Below is a table showing the annual benefits and costs for two recreation projec

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 increasing numbers of users over 10 years Project B will maintain the area to accommodate the current use levels only Project A Project EB Costs BenefitsYear 750 950 1,150 1,350 1,550 1,750 1,950 2,150 2,350 2,550 Costs Benefits 2,000 175 175 175 175 175 175 175 175 175 Year 6,500 350 350 350 350 350 350 350 350 350 750 750 750 750 750 750 750 750 750 750 4 4 6 6 10 10 1. (12 points) Calculate the Net Present 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 The formula for present value is: PV = 2. 3. 4. (6 points) Based on the net present value, which project would you choose? (6 points) If you were only looking at the B/C ratio which would you choose? (12 points) Calculate the Net Present Value of each project using a 10% discount rate

Explanation / 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

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 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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