Introduction to Finance

Financial Calculator Solution:
Inputs: 10 
8 
1000
N 
%i 
FV
Press: CPT PV
Solution: 463.19
Excel
 
or another spreadsheet program also can be used to fi nd present values. For a simple 
present value problem, we show the calculation by hand in spreadsheet format, as well as 
using the preprogrammed PV fi nancial function. What would be the present value of receiving 
$1,000 two years from now if the annual discount rate is 8 percent?
Spreadsheet Solution:
When making the calculation by hand, we enter 0.08 as the interest rate in Cell B1, then 
the time periods beginning with 0 in Cell B2 and so forth, and a cash fl ow of 1000 in Cell 
D3. In Cell C4 we insert the equation = D3/(1 + B1)^1 and get $925.93. Then, in Cell B4 we 
enter the equation = C4/(1 + B1)^1, with the result being $857.34. Of course, we could have 
solved for the present value in one step by entering in Cell B4 the equation = D3/(1 + B1)^2 
and found 857.34 directly.
The bottom portion of the spreadsheet solution example illustrates the use of the Excel’s
 
fi nancial function called present value (PV). In order to get a positive PV value, we enter 
–1000 as the cash fl ow in time period 2. Click on the Excel fi nancial wizard (
fx
) icon, then 
Financial, then PV, and then OK to bring up the dialogue box where the PV components 
for the problem at hand are requested. The equation is PV(Rate, Nper, Pmt, FV, Type). The 
Rate is 0.08; Nper is the number of time periods, or two in this example; Pmt is zero, since 
there are no periodic payments; FV is –1000; and Type is 0, refl ecting that payments occur at 
the end of the period. This equates to PV(0.08,2,0,–1000,0). Pressing OK results in a PV of 
$857.34, or $857 rounded. Because the PV function in Excel
 
is programmed to give a negative 
number when there is a positive future value, much like the PV solutions on most calculators, 
we entered the FV as a negative number to get a positive PV. Of course, rather than inserting 
numbers, one could insert specifi c cell references in the PV function. 
If the investment had been discounted for ten years, the PV function inputs would have been 
PV(0.08,10,0,–1000,0). Pressing OK would result in an answer of $463.19, or $463 rounded.
In addition, tables have been prepared to simplify the calculation eff ort if fi nancial calcu-
lators or computer programs are not available. Equation 9.3 can be rewritten as,
PV = FV
n
(PVIF
r
,
n
) (9.4)
where the 1 ÷ (1 + 
r
)
n