Question

Suppose you are deciding whether you should go to college. If you go to college, you will pay $10,000 total in tuition, textbooks, and room and board every year for 4 years, with the first payment being made immediately and then the next three payments 1 year apart. Upon graduating, you expect to get a job earning $50,000 per year for the next 40 years. Assume that your first paycheck arrives exactly 1 year after you start working and you continue getting paid annually thereafter. Also assume that there are no raises in that particular field. If you do not go to college, you can start working immediately. The pay, however, is lower. You would expect to work for 44 years and earn $34,000 per year, with your first paycheck arriving exactly 1 year from now, and you continue getting paid annually thereafter. For the questions below, round all numbers to two decimals.
Part 1 Assume the interest rate is 7%. If you were to attend college, the present value of your tuition payments would total _______ $
Part 2 Suppose you go to college and graduate after 4 years. Because you will work for 40 years after you graduate, and because 40 years is a long time, treating the stream of payments as a perpetuity will provide a reasonable approximation of the present value of the payment stream. The present value of your annual earnings of $50,000 as a college graduate is _______$
Part 3 The net present value of going to college is _____$
Part 4 If you do not go to college, you will be working even longer than before. Once again, you may treat the stream of income from your job as a consol or perpetuity. The present value of your annual earnings of $34,000 if you don't go to college is ________$

Answer 1

Answer:

Part 1. If you were to attend college, the present value of your tuition payments would total _______

$33,870.00

Part 2. The present value of your annual earnings of $50,000 as a college graduate is _______

$741,407.10

Part 3 The net present value of going to college is _____

$707,537.10

Part 4. The present value of your annual earnings of $34,000 if you don't go to college is ________

$719,270

Explanation:

a) Data and Calculations:

Annual Tuition, etc = $10,000

Number of college years = 4

Interest rate = 7%

Present Value Annuity Factor = 3.387

PV of $10,000 = $10,000 * 3.387 = $33,870

Annual salary after college in 4 years' time = $50,000

Number of years earning salary = 40 years

Present value annuity factor = 19.434 * 0.763 = 14.828142 (reduced to earnings after 4 years)

PV of $50,000 = $50,000 * 14.828142 = $741,407.10

NPV of going to college = $741,407.10 - $33,870 = $707,537.10

Annual salary without college = $34,000

Number of years earning salary without college = 44 years

Present value annuity factor = 21.155

PV of $34,000 in perpetuity = $34,000 * 21.155 = $719,270