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 $76k 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 $117k per year until you retire at age 55. The master’s program you are interested in costs $22k per year.

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

Required: At an opportunity cost of 7%, determine the percentage difference between your most and least profitable alternatives, with the least profitable option as the basis for your calculation.


Answer% Intermediate calculations must be rounded to 3 decimal places (at least). Input your answer as a percent rounded to 2 decimal places (for example: 28.31%).

Answer 1

Sol:

1st Alternative

If you choose to remain at your job.

Cash flow per period (C) = $76k

Interest rate (r) = 7%

Period (n) = 55 - 30 = 25 years

PV of annuity = C x (1 - (1 + r)^-n) / r

PV = 76 x (1 - (1 + 7%)^-25) / 7%

PV = 76 x (1 - (1 + 0.07)^-25) / 0.07

PV = 76 x (1 - (1.07^-25) / 0.07

PV = 76 x 11.654

PV = $885.672k

2nd Alternative

If you go back to university for master program:

Cash flow per period (C) = $117k

Interest rate (r) = 7%

Period (n) = 55 - 30 = 25 years

PV = 117 x (1 - (1 + 7%)^-25) / 7%

PV = 117 x (1 - (1 + 0.07)^-25) / 0.07

PV = 117 x (1 - (1.07^-25) / 0.07

PV = 117 x 11.654

PV = $1363.469

We have to discount PV by 2 years

PV = 1363.469/1.07^2

PV = $1190.907

2 years Master Program cost = $22k per year

= 1190.907 - 22 - (22 / 1.07) = $1148.346

Opportunity cost will be $1148.346 - $885.672 / $885.672 = 0.296582 or 29.66%

Percentage difference between your most and least profitable alternatives is 29.66%

Therefore pursuing master program will increase the income by 29.66%, hence it is feasible and make sense.