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Solutions to end-of-chapter problems
Engineering Economy, 8th edition
Leland Blank and Anthony Tarquin
Chapter 8
Rate of Return Analysis: Multiple Alternatives
Understanding Incremental ROR
8.1 Alternative B is preferred if the rate of return on the increment of investment
8.3 The rate of return on the increment is less than 0%.
8.4 By switching the position of the two cash flows, the interpretation changes completely. The
8.5 The company should select the lower cost infrared model because the rate of return on the
8.8 Overall ROR = [30,000(0.20) + 70,000(0.14)]/100,000
8.10 (a) 40,000(0.14) + (200,000 – 40,000)(i*Z1) = 200,000(0.26)
8.11 200,000(0.28) + 100,000(0.42) + 400,000(0.19) = 700,000(x)
8.13 (a) Incremental investment analysis is not required. Alternative X should be selected
because the rate of return on the increment is known to be lower than 20%
8.14 (a) Incremental CF, year 0: -25,000 – (-15,000) = $-10,000
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8.15 Year System X, $ System Z, $ (Z – X), $
0 -40,000 -95,000 -55,000
8.16 (a) - First costP - (-30,000) = -53,000
(b) -11,000 – (-M&OA) = 21,000
(c) ResaleP – 4000 = 8000
8.17 The incremental cash flow equation is 0 = -65,000 + x(P/A,25%,4), where x is
the difference in the AOC.
Incremental ROR Comparison (Two Alternatives)
8.18 Solve for ∆i* by trial and error or spreadsheet
8.19 (a) Find rate of return on incremental cash flow
(b) Incremental ROR is less than MARR; select Ford Explorer
8.20 0 = - (2,300,000 – 1,200,000) + {[(360,000 + 56,000 -125,000] – [(270,000 –
From interest tables, ∆i* is between 2 and 3%
8.21 Write ROR equation for increment between B and A
Solve for ∆i* by interpolation or spreadsheet
8.22 Write PW-based incremental ROR equation using CFVS – CFDS
8.23 By hand, in $1000 units
(a) X vs. DN: i*X: 0 = -84 + (96 - 31)(P/A,i*X,3) + 40(P/F, i*X,3)
i*X = 67.9%
(b) Incremental CF amounts for (Y-X)
Incremental first cost = $-62,000
(c) Incremental ROR is the correct basis; selecting robot X in part (a) is incorrect
By spreadsheet
8.24 (a) 0 = -10,000 + 1200(P/A,∆i*,4) + 12,000(P/F,∆i*,2) + 1000(P/F,∆i*,4)
(b) If n105 = 4 years, the incremental ROR equation changes to
8.25 (a) 0 = -17,000 + 400(P/A,∆i*,6) + 17,000(P/F,∆i*,3) + 1700(P/F,∆i*,6)
Solve for ∆i* by trial and error or spreadsheet
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of McGraw-Hill Education.
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∆i* = 6.84% < MARR = 10%
Select alternative P
(b) AWP = -18,000(A/P,10%,3) - 4000 + 1000(A/F,10%,3)
Select P, though neither option makes MARR = 10%
8.26 Revenue projects; determine i* first. Monetary units are in $1000
8.27 By hand: Let x = M & O costs. Perform an incremental cash flow analysis.
0 = -75,000 + (-x + 50,000)(P/A,20%,5) + 20,000(P/F,20%,5)
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of McGraw-Hill Education.
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8.28 (a) Breakeven ROR is the ∆i* for a perpetual investment
8.29 Sample further information items to request before saying ‘yes”:
• What about multiple ∆i* values?
