Question

5. Assume the cost of college this year, and each of the next 3 years is $5,000. Your opportunity cost in foregone earnings if you go is $22,000 each of these years. The benefits accrue over your lifetime, as an increase in earnings over the alternative of $30,000 a year for 40 years starting in year 4. Assume the interest rate is 5%.

a. Calculate the present value of going to college. Should you go? Be sure to show your work.

Answer 1

Cost of going to college (4 years) = $5,000 per year

Opportunity cost forgone in each of 4 years = $22,000 per year

Total costs = $5,000 + $22,000 = $27,000

At the interest rate of 5%, the present value of the above costs = $27,000 x (P/A, 5%, 4) = $27,000 x 3.546 = $95,742

Benefits are accrued starting from year 4 as an increase in earnings of $30,000 for 40 years

The benefits must be first discounted as worth at the end 3 years and then this future worth has to be converted to present worth

Present worth of benefits = $30,000 x (P/A,5%,40) x (P/F,5%,3) = $30,000x17.159x0.8638 = $444,658

Therefore, the net present value of going to college = PW(benefits)-PW(costs) = $444,658 - $95,742 = $348,916 (>0)

As the PW of going to college is positive, you should go to college.