Question

A student in economics has completed her undergraduate degree and has been accepted into a one-year postgraduate business programme. Upon completion of this degree she will earn an additional $2,000 a year for each of the next 50 years. She will give up $18,000 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 5%, should she accept the offer into the business programme? Explain. (b) What is the internal rate of return of attending this business programme? How does your answer indicate conditions for which it is worthwhile to attend this programme?

Answer 1

Assume year end cash flows

a)

Opportunity cost=$18000

Education material costs=$2000

Total Cost=$18000+2000=$20,000

Let us calculate the present worth of additional $2000 to be received for 50 years

PW=2000*(P/A,5%,50)

PW=2000*18.25592546=$36,511.85

Since both the figures are evaluated at the end of year 1 horizon. These an be compared.

PW of additional income is less than total cost. She should accept the offer.

b)

It means we need to find i at which

2000*(P/A,i%,50)=20000

(P/A,i%,50)=20000/2000=10.00000

There is no direct way of calculating i in this case.

We can use MS Excel or financial calculator to get i.

I would use try and error method

So, Let us calculate (P/A,i%,50) at 6%,8%,10

We can see i lies between 8% and 10%. It is quite close to 10%

So, let us again calculate at 9.9%

We take is as our closest i.

So, i=9.9% (MS Excel gives figure as 9.9021%)

We can say IRR in our case is 9.9%. If interest rate is below 9.9% it is worthwhile to attend the program, otherwise not.