Question

A student in economics has completed her undergraduate degree and has been accepted into a one-year postgraduate business program. Upon completion of this degree she will earn an additional $3,000 a year for each of the next 40 years. She will give up $19,500 income that she would otherwise earn and sustain additional costs of $2,000 for educational materials such as books. She cares only about the financial implications of her decisions.

(a) If the interest rate for borrowing and investing is the same, at amount 8%, should she accept the offer into the business program? Explain.

(b) What is the internal rate of return of attending this business program? How does your answer indicate conditions for which it is worthwhile to attend this program?

(c) Do your answers to parts (a) and (b) depend on wether this individual would need to borrow money or use any savings she has? Explain.

(d) How does this example explain the phenomenon that attendance in post- secondary programs tends to rise when the unemployment rate rises?

Answer 1

a)

Additional income per year=R=$3000

Number of periods=n=40

Rate of interest=i=8%

Present worth of additional income=3000*(P/F,0.08,40)=3000*11.9246=$35773.80

Present worth of Cost=Foregone amount of salary+Cost of study=19500+2000=$21,500

(Present worth of costs and additional income are calculated at the end of year 1. So, can be compared)

Present worth of additional income is more than the present worth of cost. So, student should go for degree.

b)

Internal return is the rate at which present cost of program is equal to present worth of additional income i.e.

3000*(P/F,i,40)=21,500

So, (P/F,i,40)=21500/3000=7.1667

We shall not able to solve this interest factor with the help of formula. So, we can use MS Excel or Financial calculator for this purpose. I would go for try and error method

I would estimate interest factor at 12%, 13% and 14%

Similarly we can find that (P/F,0.14,40)=7.1050

Desired interest factor (7,1667) lies between 8.2438 and 7.6344. We can see that our internal rate of return is close to 13% and is between 12% and 13%.

Let us further estimate at i=13.9% and 13.8%

Desired interest factor (7,1667) is quite close at 13.9%. MS Excel gives IRR=13.88%

If interest rate is below 13.9% it is advisable to go for degree otherwise not.

c)

There will definitely be a difference in saving return and borrowing interest rate. But saving or borrowing does not matter much. If a student goes for study at savings, he has opportunity cost of interest income and if he takes loan, he has a direct cost of borrowing. Rate of interest on savings or borrowings will make a difference.

d)

In the case of unemployment, attendance in post secondary programs increases. I may be because

1) Opportunity cost of study is less due to

a) Personal is unemployed (he has no income to loose) or

b) Personal is underemployed (he has less income to loose)

2) Increase in productivity due to further study

A degree holder will definitely have a edge over non-degree holder. Chances of getting employed (even underemployed) after degree are higher.