1. You are trying to decide on the best way to clean up a pond that can be used
ID: 2728583 • Letter: 1
Question
1. You are trying to decide on the best way to clean up a pond that can be used for recreation and are given two schedules of costs and benefits over the next ten years that area as follows:
a. If you are indifferent between current consumption and future consumption, which plan would you choose? Show the calculations you used to come up with your answer.
b. If the discount rate is 3%, which plan would you choose? what if the discount rate is 10%? Show the calculations you used to come up with your answer.
PLAN A PLAN EB YEARCosts Benefits Costs Benefits 25 75 75 75 75 75 75 75 75 75 75 400 20 20 20 20 20 20 20 20 20 20 10 10 10 10 10 10 10 10 10 10 200 20 20 20 20 20 20 20 20 20 20 100 10Explanation / Answer
a.
Evaluation of Plans:
Plan A:
Year
Costs
Benefits
Net cash flows
A
B
B-A
0
400
25
-375
1
20
75
55
2
20
75
55
3
20
75
55
4
20
75
55
5
20
75
55
6
20
75
55
7
20
75
55
8
20
75
55
9
20
75
55
10
20
75
55
Net cash flows
175
Plan B:
Year
Costs
Benefits
Net cash flows
A
B
B-A
0
10
20
10
1
10
20
10
2
10
20
10
3
10
20
10
4
10
20
10
5
10
20
10
6
10
20
10
7
10
20
10
8
10
20
10
9
10
20
10
10
200
100
-100
Net cash flows
0
The net cash flow of Plan A is more, hence we should choose plan A.
b.
Evaluation of Plans using 3% discount rate :
Calculation of NPV using Discount rate 3%:
Plan A:
Year
Net cash flows
PVF (3%)
PV
A
B
A*B
0
-375
1.00000
(375.00)
1
55
0.97087
53.40
2
55
0.94260
51.84
3
55
0.91514
50.33
4
55
0.88849
48.87
5
55
0.86261
47.44
6
55
0.83748
46.06
7
55
0.81309
44.72
8
55
0.78941
43.42
9
55
0.76642
42.15
10
55
0.74409
40.93
Net Present value (NPV)
94.16
Plan B:
Year
Net cash flows
PVF (3%)
PV
A
B
A*B
0
10
1.00000
10.00
1
10
0.97087
9.71
2
10
0.94260
9.43
3
10
0.91514
9.15
4
10
0.88849
8.88
5
10
0.86261
8.63
6
10
0.83748
8.37
7
10
0.81309
8.13
8
10
0.78941
7.89
9
10
0.76642
7.66
10
-100
0.74409
(74.41)
Net Present value (NPV)
13.45
The NPV of Plan A is higer, henve Plan A is better.
Evaluation of Plans using 10% discount rate :
Calculation of NPV using Discount rate 3%:
Plan A:
Year
Net cash flows
PVF (10%)
PV
A
B
A*B
0
-375
1.00000
(375.00)
1
55
0.90909
50.00
2
55
0.82645
45.45
3
55
0.75131
41.32
4
55
0.68301
37.57
5
55
0.62092
34.15
6
55
0.56447
31.05
7
55
0.51316
28.22
8
55
0.46651
25.66
9
55
0.42410
23.33
10
55
0.38554
21.20
Net Present value (NPV)
(37.05)
Plan B:
Year
Net cash flows
PVF (10%)
PV
A
B
A*B
0
10
1.00000
10.00
1
10
0.90909
9.09
2
10
0.82645
8.26
3
10
0.75131
7.51
4
10
0.68301
6.83
5
10
0.62092
6.21
6
10
0.56447
5.64
7
10
0.51316
5.13
8
10
0.46651
4.67
9
10
0.42410
4.24
10
-100
0.38554
(38.55)
Net Present value (NPV)
29.04
The NPV of Plan B is higher, henve Plan B is better.
a.
Evaluation of Plans:
Plan A:
Year
Costs
Benefits
Net cash flows
A
B
B-A
0
400
25
-375
1
20
75
55
2
20
75
55
3
20
75
55
4
20
75
55
5
20
75
55
6
20
75
55
7
20
75
55
8
20
75
55
9
20
75
55
10
20
75
55
Net cash flows
175
Plan B:
Year
Costs
Benefits
Net cash flows
A
B
B-A
0
10
20
10
1
10
20
10
2
10
20
10
3
10
20
10
4
10
20
10
5
10
20
10
6
10
20
10
7
10
20
10
8
10
20
10
9
10
20
10
10
200
100
-100
Net cash flows
0
The net cash flow of Plan A is more, hence we should choose plan A.
b.
Evaluation of Plans using 3% discount rate :
Calculation of NPV using Discount rate 3%:
Plan A:
Year
Net cash flows
PVF (3%)
PV
A
B
A*B
0
-375
1.00000
(375.00)
1
55
0.97087
53.40
2
55
0.94260
51.84
3
55
0.91514
50.33
4
55
0.88849
48.87
5
55
0.86261
47.44
6
55
0.83748
46.06
7
55
0.81309
44.72
8
55
0.78941
43.42
9
55
0.76642
42.15
10
55
0.74409
40.93
Net Present value (NPV)
94.16
Plan B:
Year
Net cash flows
PVF (3%)
PV
A
B
A*B
0
10
1.00000
10.00
1
10
0.97087
9.71
2
10
0.94260
9.43
3
10
0.91514
9.15
4
10
0.88849
8.88
5
10
0.86261
8.63
6
10
0.83748
8.37
7
10
0.81309
8.13
8
10
0.78941
7.89
9
10
0.76642
7.66
10
-100
0.74409
(74.41)
Net Present value (NPV)
13.45
The NPV of Plan A is higer, henve Plan A is better.
Evaluation of Plans using 10% discount rate :
Calculation of NPV using Discount rate 3%:
Plan A:
Year
Net cash flows
PVF (10%)
PV
A
B
A*B
0
-375
1.00000
(375.00)
1
55
0.90909
50.00
2
55
0.82645
45.45
3
55
0.75131
41.32
4
55
0.68301
37.57
5
55
0.62092
34.15
6
55
0.56447
31.05
7
55
0.51316
28.22
8
55
0.46651
25.66
9
55
0.42410
23.33
10
55
0.38554
21.20
Net Present value (NPV)
(37.05)
Plan B:
Year
Net cash flows
PVF (10%)
PV
A
B
A*B
0
10
1.00000
10.00
1
10
0.90909
9.09
2
10
0.82645
8.26
3
10
0.75131
7.51
4
10
0.68301
6.83
5
10
0.62092
6.21
6
10
0.56447
5.64
7
10
0.51316
5.13
8
10
0.46651
4.67
9
10
0.42410
4.24
10
-100
0.38554
(38.55)
Net Present value (NPV)
29.04
The NPV of Plan B is higher, henve Plan B is better.
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