You have been assigned the task of comparing the economic
results of three alternative designs for a state government public
works project. The estimated values for various economic
factors related to the three designs are given above. The MARR
being used is 9% and the analysis period is 15 years.
a. Use the conventional benefit/cost ratio method, with AW as the
equivalent worth measure, to select the preferred design for the
project.
b. Use the modified B/C ratio method, with PW as the equivalent
worth measure, to select the preferred design for the project.
Factor
Capital investment
Salvage value (end of year 15)
Annual O & M costs
Annual benefits to user group A
Annual benefits to other user groups
Alternative Design
1
2
3
$1,240,000 $1,763,000 $1,475,000
90,000
150,000
120,000
215,000
204,000
201,000
315,000
367,000
355,000
147,800
155,000
130,500
(a) Design 1: CR (9%) = 1,240,000(A/P,9%,15) - 90,000(A/F,90/o,15)
=150,815
B/C= 315,000 + 147,800 = 1.27 > 1
150,815 + 215,000
Design I is an acceptable base alternative.
 Annual Benefits
 Capital Recovery Amount
 Annual O&M
Conventional B/C
Increment Justified?
Current Best Design
(3-1)
22,700
28,141
-14,000
1.61
Yes
3
Select Design 3.
 (2-3)
36,500
34,718
3,000
0.97
No
3
(b) Design 1:
B/C = (315,000 + 147,800 - 215,000)(P / A, 9%, 15) = 1.64 >1
1,240,000 - 90,000 (P/F, 9%, 15)
Design 1 is an acceptable base alternative.
 PW (benefits - 0 & M)
 Capital Investment
 PW (Market Value)
Modified B/C
Increment Justified?
Current Best Design
Select Design 3.
 (3-1)
295,828
235,000
8,235
1.30
Yes
3
 (2-3)
270,033
288,000
8,235
0.97
No
3
9-28 Your company manufactures circuit boards and other electronic
parts for various commercial products. Design changes in part of
the product line, which are expected to increase sales, will require
changes in the manufacturing operation. The cost basis of new
equipment required is $220,000 (MACRS five-year property class
assets). Increased annual revenues, in year zero dollars, are
estimated to be $360,000. Increased annual expenses, in year zero
dollars, are estimated to be $239,000. The estimated market value
of equipment at the end of the six-year analysis period is $40,000.
General price inflation is estimated at 4.9% per year; the total
escalation rate on annual revenues is 2.5%, and for annual
expenses it is 5.6%; the after-tax MARR (in market terms) is 10%
per year; and t = 39%.
• a. Based on an after-tax, actual dollar analysis, what is the
maximum amount that your company can afford to spend on the
total project (i.e., changing the manufacturing operations)? Use
the PW method of analysis.
• b. Develop (show) your ATCF in real dollars.
Annual revenues in year k (A$) = 360,000(1.1025)k
Annual expenses in year k (A$) = - 239,000(l.056) k
The values in the following table are expressed in A$.
Eoy
0
1
2
3
4
5
6
6
Annual
Revenues
369,000
378,225
387,681
397,373
407,307
417,490
Annual
Expenses
-252,384
- 266,518
- 281,442
- 297,203
- 313,847
- 331,422
BTCF
Depr
TI
T(39%)
ATCF (A$)
-220,000
116,616
111,707
106,239
100,170
93,460
86,068
40,000
—
44,000
70,400
42,240
25,344
25,344
12,672
—
—
72,616
41,307
63,999
74,826
68,116
73,396
40,000
—
-28,320
- 16,110
- 24,960
- 29,182
- 26,565
- 28,624
- 15,600
-220,000
88,296
95,597
81,279
70,988
66,895
57,444
24,400
PW(10%) = ATCFk (P/F, 10%,k) = $136,557
Total investment that can be afforded (including new equipment)
= 136,557 + 220,000 = 356,557
(b) ATCFk (R$) = ATCF(A$)(P/F, 4.9%, k)
Year, k ATCFk (A$) (P/F,4.9%,k)
0
- 220,000
1.0000
1
88,296
0.9533
2
95,597
0.9088
3
81,279
0.8663
4
70,988
0.8258
5
66,895
0.7873
6
57,444
0.7505
6
24,400
0.7505
ATCF(R$)
- 220,000
84,173
86,879
70,412
58,622
52,666
43,112
18,312
10 - 13
A new steam flow monitoring device must be purchased
immediately by a local municipality. These most likely
estimates have been developed by a group of engineers
Capital investment
Annual savings
Useful life
Market value (end of year 12)
MARR
- $140,000
$25,000
12 years
$40,000
10%/year
Because considerable uncertainty surrounds these estimates, it is
desired to evaluate the sensitivity of PW to ± 50% changes in
the most likely estimates of (a) annual savings, (b) useful life,
and (c) interest rate (MARR). Graph the results and determine
to which factor the decision is most sensitive.
Annual Savings
PW(l0%)
Life
PW(l0%)
MARR
PW(i%)
-50
12,500
- 42,084
6
- 8,539
5%
103,855
% Change in Factor
-25
0
25
18,750 25,000
31,250
501
43,086
85,672
9
15
12
20,940 43,086
59,728
7.5%
12.5%
10%
70,176 43,086
21,070
50
37,500
128,257
18
72,229
15%
2,991
At the most likely estimates:
PW(10%) = - 140,000 + 25,000 (P/A, 10%, 12) + 40,000 (P/F, 10%, 12)
= 43,086
At a -50% change in Life(example):
PW(10%) = - 140,000 + 25,000 (P/A, 10%, 6) + 840,000 (P/F, 10%, 6)
= - 140,000 + 25,000 (4.3553) + 40,000 (0.5645) = - 8,538
Decision is most sensitive to the estimate of Annual Saving