The two alternatives shown below are for projects to be considered to improve th
ID: 2596289 • Letter: T
Question
The two alternatives shown below are for projects to be considered to improve the traffic at a road intersection:
Alternative 1
Alternative 2:
First cost, $
320,000
540,000
M&O costs, $/year
45,000
35,000
Benefits, $/year
110,000
150,000
Disbenefits, $/year
20,000
45,000
Based on an interest rate of 7% per year and a 10 year study period determine the following:
Calculate the Benefits/Cost ratio for Alternative 1
Calculate the Benefits/Cost ratio for Alternative 2
Perform an incremental Benefits/Cost analysis for the two alternatives
Determine which alternative the city council should choose
B/C ratio for Alternative 1
B/C ratio for Alternative 2
Incremental B/C ratio
Alternative to be chosen
-2.09
Choose Alternative 2
-3.46
-1.54
Choose Do Nothing
2.09
3.46
1.54
Choose Alternative 1
Alternative 1
Alternative 2:
First cost, $
320,000
540,000
M&O costs, $/year
45,000
35,000
Benefits, $/year
110,000
150,000
Disbenefits, $/year
20,000
45,000
Explanation / Answer
1. Calculation of Present Value of Benefits & Cost of Alternative 1
Particulars
Amount (In $)
(A)
Time(n)
Present Value Factor (1/ (1.07)n), i=7%
(B)
Present Value Amount (In $)
(A x B)
Costs
Initial Investment
320,000
0
1
320,000
M&O
45,000
1-10
7.02
315,900
TOTAL CASH OUTFLOWS
635,900
Benefits:
Net Benefits (110,000 – 20,000)
90,000
1-10
7.02
631,800
Benefit to cost ratio = Present Value of Benefits / Present Value of Costs.
= 631,800 / 635,900 = 0.99355
2. Calculation of Present Value of Benefits & Cost of Alternative 2
Particulars
Amount (In $)
(A)
Time(n)
Present Value Factor (1/ (1.07)n), i=7%
(B)
Present Value Amount (In $)
(A x B)
Costs
Initial Investment
540,000
0
1
540,000
M&O
35,000
1-10
7.02
245,700
TOTAL CASH OUTFLOWS
785,700
Benefits:
Net Benefits (150,000 – 45,000)
105,000
1-10
7.02
737,100
Benefit to cost ratio = Present Value of Benefits / Present Value of Costs.
= 737,100 / 785,700 = 0.93814.
3. Calculation of Incremental Benefit/ Cost analysis
Incremental cost of Alternative 2 over 1 = $785,700 - 635,900 = $149,800
Incremental Benefit of Alternative 2 over 1 = $737,100 - 631,800 = $105,300
Incremental B/C ratio = 105,300 / 149,800 = 0.7029
4. Since the incremental B/C ratio is less than the B/C ratio of Alternative 1 & NPV of Alternatiive 1 is more than (or less in case of negative NPV) the alternative 2, the same should be chosen by the Council.
Particulars
Amount (In $)
(A)
Time(n)
Present Value Factor (1/ (1.07)n), i=7%
(B)
Present Value Amount (In $)
(A x B)
Costs
Initial Investment
320,000
0
1
320,000
M&O
45,000
1-10
7.02
315,900
TOTAL CASH OUTFLOWS
635,900
Benefits:
Net Benefits (110,000 – 20,000)
90,000
1-10
7.02
631,800
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