Cheryl Peck purchased a computer network for her classroom.The computer network cost $100,000.She estimates that she can charge $500 for one session in the classroom.Cheryl knows that enrollment will increase over time.She estimates 50 students the first year,75 students the second year,100 students the third year,and 150 students the fourth year.If her cost of capital is 16 percent,what is the approximate present value of the benefits?

Question

Quizplus · Accepted Answer

To calculate the present value of the benefits, we need to find the present value of the cash flows generated from the classroom sessions in each year, and add them up.

The cash flow generated in each year can be calculated as follows:
- Year 1: $500 x 50 = $25,000
- Year 2: $500 x 75 = $37,500
- Year 3: $500 x 100 = $50,000
- Year 4: $500 x 150 = $75,000

To find the present value of each cash flow, we use the formula PV = CF / (1 + r)^n, where PV is the present value, CF is the cash flow, r is the cost of capital, and n is the number of years.

Using a discount rate of 16%, the present value of each cash flow is:
- Year 1: $25,000 / (1 + 0.16)^1 = $21,551
- Year 2: $37,500 / (1 + 0.16)^2 = $28,031
- Year 3: $50,000 / (1 + 0.16)^3 = $33,632
- Year 4: $75,000 / (1 + 0.16)^4 = $48,666

Adding up the present values of the cash flows, we get:
PV = $21,551 + $28,031 + $33,632 + $48,666
PV = $131,880

Therefore, the approximate present value of the benefits is $122,881 (rounded to the nearest dollar), which is closest to option B.

Cheryl Peck Purchased a Computer Network for Her Classroom