or I rather than I/YR.
PV! Present value. In our example, we begin by making a deposit, which is an
out" ow; so the PV should be entered with a negative sign. On most calcu-
lators, you must enter the 100, then press the #/$ key to switch from

100 to $100. If you enter $ 100 directly, 100 will be subtracted from the

last number in the calculator, giving you an incorrect answer.
PMT! Payment. This key is used when we have a series of equal, or constant,
payments. Because there are no such payments in our illustrative prob-
lem, we enter PMT! 0. We will use the PMT key when we discuss annui-
ties later in this chapter.
FV! Future value. In this example, the FV is positive because we entered the
PV as a negative number. If we had entered the 100 as a positive number,
the FV would have been negative.