Introduction to Finance

529
Financial calculators can compute NPV. For example, for project A, we can enter the 
following:
For HP 10 B II Financial Calculator:
–20,000 CF
j
5800 CF
j
5800 CF
j
5800 CF
j
5800 CF
j
5800 CF
j
10
i
(interest rate key)
Pushing the NPV key next, we have an exact answer for the NPV: $1,986.56.
For the TI BA II Plus Financial Calculator, we do the following calculations:
To
Press
Display
Select Cash Flow worksheet. 
CF
CFo = 0.00
Enter initial cash flow. 
20000 +/– 
ENTER
CFo = –20,000
Enter cash flow for first year.
↓ 
5800 
ENTER
C01 = 5,800
↓
F01 = 1.00
Enter cash flows for the second year
↓ 
5800 
ENTER
C01 = 5,800
↓
F01 = 1.00
Enter cash flows for the third year
↓ 
5800 
ENTER
C01 = 5,800
↓
F01 = 1.00
Enter cash flows for the fourth year
↓ 
5800 
ENTER
C01 = 5,800
↓
F01 = 1.00
Enter cash flows for the fifth year
↓ 
5800 
ENTER
C01 = 5,800
↓
F01 = 1.00
Computing NPV
To
Press
Display
Prepare to compute NPV
NPV
I = 0.00
Enter interest rate per period
10 ENTER
I = 10.00
Compute NPV
↓ CPT
NPV = 1,986.56
Doing this calculation for project B, we fi nd its NPV is $992.01.
A shortcut method can be used to calculate the NPV for project A. Since the cash infl ows 
form an annuity, we could have used the present value interest factor of an annuity (PVIFA) 
at 10 percent for fi ve years from Table 4 in the Appendix, which is 3.791. The NPV can be 
calculated, as follows:
$5,800 × 3.791 = $21,988 PV cash infl ows
– 20,000 Initial outlay
$1,988 Net present value
The $1,988 NPV fi gure using PVIFA diff ers slightly from the $1,982 using PVIF because 
of rounding the PVIFs in the Appendix tables. When cash infl ows are not in the form of an 
annuity, as in the case of project B, the longer calculation process shown in Table 17.3 must 
be used to fi nd the net present value.

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530
C H A PT E R 1 7 Capital Budgeting Analysis
Projects with negative NPVs are unacceptable to a fi rm. They provide returns lower than 
the cost of capital and would cause the fi rm’s value to fall. In our example, projects A and 
B have positive NPVs and are acceptable. If they are mutually exclusive projects, managers 
should chose project A as its NPV of $1,986.56 is higher than project B’s NPV of $992.01. 
Clearly, the fi nancial manager must make capital budgeting decisions on the basis of their 
expected impact on the fi rm’s value.
Using Spreadsheet Functions 
In addition to multiplying with factors found in a PV table or using a fi nancial calculator, elec-
tronic spreadsheet packages, such as Excel, make the task of computing a NPV simple, too. Sup-
pose we have the cash fl ows for project A in column B, rows 2 through 7 of an Excel spreadsheet:
To compute the NPV, we can use Excel’s NPV function, with modifi cation. We need to modify 
its use because Excel’s NPV does not calculate NPV as we do in this chapter. Excel’s NPV 
function computes the sum of PVs assuming the value in the fi rst cell listed is to be discounted 
back one period, the value in the second cell is to be discounted back two periods, and so on. 
But most capital budgeting problems have a “time zero,” or “current,” investment that is not 
discounted; in our example, the investment of $20,000 at time zero is expressed in PV terms.
To get around this problem, we use Excel’s NPV function to fi nd the sum of the PVs in peri-
ods one through the end of the project (cells B3 through B7 in our case) and then add the initial 
negative investment cash outfl ow of $20,000 in cell B2. In the above example, in cell B8, we typed 
= NPV (10%, B3:B7) + B2, and the spreadsheet computes an exact value of the NPV: $1,986.56.
The NPV function has the following form: 
= NPV (discount rate, cell of time one cash fl ow : cell of last cash fl ow)
The discount rate can be typed as a percentage (10%) or as a decimal equivalent (0.1). If you 
type in the “%” symbol, Excel assumes the number is a percentage; otherwise, the decimal 
equivalent is assumed. Be careful: if you key in “10” rather than “10%,” the spreadsheet will 
use a discount rate of 1000%.
17.4
Capital Budgeting Techniques—
Internal Rate of Return
We know from our discussion of bonds in Chapter 10 that an inverse relationship, or “seesaw 
eff ect,” exists between bond prices and interest rates. As investors’ required rates of return rise, 
bond prices fall; as investors’ required rates of return fall, bond prices rise. A similar relationship 
exists between NPV and a fi rm’s required rate of return, or a project’s cost of capital. For a given 
set of cash fl ows, a higher cost of capital will lead to a lower NPV; a lower cost of capital, however, 
will increase a project’s NPV.