Below is a table showing the annual benefits and costs for two recreation projec
ID: 1121604 • Letter: B
Question
Below is a table showing the annual benefits and costs for two recreation projects.
Project A, which has a larger up-front cost, will increase the capacity of the recreation area allowing for increasing numbers of users over 10 years.
Project B will maintain the area to accommodate the current use levels only.
Project A
Project B
Year
Costs
Benefits
Year
Costs
Benefits
1
6,500
750
1
2,000
750
2
350
950
2
175
750
3
350
1,150
3
175
750
4
350
1,350
4
175
750
5
350
1,550
5
175
750
6
350
1,750
6
175
750
7
350
1,950
7
175
750
8
350
2,150
8
175
750
9
350
2,350
9
175
750
10
350
2,550
10
175
750
Calculate the Net Present Value of each project using a 4% discount rate.
Project A
Project B
Year
Costs
Benefits
Year
Costs
Benefits
1
6,500
750
1
2,000
750
2
350
950
2
175
750
3
350
1,150
3
175
750
4
350
1,350
4
175
750
5
350
1,550
5
175
750
6
350
1,750
6
175
750
7
350
1,950
7
175
750
8
350
2,150
8
175
750
9
350
2,350
9
175
750
10
350
2,550
10
175
750
Explanation / Answer
Net annual benefit (NAB) = Annual benefit - Annual cost
Net present value for the NAB is computed as follows.
Project - A Year Benefit Cost NAB PV factor @4% Discounted NAB (A) (B) (C) = (A) - (B) (D) (C) x (D) 1 750 6,500 -5,750 0.9615 -5,528.85 2 950 350 600 0.9246 554.73 3 1,150 350 800 0.8890 711.20 4 1,350 350 1,000 0.8548 854.80 5 1,550 350 1,200 0.8219 986.31 6 1,750 350 1,400 0.7903 1,106.44 7 1,950 350 1,600 0.7599 1,215.87 8 2,150 350 1,800 0.7307 1,315.24 9 2,350 350 2,000 0.7026 1,405.17 10 2,550 350 2,200 0.6756 1,486.24 Net Present Value ($) = 4,107.17 Project - B Year Benefit Cost NAB PV factor @4% Discounted NAB (A) (B) (C) = (A) - (B) (D) (C) x (D) 1 750 2,000 -1,250 0.9615 -1,201.92 2 750 175 575 0.9246 531.62 3 750 175 575 0.8890 511.17 4 750 175 575 0.8548 491.51 5 750 175 575 0.8219 472.61 6 750 175 575 0.7903 454.43 7 750 175 575 0.7599 436.95 8 750 175 575 0.7307 420.15 9 750 175 575 0.7026 403.99 10 750 175 575 0.6756 388.45 Net Present Value ($) = 2,908.96Related Questions
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