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Solutions to end–of–chapter problems
Engineering Economy, 7th edition
Leland Blank and Anthony Tarquin
Chapter 7
Rate of Return Analysis: One Project
7.1 (a) The return would be -100%, if the entire initial investment were lost with no return.
7.2 Interest charged on principal:
Interest on principal = 1,000,000(3)(0.10) = $300,000
Interest charged on unrecovered balance:
Annual payment = 1,000,000(A/P,10%,3)
7.4 Amount of each payment = 50,000(A/P,10%,5)
Find i from equation, table, or spreadsheet
7.7 0 = -3.1 + (2)(0.2)(P/A,i,10)
7.8 0 = -108,000,000 + 59(160,000)(P/A,i%,20)
7.9 Hand:
0 = -3000 – 200(P/A,i,3)(P/F,i,1) – 90(P/A,i,3)(P/F,i,5) + 7000(P/F,i,8)
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7.10 0 = -2000 + 7000(P/F,i,2)
7.11 0 = -17,000 + 2500(P/A,i,5) + 1000(P/G,i,5) + 3000(P/F,i,5)
7.12 0 = -2900(F/A,i,9) – 2000 + 40,000
7.13 1,064,247 = 1,694,247(P/F,i,15)
7.14 0 = -65,220(P/A,i,4) + (57,925 – 35,220)(P/A,i,31)(P/F,i,4)
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7.15 (a) Effective dividend rate = 5.38(1 – 0.35) = 3.5% per year
7.16 In $1 million units,
0 = -100 – 400(0.1) + 20(P/A,i,10)
7.17 Spending $60,000 now will result in savings of $28,000 in years 0, 3 and 6.
7.18 Hand: In $1 million units,
0 = -500 + 1.8(0.1)(2500)(P/F,i,2) + 500(1.8)(0.9)(P/A,i,5)(P/F,i,5) – 10(P/A,i,10)
7.19 3 years = 3(52) = 156 weeks
7.20 Hand: Find the equivalent value of both series in year 10
0 = -(4,000,000/10)(F/A,i%,10) + 270,000/i
7.21 A nonconventional cash flow series is one wherein the signs on the net cash flows change
7.22 NCF swings indicating multiple ROR roots can occur for:
7.26 According to Norstrom’s criterion, there is only one positive root in a rate of return
7.30 Year 0 1 2 3 4
7.31 (a) Year 0 1 2 3 4 5 6
NCF, $ -30 -2 -6 +21 +30 +18 +40
7.32
Descartes’ rule of signs: 2 sign changes
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7.33
(c) Descartes’ rule of signs: 2 sign changes
7.34
(a) Descartes’ rule of signs: 2 sign changes
7.35 Norstrom’s criterion predicts one positive root. The rates of 0% and 31.6% are found.
7.37 The investment rate is usually higher than the borrowing rate because viable companies can
7.38 Follow the steps of the modified ROR procedure.
PW0 = – 32,000(P/F,10%,1) – 25,000(P/F,10%,2)
7.39 Hand: Follow the steps of the modified ROR procedure.
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7.40 (a) There are three changes in sign on the net cash flow, so there are three possible rate
(b) PW0 = -8000(P/A,8%,6) – 8000(P/A,8%,2)(P/F,8%,7)
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(c) Use the same spreadsheet functions as Figure 7-12 to display the ROIC of i″ = 3.78%.
(d) The IRR function displays i* = 3.78%. It is the same as ROIC = 3.78% because the FW
7.41 ii = 20% and ib = 9%. Follow the steps of the modified ROR procedure.
PW0 = -400,000 – 30,000(P/F,9%,3)
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7.42 (a) Descartes’ rule of signs: 2 sign changes
(c) Apply net-investment procedure steps because the investment rate ii = 15% is not equal
Hand solution:
Step 2: Set F4 = 0 and solve for i″ by trial and error.
Spreadsheet solution: Using the format and functions of Figure 7-12, i″ = 26.62%.
7.43 Descartes’ rule of signs: 4 sign changes
Norstrom’s criterion: series starts positive; no help
Step 2: Set F4 = 0 and solve for i″
7.44 Apply ROIC procedure , because investment rate ii = l5% is not equal to i* = 44.1% per
year. In $100 units,
F4 = (-1000 – 7000 i″ – 11,000 i″2 – 5000i3)(1 + i″) + 20,000
7.45 1250 = (25,000)(b)/2
7.46 I = 10,000(0.08)/4
= $200 every three months
7.48 I = 50,000(0.08)/4
7.49 I = 20,000(0.08)/2
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7.50 I = 9,125,000(0.04)/4 = $91,250 per quarter
7.51 Since the amount paid by the investor is equal to the face value of the bond, the rate of
7.52 I = 5000(0.06)/2
7.53 0 = -2000 + 10,000(P/F,i,15)
7.54 I = 25,000,000(0.05)/2
7.55 I = 10,000(0.08)/4
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7.56 (a) I = 10,000,000(0.12)/4
7.57 I = 5000(0.10)/2
7.64 NCF, $ -5000 +8000 -2000 +6000
7.65 -41,000 + x = 9000
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Solution to Case Study, Chapter 7
There is not always a definitive answer to case study exercises. Here are example responses
DEVELOPING AND SELLING AN INNOVATIVE IDEA
4. Descartes’ rule of signs: 3 sign changes
5. Continue the NCF series starting in year 13. Next 12 years of NCF at 12% has