стр. 96 
The advantages of the NPV method are that it obviously recognizes the time value of money and
it is easy to compute whether the cash flows form an annuity or vary from period to period.
205
CAPITAL BUDGETING (INCLUDING LEASING)
CHAP. 81
Internal Rate of Return
Internal rate of return (IRR) is defined as the rate of interest that equates I with the PV of future
cash inflows. In other words, at IRR,
I = PV
or
NPV = 0
Decision rule: Accept the project if the IRR exceeds the cost of capital. Otherwise, reject it.
EXAMPLE 8.9 Assume the same data given in Example 8.8, and set the following equality (I = PV):
$12,950 = $3,000 X PVIFA
which stands somewhere between 18 percent and 20 percent in the 10year line of Appendix D. The interpolation
follows:
PV Factor
18% 4.494 4.494
IRR 4.317

4.192
20%
0.302
Difference 0.177

Therefore,
0.177
IRR = 18% +(20%  18%)
0.302
= 18% + 0.586(2%) = 18%+ 1.17% = 19.17%
Since the IRR of the investment is greater than the cost of capital (12 percent), accept the project.
The advantage of using the IRR method is that it does consider the time value of money and,
therefore, is more exact and realistic than the ARR method.
The shortcomings of this method are that (1)it is timeconsuming to compute, especially when the
cash inflows are not even, although most business calculators have a program to calculate IRR, and (2)
it fails to recognize the varying sizes of investment in competing projects and their respective dollar
profitabilities.
When cash inflows are not even, IRR is computed by the trialanderror method, as follows:
1. Compute NPV at cost o capital, denoted here as tl .
f
2. See if NPV is positive or negative.
3. If NPV is positive, then pick another rate (r2) much higher than rl. If NPV is negative, then pick
another rate ( r 2 )much smaller than tl .'The true IRR, at which NPV = 0, must lie somewhere
in between these two rates.
4 Compute NPV using r2.
.
5. Interpolate to get the exact rate.
206 CAPITAL BUDGETING (INCLUDING LEASING) [CHAP. 8
EXAMPLE 8.10 Consider the following investment whose cash flows are different from year to year:
AfterTax Cash M o w s ($)
Year
1 1,OOo
2 2,500
1,500
3
Assume that the amount of initial investment is $3,000 and the cost of capital is 14 percent.
1. NPV at 14 percent:
Total PV
Cash M o w ($)
Year PV Factor at 14% ($ Rounded)
1 1,000 0.8772 877
2,500 0.7695 1,924
2

1,500 0.6750
3 1,013

3,814
Therefore,
NPV = $3,814  $3,000 = $814
2. We see that NPV = $813 is positive at rl 14%.
=
3. Pick, say, 30 percent to play safe as r2.
4. Computing NPV at rz = 30%:
Total PV
Cash M o w ($)
Year PV Factor at 30% ($ Rounded)
1 1,000 0.7694 769
2,500 0.5921 1,480
2

1,500 0.4558 684
3

2,933
Therefore,
= $2,933  $3,000 = $67
NPV
5. Interpolate:
NPV
$814
14% $814
0
IRR
 (67)
30y
o
 $881
$814
Difference 
Therefore,
$814
14% + (30%  14%)
IRR =
$881
= 14% + 0.924(16%) = 14% + 14.78% = 28.78%
207
CAPITAL BUDGETING (INCLUDING LEASING)
CHAP. 81
Profitability Index (BenefitlCost Ratio)
The profitability index is the ratio of the total PV of future cash inflows to the initial investment,
that is, PV/I. This index is used as a means of ranking projects in descending order of attractiveness. If
the profitability index is greater than 1,then accept the project.
Decision rule: If the profitability index is greater than 1,then accept the project.
EXAMPLE 8.11 Using the data in Example 8.8, the profitability index is
PV $16,950
стр. 96 