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Unformatted text preview: Homework 23 Solution
7.11 We have a mix of present values and annual values, so the first thing we have to do is settle on one or
the other. If we turn everything into an annual value and use the conventional B/C ratio:
0.1019 AW Benefits $3,800,000 A  P,8%, 20 $65,000 $322,038
0.1019 AW Costs $1, 200,000 A  P,8%, 20 $300,000 $422, 223 B C
7.12 $322,038 0.76
$422, 223 If we use the conventional B/C ratio, then
B C PW of benefits
1
capital costs PW of O&M costs capital costs PW of O&M costs PW of benefits
capital costs PW benefits O&M costs If we use the modified B/C ratio, then
B C PW of benefits PW of O&M costs
1
capital costs capital costs PW benefits O&M costs which is the exact same equation. So either way
7.3601 capital costs $800,000 $600,000 P  A,6%,10 $1, 472,000
7.14 Since all of the values except the initial cost are stated as annual values, we’ll start by converting the
initial cost to an annual equivalent cost (the capital recovery amount). Since the project is assumed to
last indefinitely, the capital recovery amount can be calculated as:
A Pi $2,300,000 0.06 $138,000
If we use the conventional B/C ratio, then
B C annual benefits annual disbenefits
$340K $40K 1.16
capital recovery amount annual operating costs $138K $120K If we use the modified B/C ratio, then
B C annual benefits annual disbenefits annual operating costs $340K $40K $120K 1.30
capital recovery amount
$138K 7.17 We’ve been told to count the ticket revenue as a disbenefit to the public:
Disbenefits = $85/ticket × 1100 tickets/month = $93,500/month
The benefit to the public is the reduction is accidents from 33 per month to 18 per month. At an average
cost of $41,000 per accident:
Benefits = $41,000/accident × 15 accidents/month = $615,000/month
Since these are both monthly amounts, we need to turn the equipment cost into an equivalent uniform
monthly cost:
0.0304 Capital Recovery $750,000 A  P,0.5%,36 $22,800 month
Since there are no stated O&M costs the conventional and modified B/C ratios are the same:
B C
7.20 annual benefits annual disbenefits $615,000 $93,500 22.9
capital recovery amount
$22,800 In this problem, the benefit to the water utility customers lies in not having to send the samples to an
outside lab (at a cost of $1250 per sample):
Benefits = $1250/sample × 140 samples/year = $175,000/year
The O&M costs include the cost of expendable supplies and the cost of the chemist:
O&M Costs = $19,000/year + $56,000/year = $75,000/year
Finally, the equivalent annual cost of the equipment itself, amortized over 5 years, is
0.2374 Capital Recovery $595,000 A  P,6%,5 $141, 250 year
If we use the conventional B/C ratio, then
B C annual benefits
$175,000 0.81
capital recovery amount annual operating costs $141, 250 $75,000 If we use the modified B/C ratio, then
B C annual benefits annual operating costs $175,000 $75,000 0.71
capital recovery amount
$141, 250 Either way, this is not a good investment; the utility should continue sending the samples out for
processing. ...
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 Fall '08
 Moore,L

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