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FW3 = 3000(F/P,15%,2) + 15,000(F/P,15%,1)
= 3000(1.3225) + 15,000(1.1500)
= $21,218
Find i′ at which PW0 is equivalent to FW3
–10,757(F/P,i′,3) = 21,218
i’ = (21,218/10,757)1/3 -1
= 0.254 (25.4% per year)
(b) By MIRR with ib = 10% and ii = 30%
i’ = 31.7% per year
7.42 PW0 = -50,000 – 8000(P/F,12%,7)
7.43 (a) Descartes’ rule of signs: 2 sign changes; up to two i* values
(b) 0 = –65 + 30(P/F,i*,1) + 84(P/F,i*,2) – 10(P/F,i*,3) – 12(P/F,i*,4)
(c) Apply net-investment procedure steps because the investment rate ii = 15% is not
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equal to i* rate of 28.6% per year.
Hand solution:
Step 1: F0 = -65 F0 < 0; use i″
Step 2: Set F4 = 0 and solve for i″ by trial and error.
Solve by quadratic equation, trial and error, or spreadsheet
Spreadsheet solution: Using the format and functions of Figure 7-13, i″ = 26.62%.
Before Goal Seek After Goal Seek Goal Seek template
Bonds
7.45 75 = 5000(b)/4
7.47 0 = –9250 + 50,000(P/F,i*,18)
7.48 (a) Dividend = 1000(0.05)/2 = $25 per 6 months
7.50 0 = –60,000 + 50,000(0.14)(P/A,i*,5) + 50,000(P/F,i*,5)
7.51 I = 10,000(0.08)/4 = $200 per quarter
7.52 I = 10,000(0.08)/4 = $200 per quarter
(a) 0 = –6000 + 200(P/A,i*,12) + 11,500(P/F,i*,12)
(b) Nominal i*/year = 8.13(4) = 32.5% per year
7.53 The utility would pay a penalty of $2,000,000 in return for saving 4% per year, payable
Spreadsheet Exercises
7.54 (a) Balance on loan after payment 4 = $5000
7.55 (a) Enter cash flows for years 0 to 4 in cells B2:B6
(c) Use Goal Seek tool to change $9000 estimate in year 1 to $10,688 with multiples shown
for years 3 and 4 estimates. Amounts needed are in cells B7 to B9.
7.56 (a) Spreadsheet table not shown intentionally; i* per quarter series is:
(b) Plot of i* per quarter vs. quarters 8 through 16
Quarter 8 9 10 11 12 13 14 15 16
i* value,
%/qtr
–4.79% –1.10% 1.58% 3.59% 5.13% 6.06% 6.06% 5.52% 4.30%
-6.00%
-4.00%
-2.00%
0.00%
2.00%
4.00%
6.00%
8.00%
i*, % per quarter
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(c) A required 24% per year or 6% per quarter (nominal) indicates the equipment
should be used for a period of 13 to 15 quarters (over 3 years; less than 4 years)
7.57 (a) i* = -2.71% per quarter (see spreadsheet)
7.58 (a) i1
* = -18.38% and i2
* = 8.79%
(d) Plots are shown
7.59 ROIC analysis results in i” = 11.26%, same as the IRR result. The MARR of 10% is being met
and the company is effectively using the funds invested in it.
7.60 (a) Sign changes: Descartes: 2; up to two i* values
Norstrom’s: 1; one positive i*
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Additional Problems and FE Exam Review Problems
7.61 Answer is (c)
7.66 I/quarter = 20,000(0.07)/4
7.69 0 = 1,000,000 – 20,000(P/A,i*,24) – 1,000,000(P/F,i*,24)
7.70 0 = –60,000 + 10,000(P/A,i*,10)
7.72 i* = 4500/50,000 = 0.09 (9% per year)
7.74 PW0 = -40,000 – 29,000(P/F,8%,2)
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
1. (a) 47.9%; (b) 7.0%
4. Descartes’ rule of signs: 3 sign changes