A university offers its students three financing options for a degree course that lasts exactly three years.Option AFees 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 BThe 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 payments made annually in arrear.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 earningswill 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. ii)Calculate the present value of the payments due under option B. 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. The university is concerned that this scheme exposes it to considerable financial risk.iv)Explain three risks which the university faces.
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 payments made annually in arrear.
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
i)
Calculate the present value of the payments due under option A.
ii)
Calculate the present value of the payments due under option B.
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.
The university is concerned that this scheme exposes it to considerable financial risk.
iv)
Explain three risks which the university faces.
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