Chapter 9, Problem 3.
Identify each cash flow as a benefit, disbenefit, or cost.
(a) $500,000 annual income from tourism created by a freshwater reservoir
(b) $700,000 per year maintenance by container ship port authority
(c) Expenditure of $45 million for tunnel construction on an interstate highway
(d) Elimination of $1.3 million in salaries for county residents based on reduced
international trade
(e) Reduction of $375,000 per year in car accident repairs because of improved lighting
(f) $700,000 per year loss of revenue by farmers because of highway right-of-way
purchases
Chapter 9, Solution 3.
(a) Benefit (b) Cost (c) Cost
(d) Disbenefit (e) Benefit (f) Disbenefit
Chapter 9, Problem 9.
The U.S. Environmental Protection Agency has established that 2.5% of the median
household income is a reasonable amount to pay for safe drinking water. The median
household income is $30,000 per year. For a regulation that would affect the health of
people in 1% of the households, what would the health benefits have to equal in dollars
per household (for that 1% of the households) for the B/C ratio to be equal to 1.0?
Chapter 9, Solution 9.
Annual cost = 30,000(0.025)
= $750 per year/household
Let x = number of households
Total annual cost, C = (750)(x)
Let y = $ health benefit per household for the 1% of households
Total annual benefits, B = (0.01x)(y)
1.0 = B/C = B/(750)(x)
B = (750)(x)
Substitute B = (0.01x)(y)
(0.01x)(y) = 750x
y = $75,000 per year
Chapter 9, Problem 10.
Use a spreadsheet to set up and solve Problem 9.9, and then apply the following changes.
Observe the increases and decreases in the required economic value of the health benefits
for each of these changes.
(a) Median income is $18,000 (poorer country), and percentage of household income is
reduced to 2%.
(b) Median income is $30,000 and 2.5% is spent on safe water, but only 0.5% of the
households are affected.
(c) What percentage of the households must be affected if the required health benefit and
annual income both equal $18,000? Assume the 2.5% of income estimate is maintained.
Chapter 9, Solution 10.
All parts are solved on the spreadsheet once it is formatted using cell references.
Chapter 9, Problem 16.
Calculate the B/C ratio for the following cash flow estimates at a discount rate of 6% per
year.
Item
PW of benefits, $
AW of disbenefits, $/year
First cost, $
M&O costs, $/year
Life of project, years
Cash Flow
3,800,000
45,000
2,200,000
300,000
15
Chapter 9, Solution 16.
Convert all estimates to PW values.
PW disbenefits = 45,000(P/A,6%,15)
= 45,000(9.7122)
= $437,049
PW M&O Cost = 300,000(P/A,6%,15)
= 300,000(9.7122)
= $2,913,660
B/C = 3,800,000 – 437,049__
2,200,000 + 2,913,660
= 3,362,951/5,113,660
= 0.66
Chapter 9, Problem 22.
Apply incremental B/C analysis at an interest rate of 8% per year to determine which
alternative should be selected. Use a 20-year study period, and assume the damage costs
might occur in year 6 of the study period.
Initial cost, $
Annual M&O
costs, $/year
Potential damage
costs, $
Alternative A
600,000
50,000
Alternative B
800,000
70,000
950,000
250,000
Chapter 9, Solution 22.
Alternative B has a larger total annual cost; it must be incrementally justified. Use PW
values. Benefit is the difference in damage costs. For B incrementally over A:
Incr cost = (800,000 – 600,000) + (70,000 – 50,000)(P/A,8%,20)
= $200,000 + 20,000(9.8181)
= $396,362
Incr benefit = (950,000 – 250,000)(P/F,8%,6)
= 700,000(0.6302)
= 441,140
Incr B/C = 441,140/396,362
= 1.11
Select alternative B.
Chapter 9, Problem 27.
Solar and conventional alternatives are available for providing energy at a remote space
research site. The costs associated with each alternative are shown below. Use the B/C
method to determine which should be selected at a discount rate of 0.75% per month over
a 6-year study period.
Initial cost, $
M&O cost, $/month
Salvage value, $
Conventional
2,000,000
50,000
0
Solar
4,500,000
10,000
150,000
Chapter 9, Solution 27.
Using the capital recovery costs, solar is the more costly alternative.
∆cost = (4,500,000 – 2,000,000)(A/P,0.75%,72)
– (150,000 – 0)(A/F,0.75%,72)
= 2,500,000(0.01803) – 150,000(0.01053)
= $43,496
∆benefits = 50,000 – 10,000
= $40,000
Incr B/C = 40,000/43,496 = 0.92
Select the conventional system.
Chapter 9, Problem 33.
The federal government is considering three sites in the National Wildlife Preserve for
mineral extraction. The cash flows (in millions) associated with each site are given
below. Use the B/C method to determine which site, if any, is best, if the extraction
period is limited to 5 years and the interest rate is 10% per year.
Site A
Initial cost, $
Annual cost, $/year
Annual benefits,
$/year
Annual disbenefits,
$/year
Site B
Site C
50
3
20
90
4
29
200
6
61
0.5
1.5
2.1
Chapter 9, Solution 33.
Compare A to DN since it is not necessary to select one of the sites.
A vs DN
AW of Cost = 50(A/P,10%,5) + 3
= 50(0.26380) + 3
= 16.19
AW of Benefits = 20 – 0.5
= 19.5
B/C = 19.5
16.19
= 1.20 > 1.0
Eliminate DN.
B vs A
∆C = (90 – 50)(A/P,10%,5) + (4 – 3)
= 40(0.26380) + 1
= $11.552
∆B = (29 – 20) – (1.5 – 0.5) = 8
∆B/C = 8/11.552
= 0.69 < 1.0
Eliminate B.
C vs A
∆C = (200 – 50)(A/P,10%,5) + (6 – 3)
= 150(0.26380) + 3
= 42.57
∆B = (61 – 20) – (2.1 – 0.5) = 39.4
∆B/C = 39.4/42.57
= 0.93 < 1.0
Select site A
Eliminate C
Chapter 9, Problem 43.
Four independent projects are evaluated, using B/C ratios. The ratios are as follows:
Project
B/C ratio
A
0.71
B
1.29
C
1.07
D
2.03
On the basis of these results, you should
(a) Reject B and D.
(b) Select D only.
(c) Reject A only.
(d) Compare B, C and D incrementally.
Chapter 9, Solution 43.
Answer is (c)
Chapter 9, Problem 44.
If two mutually exclusive alternatives have B/C ratios of 1.5 and 1.4 for the lower firstcost and higher first-cost alternatives, respectively,
(a) The B/C ratio on the increment between them is less than 1.4.
(b) The B/C ratio on the increment between them is between 1.4 and 1.5.
(c) The B/C ratio on the increment between them is greater than 1.4.
(d) The lower-cost alternative is the better one.
Chapter 9, Solution 44.
Answer is (a)