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BS = $144,000,000
Q vs. P: ∆B/C = (96 – 11)/(40 – 10) = 2.83
b) Alternatives are already ranked according to increasing cost, except add DN
P vs. DN: B/C = 1.1 eliminate DN
9.42 Rank alternatives by increasing total cost: DN, G, J, H, I, L, K
Eliminate H and K based on B/C < 1.0
9.43 Rank alternatives by total cost: DN, X, Y, Z, Q; eliminate X based on B/C < 1.0
9.44 Calculate AW of total cost (in $ millions), then rank according to increasing AW value
Benefits are directly estimated; ranking is: DN, Advanced, Partial, Pond, Expand
9.45 Compare all alternatives against DN using AW values
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NS vs. DN: B = $160,000 per year
D = $21,000 per year
C = 87,000(A/P,7%,10) + 64,000
= 87,000(0.14238) + 64,000
= $76,387 per year
(B-D)/C = (160,000 – 21,000)/76,387
= 1.82 NS is acceptable
ST vs. DN: B = $74,000 per year
AC vs. DN: B = $52,000 per year
Cost-Effectiveness
9.46 Methods are independent. Calculate CER values, rank in increasing order, select
lowest CER until budget is exceeded.
CER = cost/score
Ordering: drones, aerostats, boots, motion, seismic, fence
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Total cost = 12.1 + 3.8 + 31.4 + 9.8 = $57.1 million
9.47 Strategies are independent; calculate CER values, rank in increasing order and select
those to not exceed $60/employee.
9.48 (a) Methods are independent. Calculate CER values, rank in increasing order, select
lowest CER, determine total cost.
Lowest CER is 64 for out-patient. Annual program cost is
(b) Rank by CER and select techniques to treat up to 1100 people. Select out-patient, NRT,
9.49 (a) CERW = 355/20 = 17.8
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CERZ = 102/7 = 14.6
(b) Order alternatives according to E: Z, X, W, Y; perform incremental comparison.
9.50 Minutes are the cost, C, and points gained are the effectiveness measure, E. Order on basis
of E and calculate CER values, then perform ∆C/E analysis.
E = 5; Friend: C/E = 10/5 = 2
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TA vs. friend: ∆C/E = (15-10)/(20-5) = 0.33
0.33 < 2; friend is dominated; go to TA for assistance
Public Sector Ethics
9.52 A discussion question open for different responses.
9.53 Some example projects to be described might be:
• Change of ingress and egress ramps for all major thoroughfares
Spreadsheet Exercises
9.54 All monetary units are $10,000
9.55 (a) Row 9 verifies the overall B/C values (screen image #1, row 9)
Screen image #1 Screen image #2
Screen image #3 Screen image #4
9.56 (a) Site A is selected (Screen image #1)
Screen image #1 Screen image #2
9.57 (a) Screen image #1: projects M and N are acceptable; O and P are not.
(b) Use Goal Seek to determine maximum M&O costs.
Screen image #1
Screen image #2
Screen image #3
Additional Problems and FE Exam Review Questions
9.58 Answer is (c)
9.64 Reject B because B/C ratio < 1.0. Since overall B/C ratio was higher for C than for A and
it
9.68 B has a larger total cost than A, and B/CB < B/CA, then ∆B/C < B/CB.
9.71 B/C = (600,000 – 400,000)/[700,000(A/P,6%,10) + 25,000]
= 200,000/[700,000(0.13587) + 25,000]
= 1.67
9.74 B/C = (360,000 – 42,000)/[2,000,000(0.06)]
= 2.65
Solution to Case Study, Chapter 9
Sometimes, there is not a definitive answer to a case study exercise. Here are example responses.
HIGHWAY LIGHTING OPTIONS TO REDUCE TRAFFIC ACCIDENTS
Computations similar to those for benefits (B), costs (C) and effectiveness measure (E) of
accidents prevented in the case study for each alternative results in the following estimates.
Benefits
Effectiveness
Cost, $ per year
Alternative
B, $/year
Measure, C
Poles
Power
Total
W
1,482,000
247
1,088,479
459,024
1,547,503
X
889,200
148
544,240
229,512
773,752
Y
1,111,500
185
777,485
401,646
1,179,131
Z
744,000
124
388,743
200,823
589,566
1. B/C analysis order based on total costs: Z, X, Y, W. Challenger is placed first below.
Z vs. DN: B/C = 744,000/589,566 = 1.26 eliminate DN
2. C/E analysis order based on effectiveness measure, E: Z, X, Y, W. Challenger listed first.
Calculate C/E for each alternative.
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Z vs. DN: C/E = 4755 basis for comparison
X vs. Z: ∆C/E = (773,752-589,566)/(148-124) = 7674 > 4755 no dominance, keep both
Y vs. X: ∆C/E = (1,179,131-773,752)/(185-148) = 10,956 > 5228 no dominance, keep both
W vs. Y: ∆C/E = (1,547,503-1,179,131)/(247-185) = 5941 < 6374 dominance, eliminate Y
Remaining alternatives in order are: Z, X, W
Three alternatives -- Z, X and W -- are indicated as a possible choice. The decision for
one must be made on a basis other than C/E, probably the amount of budget available.
3. Ratio of night/day accidents, lighted = 839/2069 = 0.406
If the same ratio is applied to unlighted sections, number of accidents prevented is calculated
as follows:
4. For Z to be justified, the incremental comparison of W vs. Z would have to be ≥ 1.0. The
benefits would have to increase. Find BW in the incremental comparison.
The difference in the number of accidents would have to increase from 247 to:
