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. See Hint Part 1 (1 point) Assume the interest rate is 7%. If you were to attend college, the present value of your tuition payments would total $ See Hint (1 point) 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 $ See Hint (1 point) Part 3 The net present value of going to college is $ See Hint (1 point) 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

Part 1

Present value of tuition payments:

= 10,000 + (10,000 / (1 + 7%)) + (10,000 / 1.07²) + (10,000 + 1.07³)

= $36,243.16

Part 2

This is a deferred perpetuity because you only start getting paid when you start work 4 years later:

Present value of deferred perpetuity:

= Amount / Discount rate ( 1 / (1 + discount rate)^n

= 50,000 / 0.07 * (1 / 1.07)⁴

= $544,925.15

Part 3

Net present value of going to college:

= Present value of salary - cost of college

= 544,925.15 - 36,243.16

= $508,681.99

Part 4

This is not a deferred perpetuity so your present value is:

= Amount/ discount rate

= 34,000 / 0.07

= $485,714.29