Suppose that if you hadn’t gone to college you could have found a full-time job

Question

Suppose that if you hadn’t gone to college you could have found a full-time job that paid $50,000. Suppose that you will graduate UCI on time (i.e., 4 years after you left high school) and find a full-time job that pays $70,000 per year. (a) Imagine that you have just left high school and are weighing up the pros and cons of going to UCI (you have your UCI offer but don’t need to take it). You know that you can earn $50,000 now. You also know that if you go to UCI you will be able to find a job that pays $70,000 when you graduate, in 4 years time. At the time that you left high school, what was the present value of the lifetime earnings associated with working in the $50,000 job and what was the present value of the lifetime earnings associated with going to UCI and then getting the $70,000 job? Assume that in both scenarios your pay will stay fixed forever and you will live forever(!). Assume that the interest rate is 5%. [Hint: its important to remember that under the UCI option you don’t start earning the $70,000 for 4 years]. [3 points] (b) More realistically, suppose that you work for 50 years under the non-UCI option and 46 years under the UCI option (i.e., you retire at age 68 whichever option you choose). Now recalculate the present values that you calculated in part (a). Does it change which option offers the highest value of lifetime earnings? Say yes or no and explain. [4 points] [Hint: you might like to adapt the following formula for the PV of an earnings stream y received for t years (given an interest rate r)

(c) Suppose it seems like UCI is the better option in terms of the present value of lifetime earnings, but you realize
that you need to fund your living expenses while at UCI. Suppose your parents will give you a loan of $10,000
for each year that you are at UCI, but require that you pay it back afterwards at an annual interest rate of
5%. Does that change the present value of lifetime income associated with the UCI option? Say yes or no
and explain. [2 points]
(d) Suppose that your parents can’t afford to give you a loan but your Dad runs a business and says that you can
work 15 hours a week for him while you are in college, and he will pay you $10,000 per year. Does that change
the present value of lifetime income associated with the UCI option? Say yes or no and explain.

Explanation / Answer

Answer-a The rate of interest is = 5% Salary received after the course completition = $70,000 Time = 4 years Therefore present value = $57,589.17 and the present value of the current salary = $50,000 Therefore the option to Join the course and take salary of $70000 is better. Answer-b For Non-UCI option number of years = 50 salary = $50,000 interest rate = 5% Therefore PV = $912,796.27 For UCI option number of years = 46 salary = $70,000 interest rate = 5% Therefore PV = $1,251,604.65 Here also UCI option is more beneficial. Answer-c For UCI option Loan amount per year = $10,000 number of years = 4 Rate of interest = 5% So the PV of cost burden = $35,459.51 Therefore NPV of UCI option = $1,251,604.65 - $35,459.51 = $1,216,145.15 Which is still a better option. Answer-d Yes in that case the PV of UCI option will increase.

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