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Copyright © 2018 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
12
Linear Programming and Capital Budgeting
12.22 To develop the 0-1 ILP formulation, first calculate PWE, since it was not included
in Table 12-2. All amounts are in $1000 units.
The linear programming formulation is:
(a) For b = $20 million: The spreadsheet solution uses the template in Figure 12-5.
Copyright © 2018 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
13
(b) b = $13 million: Reset the budget constraint to b = $13,000 in Solver and obtain a
12.23 Use the Figure 12-5 template at 8% with an investment limit of $4 million.
12.24 Enter the NCF values from Problem 12.21 into the capital budgeting template and a
constraint of b = $3,000,000 into Solver. Select projects 1 and 2 for Z = $199,496 with all
$3 million invested.
12.25 Linear programming model: In $1000 units,
Spreadsheet solution: Enter all estimates on a spreadsheet with a b = $1600 constraint
in Solver to obtain the answer:
12.26 Build a spreadsheet and use Solver repeatedly at increasing values of b to find the
vendor combinations that maximize the value of Z; then develop a scatter graph.
Other Ranking Measures
12.27 (a) IROR: 0 = -750,000 + 135,000(P/A,i*,10)
(b) By all three measures, since IROR > 12%; PI > 1.0 and PW > 0 at MARR = 12%
12.28 (a) Select projects A, B and C with a total $55,000 investment.
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written consent of McGraw-Hill Education.
16
12.29 IROR:
0 = -400,000 + (192,000 – 75,000)(P/A,i*,5) + 80,000(P/F,i*,5)
i* = 18.09%
PI:
PW of NCF = (192,000 – 75,000)(P/A,12%,5) + 400,000(0.20)(P/F,12%,5)
= (192,000 – 75,000)(3.6048) + 80,000(0.5674)
= $467,154
PW of first cost = -400,000
PI = 467,154/400,000
= 1.17
12.30 (a) PI1 = 900,000(P/A,10%,7)/4,000,000
PI4 = 3,600,000(P/A,10%,10)/15,000,000
PI5 = 5,000,000(P/A,10%,8)/30,000,000
Projects in PI order 2 4 3 1
12.31 By hand:
(a) Find IROR for each project, rank by decreasing IROR and then select projects
within the budget constraint of $120,000.
For X: 0 = -30,000 + 9000(P/A,i*,10)
i* = 21.4%
Projects in IROR order Y X A B Z
(b) Overall ROR = [15,000(30.4%) + 30,000(27.3%) + 70,000(24.0%)
By spreadsheet:
(a) Select projects Y, X, and A with a total investment of $115,000 (column G)
12.32 (a) By hand: Find IROR for each project; select highest ones within budget
constraint of $100 million.
i* = 6.5%
By spreadsheet: Select Y and W after ranking (row 12); invest $57 million
(b) Find i* of Y and W
(c) The $43 million not committed makes MARR = 12% elsewhere.
PIB = 2800(P/A,10%,10)/15,000
Rank order by PI C A D B
Select projects C, A, and D; invest $113,000. E is eliminated with PI < 1.0
(b) Rank order by IROR C A D B
Select C, A, and D; invest a total of $113,000. E is eliminated with IROR < 10%
12.34 The IROR, PI, and PW values are shown in the table below. Sample calculations for
project F are:
Projects G and K can be eliminated since their IROR, PI and PW are not acceptable.
First Annual Income,
Project Cost, $ $ per year IROR, % PI PW, $
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written consent of McGraw-Hill Education.
20
J -50,000 26,000 52.0 2.08 54,000
K -9000 2,100 23.3 0.93 -600
(a) b = $700,000
(1) IROR: Projects selected are I, J, and H with $670,000 invested
IROR rank I J H F
(2) PI: Projects selected are I, J, and H with $670,000 invested
PI rank I J H F
(3) PW: Projects selected are I, H and J with $670,000 invested
PW rank I H J F
(b) b = $600,000
(Note: The PW-based selection is different for the reduced budget of $600,000)
Additional Problems and FE Exam Review Problems
12.35 Answer is (c)
12.36 Answer is (d)
Answer is (b)
12.41 There are 24 = 16 possible bundles. Considering the selection restriction and the
$400,000 limitation, the viable bundles are:
12.42 Answer is (a)
