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Unformatted text preview: Homework 24 Solution
7.22 The problem statement says “select one” so we have to assume that “do nothing” is not an option even
though these look like the equivalent of “revenue” projects because they have direct benefits.
If we use the modified B/C definition, the only cost in the denominator is the initial cost (there is no
salvage value) so we need to determine if the additional $49,000 it would cost to use the new sensors is
justified by the additional benefits.
Since all of the remaining costs are annual values, we’ll amortize the $49,000 cost difference over the
10year study period:
0.14238 C $49,000 A  P,7%,10 $6977 per year
Counting the O&M costs as disbenefits, the annual benefits of the two options are
BEC = $110,000 – $26,000 – $49,000 = $35,000
BNS = $160,000 – $64,000 = $96,000
B = $96,000 – $35,000 = $61,000 per year So the incremental B/C ratio is
B C $61,000 1
$6977 Therefore, select the moreexpensive NS option.
We could have also used the conventional B/C definition. In that case, we’d have to include the O&M
costs in the denominator. Now the costs of the two options are
CEC = $38,000 (0.14238) + $49,000 = $54,410
CNS = $87,000 (0.14238) + $64,000 = $76,387
C = $76,387 – $54,410 = $21,977 Omitting the O&M costs, the annual benefits of the two options are
BEC = $110,000 – $26,000 = $84,000
BNS = $160,000
B = $160,000 – $84,000 = $76,000 per year So the incremental B/C ratio is B C
Therefore, select the moreexpensive NS option. $76,000 1
$21,977 7.24a Program 1 will cost $60 per household and provide benefits of $1.25 per month per household. Program 2
will cost $500 per household and provide benefits of $8.00 per month per household. If the programs
are mutually exclusive, then our only options are to choose Program 1, choose Program 2, or Do Nothing.
Starting with the less expensive option (Program 1) we have to determine if the benefits of Program 1
outweigh the costs relative to doing nothing:
51.7256 $1.25 $0 P  A,0.5%,60 $64.66 1
B C $60 $0 $60.00 Choose 1 So Program 1 is better than doing nothing. So next we have to compare Program 2 to Program 1:
51.7256 $8.00 $1.25 P  A,0.5%,60 $349.15 1
B C $500 $60 $440.00 Reject 2 So Program 2 is not better than Program 1; select Program 1.
7.24b If the alternative are independent, we can do both projects if each has a B/C ratio greater than one. Now
each project is simply evaluated against doing nothing:
51.7256 B C1 $1.25 $0 P  A,0.5%,60 $64.66 1 $60 $0 $60.00 Choose 1 51.7256 B C1 $8 $0 P  A,0.5%,60 $500 $0 $413.80 1 Reject 2
$500.00 So select Program 1 and reject Program 2.
7.25 In this case, there are no direct benefits, so it can be assumed that “do nothing” is not an option. Since
the only benefits are due to differences in usage fees, we must use the modified B/C definition. So the
first thing we have to do is calculate the capital recovery amount for each alternative:
0.24389 0.17389 CR conv $200,000 A  P,7%,5 $10,000 A  F,7%,5 $47,039 year
0.24389 0.17389 CR solar $1,300,000 A  P,7%,5 $130,000 A  F,7%,5 $294, 451 year
So the incremental B/C ratio is:
B C 9000 80,000 $294, 451 $47,039 $71,000 1
$247, 412 So the solar option is not better than the convention option; select Conventional Option.
7.26 For this problem, there are direct benefits in the form of annual income, so these are revenue projects
and you have to assume that “do nothing” is an option. The project statement also says to count the
O&M costs as disbenefits, which is the same as saying “use the modified B/C definition,” so the first
thing we have to do is calculate the capital recovery amount for each method:
0.16275 CR1 $15,000 A  P,10%,10 $2441 year 0.16275 CR 2 $19,000 A  P,10%,10 $3092 year
0.16275 CR 3 $25,000 A  P,10%,10 $4069 year
0.16275 CR 4 $33,000 A  P,10%,10 $5371 year
These are already in order of increasing CR, so we start by comparing Method 1 to Do Nothing:
B C $16,000 $10,000 $0
$2441 $0 $6000 1 Choose 1
$2441 Next we compare Method 2 to Method 1:
B C $20,000 $12,000 $16,000 $10,000 $3092 $2441 $2000 1 Choose 2
$651 $2000 1 Choose 3
$977 $1000 1 Reject 4
$1302 Next we compare Method 3 to Method 2:
B C $19,000 $9,000 $20,000 $12,000 $4069 $3092 Finally we compare Method 4 to Method 3:
B C $22,000 $11,000 $19,000 $9,000 $5371 $4069 So the final answer is to select Method 3.
7.27 If we assume the bridges last forever, then (AP,6%,) = 0.06 and the capital recovery amounts for the
three locations are
CRS = $50,000,000 (0.06) + $150,000 = $3,150,000
CRD = $75,000,000 (0.06) + $130,000 = $4,630,000
CRN = $60,000,000 (0.06) + $140,000 = $3,740,000
So the ranking of alternative relative to increasing capital recovery amount is S, N, D. Since “Do
Nothing” is not an option, we start by competing N against S:
B C $5,900,000 $7,600,000 $1,700,000 1
$3,740,000 $3,150,000 $590,000 Choose S Next we evaluate D against S:
B C $4,100,000 $7,600,000 $3,500,000 1
$4,630,000 $3,150,000 $1, 480,000 So the answer is to select Location D (the downtown bridge). Choose D ...
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This note was uploaded on 12/07/2011 for the course CIVL 4111 taught by Professor Moore,l during the Fall '08 term at U. Memphis.
 Fall '08
 Moore,L

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