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 12 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 by the classroom sessions in each year. Using the formula for present value of a perpetuity, we can find the present value of the cash flow in each year as follows:

Year 1: PV = $500 / 1.12 = $446.43 per student
Year 2: PV = $500 / (1.12^2) = $397.99 per student
Year 3: PV = $500 / (1.12^3) = $355.77 per student
Year 4: PV = $500 / (1.12^4) = $318.50 per student

Total PV of benefits = (50 x $446.43) + (75 x $397.99) + (100 x $355.77) + (150 x $318.50) = $67,735.47

To check the approximation, we can use the formula for present value of an annuity to get:

PV = $500 x [(1 - (1/1.12^4))/0.12] = $135,470.87

Therefore, the best choice is B, $135,471, because it is the closest approximated value to the calculated present value of the benefits.

Cheryl Peck Purchased a Computer Network for Her Classroom