Question

Sandra and Michael Wilson are the parents of Rory who just turned 5 years old (coincidentally on the same date that primary, secondary and university academic years commence). They own a four-bedroom home in Edinburgh. Sandra is a partner in a local dental practice and Michael is a stay at home dad. Sandra earns £100,000 a year (after tax).

Now that Rory is starting primary school, thoughts have turned to saving for his education. Rory is enrolled to attend a state (i.e. non fee-paying) primary school. The Wilsons plan to send Rory to a private secondary school (when he turns 11). The school is prestigious and its fees are set accordingly. Currently tuition is £20,000 per school year and are projected to rise at the rate of inflation. Currently around 2% per annum.

The Wilsons hope that Rory will subsequently attend their alma mater, Oxford University when he turns 18. Most undergraduate courses at Oxford have a four academic year duration. Undergraduate fees at Oxford are currently £9250 per annum and are projected to rise faster than inflation, at a rate of 4% per annum. In addition, as Rory would be living away from home if he attended Oxford, his parents envisage that his living costs (primarily student accommodation and food) would amount to £10,000 per annum (expressed in today’s prices). These living costs are projected to increase at the rate of inflation, 2% per annum.

Using a discount rate of 7%, what is the present value of the combined projected spend on Rory’s private school fees, university tuition and living costs? (Assume that all fees and living costs are incurred at the beginning of each academic year e.g. Rory’s first school fee invoice will arrive in exactly 6 years which coincides with his first day at secondary school when he turns 11).

The Wilsons plan to fund the expenditure on private school fees from Sandra’s income. They would however like to start investing today in a fund that would be used to pay Rory’s university fees and living costs. They would like to make an equal annual payment into that fund every year (starting in one years’ time) with a view to accumulating £120,000 by Rory’s 18th birthday. This £120,000 would then be drawn down over Rory’s time at Oxford to meet expenses as they come due.

How much money would they have to deposit into the fund every year (with the first payment one year from now) to meet that target assuming a conservative fund return estimate of 3% a year. Will the accumulated amount be enough to cover the joint fees and living costs during Rory’s time at Oxford?

Answer 1

1). Present Value of all fees and living costs = 135,947.70

Formula	Private school fees:
	Current fees/year (F0)	20,000
	Inflation rate (g)	2%
F0*(1+g)^6	Fees after 6 years (F6)	22,523.25
	Number of years of school (n)	7
	Discount rate (i)	7%
Growing annuity due: (F6/i-g)*(1-((1+g)/(1+i)^n)*(1+i)	PV of fees when private school starts (PV6)	1,37,203.63
PV6/(1+i)^6	PV of private school fees now	91,424.57
	University tuition fees:
	Current undergrad fees (F0)	9,250
	Growth rate (g)	4%
F0*(1+g)^13	Fees after 13 years (F13)	15,401.93
	Number of years of college (n)	4
	Discount rate (i)	7%
Growing annuity due: (F13/i-g)*(1-((1+g)/(1+i)^n)*(1+i)	PV of undergrad fees when college starts (PV13)	59,064.83
PV13/(1+i)^13	PV of undergrad fees now (PV0)	24,509.80
	Living costs in Oxford:
	Current living costs (F0)	10,000
	Growth rate (g)	2%
F0*(1+g)^13	Living costs after 13 years (F13)	12,936.07
	Number of years of costs	4
	Discount rate (i)	7%
Growing annuity due: (F13/i-g)*(1-((1+g)/(1+i)^n)*(1+i)	PV of living costs when college starts (PV13)	48,229.00
PV13/(1+i)^13	Pv of living costs now (PV0)	20,013.32
School fees PV0 + Undergrad PV0 + Living costs PV0	Total Present Value of all expenses	135,947.70

2). The fund has to equal 120,000 in 12 years time as they will start investing after 1 year when Rory is 6 years old.

FV = 120,000; PV = 0; rate = 3%; N = 12; Type = 1 (or mode = Beg.), CPT PMT.

PMT = 8,209.18

They would need to make annual payments of 8,209.18 to have a fund of 120,000 when Rory turns 18.

3). The total present value of tuition fees and living costs (when Rory turns 18) adds up to

59,064.83 + 48,229 = 107,293.83 (Refer to the table in part 1.)

So, the fund will be sufficient to cover college expenses.