978-0073523439 Chapter 12 Part 2

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.

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.

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, $

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)