Engineering Economy, 8th edition
Leland Blank and Anthony Tarquin
Chapter 12
Independent Projects with Budget Limitation
Capital Rationing and Independent Projects
12.1 1. Several independent projects are identified with cash flow estimates for each
12.4 DN, A, B, C, AB, AC, BC, ABC
12.5 There are a total of 26 = 64 possible bundles; only 9 are within budget constraint of
12.6 (a) Acceptable (b) Non-acceptable
DN 2
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1,2,3,4
12.7 Acceptable: Non–acceptable
DN 2
1 1,5
3 1,2
Selecting Independent Projects using PW Analysis
12.8 (a) Select the bundle with the largest positive PW value that does not violate the budget
12.9 Eliminate projects 1 and 4, since PW < 0
12.10 (a) By hand
Sample calculations of PW for bundles
PWA = -25,000 + 6000(P/A,15%,4) + 4000(P/F,15%,4)
= $–10,460
Bundle Proposals PW at 15%, $
(b) By spreadsheet: Select bundle 4 (Project C) with the only PW > 0
12.11 (a) By hand:
PWS2 = –400 + (450 – 200)(P/A,20%,5)
(b) By spreadsheet:
$800,000 limit: Select product lines R1 and S2 with PW = $446,714 (column G)
12.12 Develop bundles with less than $240,000 investment; select the one with the
largest PW.
Bundle Projects Investment, $ NCF, $/Year PW, $
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4 E -220,000 39,000 -11,939
5 F -200,000 82,000 237,462
6 AB -225,000 74,000 169,784
7 AC -220,000 125,000 446,864
8 DN 0 0 0
PW1 = –100,000 + 50,000(P/A,10%,8)
= $166,746
PW2 = –125,000 + 24,000(P/A,10%,8)
PW3 = -120,000 + 75,000(P/A,10%,8)
PW4 = –220,000 + 39,000(P/A,10%,8)
PW5 = –200,000 + 82,000(P/A,10%,8)
All other PW values are obtained by adding the respective PW for bundles 1
12.13 (a) Budget = $800,000 i = 10% 6 viable bundles
Bundle Projects NCFj0, $ NCFjt, $ SV, $ PW at 10%, $
1 X -250,000 50,000 45,000 -60,770
PWj = NCFj(P/A,10%,4) + S(P/F,10%,4) – NCFj0
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(b) Set PW3 = 0 and determine NCF3
PW3 = 0 = NCF3(P/A,10%,4) + 100,000(P/F,10%,4) – 550,000
0 = NCF3(3.1699) + 100,000(0.6830) – 550,000
NCF3 = $151,961
(cell E7)
12.15 By hand: Determine the PW for each project
PWA = -1,500,000 + 360,000(P/A,10%,8) = $420,564
By spreadsheet: Enter the following to display the project PW value.
A: = -PV(10%,8,360000)-1500000 Display: $420,573
Formulate acceptable bundles from the 24 = 16 possibilities, without both B and C,
(a) With b = $4 million, select projects A and C with PW = $970,860.
Investment PW, $
Bundle $ million (by hand)
A,C -3.3 970,860
(b) With b = $5.5 million, select projects A and B with PW = $1,107,324
Investment
Bundle $ Million PW, $
DN 0 0
12.16 (a) b = $710,000 i = 10% nj = 4 or 6 years 5 viable bundles
Bundle, j Projects NCFj0, $ NCFjt, $ S, $ PW, $
1 Do nothing 0 0 0 0
(b) Develop the spreadsheet so that the annual NCF values can be adjusted using Goal
Seek. Functions are shown below.
Repeatedly apply Goal Seek to find NCF values that force the PW values to equal
that of bundle 4, namely PW3 = $119,736, per the spreadsheet PW value for bundle
3. The spreadsheet for bundle 1 (project A) is shown below. NCF values for all
NCFAB = $169,039 compared to the estimated $140,000
12.17 (a) For b = $25,000 only 4 bundles of the 32 possibilities are viable.
Bundle Projects Investment, $ PW at 12%, $
Select projects S and M with PW = $11,540 and $25,000 invested.
(b) With b = $49,000, 5 additional bundles are viable.
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8 AM -36,000 15,100
9 ME -35,000 3,010
Select projects S and A with PW = $20,640 and $41,000 invested.
(c) Select all projects since they each have PW > 0 at 12% per year.
12.18 (a) By hand: The bundles and PW values are determined at MARR = 8% per year.
Initial NCF, Life, PW at
Bundle Projects Investment, $M $ per year years 8%, $__
360,000 6-8
12.18 (cont.)
Initial NCF, Life, PW at
(b) By spreadsheet: Set up a spreadsheet for all 8 bundles. Bundle 8 is DN with
PW = 0. Select projects 1 and 4 with the largest PW = $1,284,734
and invest $3.5 million.
12.19 Budget limit b = $15,000 MARR = 12% per year
NCF for PW at
12.20 (a) Spreadsheet solution for Problem 12.19 as stated. Projects 1 and 3 are selected with
PW = $3893 with $14,000 invested.
(b) Spreadsheet solution for 14 viable bundles (6 additional) indicates selection of
bundle 14 (projects 1, 3, and 4) with PW = $4697 and $24,000 invested.
12.21 (a) Spreadsheet shows the solution. Select projects 1 and 2 for an investment of $3.0
million and PW = $199,496.