Question Two

A university offers its students three financing options for a degree course that lasts exactly three years.

Option A

Fees are paid during the term of the course monthly in advance. The fees are $10,000$ per annum in the first year and rise by $5\%$ on the first and second anniversaries of the start of the course.

Option B

The university makes a loan to the students which is repaid in instalments after the end of the course. The instalments are determined as follows:

No payments are made until three years after the end of the course.

Over the following $15$ years, students pay the university $1,300$ per year, quarterly in advance.

After $15$ years of payments, the quarterly instalments are increased to $1,500$ per year, quarterly in advance.

After a further $15$ years of payments, the quarterly instalments are increased to $1,800$ per year, quarterly in advance, for a further $15-$year period after which there are no more payments.

Option C

Students pay to the university $3\%$ of all their future earnings from work, with the paymen made annually in arrear.

$2$

A particular student wishes to attend the university. He expects to leave university at the end of the three$-$year course and immediately obtain employment. The student expects that his earnings

will rise by $3\%$ per annum compound at the end of each year for $10$ years and then he will take a five$-$year career break.

After the career break, he expects to restart work on the salary he was earning when the career break started. He then expects to receive salary increases of $1\%$ per annum compound at the end of each year until retiring $45$ years after graduating.

The student wishes to take the financing option with the lowest net present value at a rate of interest of $3\%$ per annum effective.

i$)$ Calculate the present value of the payments due under option A$.[4$ marks$]$

ii$)$ Calculate the present value of the payments due under option B$.[5$ marks$]$

iii$)$ Calculate the initial level of salary that will lead the payments under option $C$ to have the lowest present value of the three options.

$[8$ marks$]$

The university is concerned that this scheme exposes it to considerable financial risk.

iv$)$ Explain three risks which the university faces.

$[4$ marks$]$