Multiple Alternative ( > 2) Comparison
8.30 Select the one with the lowest initial investment cost because none of the
8.31 (a) A vs DN: 0 = -30,000(A/P,i*,8) + 4000 + 1000(A/F,i*,8)
Solve for i* by trial and error or spreadsheet
(b) Revenue alternatives; compare to DN initially
A vs DN: 0 = -30,000(A/P,i*,8) + 4000 + 1000(A/F,i*,8)
Solve for i* by trial and error or spreadsheet
8.32 Rank cost alternatives by increasing initial investment: 1, 3, 4, 2
8.33 These are revenue alternatives; add DN
(a) 8 vs. DN: 0 = -30,000(A/P,i*,5) + (26,500 – 14,000) + 2000(A/F,i*,5)
10 vs. 8: 0 = -4000(A/P,∆i*,5) + (14,500 – 12,500) + 500(A/F,∆i*,5)
8.34 (a) Select all proposals with overall ROR ≥ 17%
(b) Compare alternatives incrementally after ranking: DN, A, B, C, D
A to DN: ∆i* = 11.7% < 14.5% Eliminate A
(c) Compare alternatives incrementally after ranking: DN, A, B, C, D
8.35 (a) Select all projects whose ROR ≥ MARR of 15%. Select A, B, and C
(b) Eliminate all alternatives with ROR < MARR; compare others incrementally:
8.36 Proposals are independent; compare each against DN only
Product 1: 0 = -340,000 + (180,000 – 70,000)(P/A,i*,5)
8.37 (a) Proposals are independent; Select A and C
8.38 (a) Initial cost, Machine 1: - 60,000 - (-16,000) = $-44,000
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of McGraw-Hill Education.
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Incremental ROR 4 vs. 3: 0 = -26,000 + 5000(P/A,∆i*,10); ∆i*= 14.08%
(b) Machines are ranked according to initial investment: 1, 2, 3, 4; MARR = 18%
Compare 1 to DN: i* = 18.6% > MARR eliminate DN
8.39 (a) Find ROR for each increment of investment using the general relation
where II = incremental investment
(b) Revenue = A = Pi
E: A = 20,000(0.20) = $4000
(c) Conduct incremental analysis using results from part (a) with MARR = 16%
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Therefore, select Alternative F
(d) Conduct incremental analysis using results from part (a) with MARR = 11%
(e) Conduct incremental analysis using results from part (a) with MARR = 19%
E vs DN: i* = 20% > MARR, eliminate DN
Select F as first alternative; compare remaining alternatives incrementally.
Therefore, select alternatives F and G
Spreadsheet Exercises
(b) Ranking inconsistency is present. Based on AW analysis over 6 years, select Model 400
8.41 (a) Determine if methods are economically justified. From row 14,
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of McGraw-Hill Education.
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i*B = 6.25% > MARR = 5%; justified
i*I = 4.52% < MARR = 5%, not justified
Incremental ROR is not needed; select method B
(b) Neither method is justified at MARR = 8%. Since one of the methods must be installed,
8.42 (a) Graph of breakeven ROR is approximately 8.5% per year in both renditions.
(b) If MARR > approximately 8.5%, the lower-investment system A is selected.
8.43 (a) Select C and D with i* values exceeding MARR (rows 21 and 22).
8.44 (a) Spreadsheet analysis results in selection of 25 m3 truck bed size.
Additional Problems and FE Exam Review Questions
8.45 Answer is (b)
8.54 Rank alternatives in terms of increasing first cost: DN, A, B, C, D, E
Eliminate alternatives A and C because i* < MARR =15%
8.57 Rank Alternatives: C, A, B. D, E; perform incremental ROR analysis for n = ∞
Solution to Case Study 1, Chapter 8
Sometimes, there is not a definitive answer to a case study exercise. Here are example responses.
PEFORMING ROR ANALYSIS FOR 3D PRINTER AND IIoT TECHNOLOGY
1. PW at 12% is shown in row 29. Select server #2 (n = 8) with the largest PW value.
2. #1 (n = 3) is eliminated. It has i* < MARR = 12%. Perform an incremental analysis of #1 (n
3. PW at 2000% > $0.05. ∆i* is infinity, as shown in cell K45, where an error for IRR(K4:K44)
is indicated.
Some rows hidden
Solution to Case Study 2, Chapter 8
Sometimes, there is not a definitive answer to a case study exercise. Here are example responses.
HOW A NEW ENGINEERING GRADUATE CAN HELP HIS FATHER
1. Cash flows for each option are summarized at top of the spreadsheet. Rows 9-19 show annual
estimates for options in increasing order of initial investment: 3, 2, 1, 4, 5.
3. Do incremental ROR analysis after removing #1 and #2. See row 22. 4-to-3 comparison
4. PW vs. i charts for all 5 options are on the spreadsheet.
5. Force the breakeven rate of return between options #4
and #3 to be equal to MARR = 25%. Use trial and error
