Row 3 shows the cash flows. In this case, there is only one cash flow, shown in Cell
B3. Row 4 shows the future value of this cash flow at the end of each year. Cell C4
contains the formula for Equation 2-1. The formula could be written as $B$3*
(1.05)^C2,but we wrote it as $B$3*(1$B$1)ˆC2,which gives us the flexibil-
ity to change the interest rate in Cell B1 to see how the future value changes with
changes in interest rates. Note that the formula has a minus sign for the PV (which is
in Cell B3) to account for the minus sign of the cash flow. This formula was then
copied into Cells D4 through G4. As Cell G4 shows, the value of $100 compounded
for five years at 5 percent per year is $127.63.
You could also find the FV by putting the cursor on Cell G4, then clicking the
function wizard, then Financial, then scrolling down to FV, and then clicking OK to
bring up the FV dialog box. Then enter B1 or .05 for Rate, G2 or 5 for Nper, 0 or
leave blank for Pmt because there are no periodic payments, B3 or 100 for Pv, and
0 or leave blank for Type to indicate that payments occur at the end of the period.
Then, when you click OK, you get the future value, $127.63.
Note that the dialog box prompts you to fill in the arguments in an equation.
The equation itself, in Excel format, is FV(Rate,Nper,Pmt,Pv,Type)
FV(.05,5,0,100,0). Rather than insert numbers, you could input cell references
for Rate, Nper, Pmt, and Pv. Either way, whenExcelsees the equation, it knows
to use our Equation 2-2 to fill in the specified arguments, and to deposit the re-
sult in the cell where the cursor was located when you began the process. If
someone really knows what they are doing and has memorized the formula, they
can skip both the time line and the function wizard and just insert data into the
formula to get the answer. But until you become an expert, we recommend that
you use time lines to visualize the problem and the function wizard to complete
the formula.
Comparing the Three Procedures
The first step in solving any time value problem is to understand the verbal descrip-
tion of the problem well enough to diagram it on a time line. Woody Allen said that 90
percent of success is just showing up. With time value problems, 90 percent of success
is correctly setting up the time line.
After you diagram the problem on a time line, your next step is to pick an approach
to solve the problem. Which of the three approaches should you use—numerical, fi-
nancial calculator, or spreadsheet? In general, you should use the easiest approach. But
which is easiest? The answer depends on the particular situation.
All business students should know Equation 2-1 by heart and should also know
how to use a financial calculator. So, for simple problems such as finding the future
value of a single payment, it is probably easiest and quickest to use either the numeri-
cal approach or a financial calculator.
For problems with more than a couple of cash flows, the numerical approach is
usually too time consuming, so here either the calculator or spreadsheet ap-
proaches would generally be used. Calculators are portable and quick to set up,
but if many calculations of the same type must be done, or if you want to see how
changes in an input such as the interest rate affect the future value, the spread-
sheet approach is generally more efficient. If the problem has many irregular cash
flows, or if you want to analyze many scenarios with different cash flows, then the
spreadsheet approach is definitely the most efficient. The important thing is that
you understand the various approaches well enough to make a rational choice,
given the nature of the problem and the equipment you have available. In any
event, you must understand the concepts behind the calculations and know how to
set up time lines in order to work complex problems. This is true for stock and
Future Value 61
Time Value of Money 59
