Question

Cindy, who will graduate from college in a year is deciding whether to go on for her master’s degree which will last two years. She figures that if she takes a job immediately, she can earn $40,000 per year in real terms for the remainder of her working years. If she goes on for two more years of graduate study, however, she can increase her earnings to $50,000 per year. The cost of tuition is $40,000 per year in real terms. Is this a worthwhile investment if the real interest rate is 5% per year?—(Assume she will retire after working for 40 years. AND SHOW YOUR WORK)

Answer 1

Option A:

Taking a job immediately:

Earning Per year	40,000	Given in question
Working years	40	Given in question
Interest rate	5%	Given in question
Discount factor for 40 years at 5% (year 1 to 40)	17.1591	((1-(1+5%)^-40))/5%
Present value of earnings	686,363	40000*17.1591

If Cindy takes up the job immediately, her present value of earnings will be $686,363

Note:

1. She will work for 40 years

2. She will get her earnings from year 1 to year 40

Option B

Two more years of graduation study:

Cost of tuition	40,000	Given in question
Tuition years	2	Given in question
Earning Per year	50,000	Given in question
Working years	40	Given in question
Interest rate	5%	Given in question
Discount factor for 2 years at 5% for year 0 and Year 1	1.9524	((1-(1+5%)^-1))/5%+1
Present value of cost of tuition	78,095	40000*1.9524
Discount factor for 40 years at 5% from years 2 to 41	16.3420	(((1-(1+5%)^-(40+1))/5%)-(((1-(1+5%)^-1))/5%))
Present value of earnings	817,099	50000*16.3420
Net present value of earnings	739,004	817099-78095

If Cindy goes on for two more years of graduation study and takes up the job then, her present value of earnings will be $739,004.

Notes:

1. Tuition fees of $40,000 to be paid immediately (in year 0) and another $40,000 in year 1

2. She will work for 40 more years after completing her graduation -  that is, her earnings of $50,000 per annum will be from year 2 to year 41.

Recommendation:

Snce the present value of earnings if she takes graudation for two years and then taking up job of $739,004 is more than the present value of earnings of $686,363 if she takes immediately, Cindy can go on doing the graudation study for 2 years and then taking up the job.