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 $74k 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 $115k per year until you retire at age 65. 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 1

Sol:

Alternative 1

If he choose to remain at his job:

Cash flow per period (C) = $74k

Interest rate (r) = 7%

Period (n) = 55 - 30 = 25 years

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

PV = 74 x [(1 - (1 + 7%)^-25) / 7%]

PV = 74 x [(1 - (1.07^-25) / 0.07]

PV = 74 x 11.65358

PV = $862.37k

Alternative 2

If he go back to university for further studies:

Cash flow per period (C) = $115k

Interest rate (r) = 7%

Period (n) = 65 - 30 = 35 years

PV = 115 x [(1 - (1 + 7%)^-35) / 7%]

PV = 115 x [(1 - (1.07^-35) / 0.07

PV = 115 x 12.94767

PV = $1488.98k

We have to discount PV by 2 years

PV = 1488.98/1.07^2

PV = 1300.53k

Master program cost for 2 years = 22k per year

= 1300.53 - 22 - 22 / 1.07 = $1257.97

Opportunity cost will be $1257.97 - $862.37/862.37 = 45.87%

Percentage difference between your most and least profitable alternatives is 45.87%

Therefore even after considering university cost, pursuing master program will increase the income by 45.87% , hence its is feasible and make sense to study further.