стр. 107 
8.12
B
A C
Investment (I) $20,000
$30,000 $50,000
Useful life 10 years 4 years 20 years
Annual cash savings $6,207 $7,725 $9,341
Rank the projects according to their attractiveness using the: ( a ) payback period; ( b ) IRR; and
( c ) NPV at 14 percent cost of capital.
228 CAPITAL BUDGETING (INCLUDING LEASING) [CHAP. 8
SOLUTlON
initial investment
Payback period
(4 =
increased revenue or savings
Project Payback Period Rank
$309000 4.833 years
= 2
A
$6,207
$20,000
B = 2.588 years 1
$7,725
C $50,000 5.353 years
= 3
$9,341
(6) The IRR ranking is:
Closed RateвЂ™ Rank
Project
3
A 16%
B 20% 1
18% 2
C
вЂњPV=I
Cash inflow X PVIFA = I
I
PVIFA =
Cash inflow
$30,000

For A: PVIFA,,lo = $6,207  4.8333
PVIFA,,4 =  2.589 
For B: $20s000
$7,725
$50,000

PVIFA,20 =
For C: = 5.3527
$9,341
NPV at 14 percent is:
(c)
NPV
h U d
( P V  I)
I
Project PV Factor Total PV Ranlr
Savings
$6,207 5.2161
A $30,000 $ 2,376 3
$32,376
B $7,725 2.9137 $22,508 $20,000 $ 2,508 2
$61,866
C $11,866
$9,341 6.6231 $50,000 1
Capital Rationing. Rand Corporation is considering five different investment opportunities.
8.13
The companyвЂ™s cost of capital is 12 percent. Data on these opportunities under consideration
are given below.
Profitability Index
IRR (%)
Project Investment ($) PV at 12%($) NPV ($) (Rounded)
1 35,000 39,325 4,325 16 1.12
2 20,000 22,930 1.15
2,930 15
27,453
3 25,000 2,453 14 1.10
4 10,Ooo 10,854 854 18 1.09
9,000
5 8,749 11 0.97
(251)
229
CHAP. 81 CAPITAL BUDGETING (INCLUDING LEASING)
Based on these data: (a) rank these five projects in the descending order of preference,
according to NPV, IRR,and profitability index (or benefitkost ratio). (b) Which ranking would
you prefer? ( c ) Based on your answer to part (b), which projects would you select if $55,000 is
the limit to be spent?
SOLUTION
Order of Preference
(4
Profitability
IRR Index
NPV
Project
2 2
1 1
3 1
2 2
3 3
4
3
1 4
4
4
5
5 5
5
(b) The profitability index approach is generally considered the most dependable method of ranking
projects competing for limited funds. It is an index of relative attractiveness,measured in terms of how
much is returned for each dollar invested.
( c ) Based on the answer in part (b), choose projects (2) and (l), for which the combined NPV would be
$7,255 ($2,930 + $4,325) with the limited budget of $55,OOO.
8 1 Capital Rationing and Mathematical Programming. Express the capital rationing problem
.4
given in Problem 8.13 as a mathematical programming problem.
SOLUTION
Labeling project (1) as X I ,project (2) as X,, so on, the problem can be stated as follows:
and
Maximize
NPV = $4,325X, + $2,93OX2 + $2,453X, + $854X4  $251X5
subject to
$35,000X1+ $20,000X2+ $25,000X3+ $10,000X4+ $9,000X55 $55,000
Xi = 0,1 (i = 1,2, . . 5 )
стр. 107 