Question

It is December 2016 and you are thinking about whether to start a Master’s program or

begin work come Jan. 1. Either way, you plan to work for 30 years before retiring (so you

will retire at t=30 if you don’t go to school and t=31 if you do go to school).

If you were to start work now you expect your starting salary to be $50,000, with the first

payment arriving exactly one year from today. Due to the poor economy you don’t foresee

a raise for the first 3 years, but after the 3

rd

year (i.e., after t=3) you expect to get a 15%

raise. You expect another 25% raise after the 10

th

year (i.e., after t=10) and constant salary

after that until your last payment at t=30.

The master’s program costs $70,000, paid immediately, and takes exactly 1 year. With a

master’s degree you believe that your starting salary will be $65,000 per year. You also

think that you will learn some skills that will increase your bargaining power in salary

negotiations. Thus, you believe that if you get a Masters your salary will grow steadily at

3% per year for your entire working life.

Assuming the discount rate is 10% and that all wages are paid at the end of the year, what

is the difference in present value between your wages going to school and not going to

school? If all you care about are these wages should you go to school? What is the most

you would be willing to pay for school under the wage assumptions in the problem?

Answer 1

If you start working immediately:

Year (n)	Period	Annual wage a	PV of wage at time t b	PV at t = 0 c
1-3	3	50,000	1,24,342.60	1,24,342.60
4-10	7	57,500	2,79,934.08	2,10,318.62
11-30	20	71,875	6,11,912.39	2,35,918.72
			PV of wages	5,70,579.94

Note:

a). Calculate the increases in annual wage.

b). Calculate the Present Value of the annual wages, at the starting point when wage changes. So, for example, annual wage becomes 57,500 at Year 4 and holds till Year 10. So, Present Value of this annual wage at the start of Year 4. Use PV function in excel.

c). Now, the PVs at the starting points have to be discounted back to the present time which is Year 0. So, use the computed PVs above, as FV and use the PV function to compute this. Example, 279,934.08 at start of Year 4, discounted for 3 years at 10% to get to Year 0. We get 235,918.72

If you do a Master's degree and then start working:

This is a growing annuity problem. It can be calculated as

P = 65,000; r = 10%; g = 3%; n = 30

So, PV of wages at the start of Year 1 = 65,000/(10%-3%)*[1-((1+3%)/(1+10%))^30]

= 799,404.45

Now, this has to be discounted for 1 more year to get to Year = 0

So, 799,404.45/(1+10%) = 726,731.32

This is the PV of the wages which you will earn if you do a Master's and then start working. (Note: this does not take into account the fee for the Master's program as it is not mentioned in the problem that the net wages have to be compared.)

1). Difference in PVs of wages = 726,731.32 - 570,579.94 = 156,151.38

2). If you care only about the wages then you should go to school as your earnings will be much higher.

3). The maximum that you should be willing to pay for the Master's fee is the difference between the two wages which is 156,151.38. If school fee exceeds this then it will be better to go to work directly.