Question

Suppose that, at age 30, you might wish to leave your job and pursue a master’s degree. If you choose to remain at your job, your employer would pay you $75k per year until retirement, at age 55. If you go back to the university, you would have to sacrifice 2 years of income, but once you graduate, you would receive $113k per year until you retire at age 65. The master’s program you are interested in costs $22 per year.

Note: The term “k” is used to represent thousands (× $1,000).

Required: At an opportunity cost of 9%, determine the percentage difference between your most and least profitable alternatives, with the least profitable option as the basis for your calculation.

Answer 1

The present value of remaining at the job will be = 76000/1.07^1 + 76000/1.07^2 + ... + 76000/1.07^25 = 885672.3

The value of the studying option will have three cash flows. Two will be the fees you will be paying in each year and the third will be the discounted value of the 115k each year. The third cash flow will be = 115000/1.07^1 + .... + 115000/1.07^33 = 1466686.

Now, the present value of the second option will be = -22000/1.07 - 22000/1.07^2 + 1466686/1.07^3 (In the question, we have been given that the fees is $22 instead of $22k. We are assuming it a typo).

PV = -22000/1.07 - 22000/1.07^2 + 1466686/1.07^3 = 1157476.268.

Hence, studying further is the more profitable choice. The required percentage figure is (1157476.268-885672.3)/885672.3 = 30.6889% = 30.69%