ooo Verizon LTE 7:03 PM * 47% Homework 5 Homework 5.docx AREC/ECON 346- Homework
ID: 1121652 • Letter: O
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ooo Verizon LTE 7:03 PM * 47% Homework 5 Homework 5.docx AREC/ECON 346- Homework 5 Due: Wednesday December 6, 11:59pmm 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 onl 00 7502,000 750 2 3509502 17S 750 75 750 75 750 6 3501,750 175 750 75 750 75 750 93502.350 9 175 750 10 350 2.55010 175 750 4 350,3504 5 350 ,5505 8 350 2,1508 1.(12 points) Calculate the Net Preset Value of each project using a 4% discount rate Use the spreadsheet attached to the assignment to do your calculations and submit it along with answers to the question below 2. (6 points) Based on the net present value, which project 3. (6 points) If you were only looking at the B/C ratio which 4. (12 points) Calculate the Net Present Value of each project 5. (6 points) Does your preferred project change with the higher 6. (8 points) Explain what is going on when the discount rate is The formula for present value is: would you choose? would you choose? using a 10% discount rate discount rate? increased. Courses Calendar To Do Notifications MessagesExplanation / Answer
Answer:
1. Net present value is calculated below by using the formula:
PV at 4% = 1/(1+4%)t where t is year and
PV of net cash flow = PV at 4% * cash flow
net cash = benefit-cost
Net present vaalue = summation of PV of net cash
Project A
Year
Costs
Benefits
Net cash
PV at 4%
PV of net cash
1
6500
750
-5750
0.961538
-5528.846154
2
350
950
600
0.924556
554.7337278
3
350
1150
800
0.888996
711.1970869
4
350
1350
1000
0.854804
854.804191
5
350
1550
1200
0.821927
986.3125281
6
350
1750
1400
0.790315
1106.440336
7
350
1950
1600
0.759918
1215.868501
8
350
2150
1800
0.73069
1315.242369
9
350
2350
2000
0.702587
1405.173471
10
350
2550
2200
0.675564
1486.241171
NPV
4107.167229
Project B
Year
Costs
Benefits
Net cash
PV at 4%
PV of net cash
1
2000
750
-1250
0.961538
-1201.923077
2
175
750
575
0.924556
531.6198225
3
175
750
575
0.888996
511.1729062
4
175
750
575
0.854804
491.5124098
5
175
750
575
0.821927
472.6080864
6
175
750
575
0.790315
454.4308523
7
175
750
575
0.759918
436.9527426
8
175
750
575
0.73069
420.1468679
9
175
750
575
0.702587
403.987373
10
175
750
575
0.675564
388.4493971
NPV
2908.957381
2) Projecthaving greater NPV should be choosen. As project A has greater NPV than NPV of B then project A should be choosen.
3) B/C ration can be calculated by dividing all benefits to all cash as follows:
B/C ratio of B = 3575/7500 = 2.097
and B/C ratio of A = 16500/9650 = 1.70
As B/C ratio of B is greater than A then B should have been selected.
4) Using 10% discount rate:
Project A
Year
Costs
Benefits
Net cash
PV at 10%
PV of net cash
1
6500
750
-5750
0.909091
-5227.272727
2
350
950
600
0.826446
495.8677686
3
350
1150
800
0.751315
601.0518407
4
350
1350
1000
0.683013
683.0134554
5
350
1550
1200
0.620921
745.1055877
6
350
1750
1400
0.564474
790.2635021
7
350
1950
1600
0.513158
821.0529892
8
350
2150
1800
0.466507
839.7132844
9
350
2350
2000
0.424098
848.1952367
10
350
2550
2200
0.385543
848.1952367
NPV
1445.186174
Project B
Year
Costs
Benefits
Net cash
PV at 10%
PV of net cash
1
2000
750
-1250
0.909091
-1136.363636
2
175
750
575
0.826446
475.2066116
3
175
750
575
0.751315
432.0060105
4
175
750
575
0.683013
392.7327368
5
175
750
575
0.620921
357.0297608
6
175
750
575
0.564474
324.5725098
7
175
750
575
0.513158
295.065918
8
175
750
575
0.466507
268.2417436
9
175
750
575
0.424098
243.8561306
10
175
750
575
0.385543
221.6873914
NPV
1874.035177
Project A
Year
Costs
Benefits
Net cash
PV at 4%
PV of net cash
1
6500
750
-5750
0.961538
-5528.846154
2
350
950
600
0.924556
554.7337278
3
350
1150
800
0.888996
711.1970869
4
350
1350
1000
0.854804
854.804191
5
350
1550
1200
0.821927
986.3125281
6
350
1750
1400
0.790315
1106.440336
7
350
1950
1600
0.759918
1215.868501
8
350
2150
1800
0.73069
1315.242369
9
350
2350
2000
0.702587
1405.173471
10
350
2550
2200
0.675564
1486.241171
NPV
4107.167229
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