# Why do folks pay university fees upfront?

In my tutorials last week, we used the HECS scheme to practice calculating net present value – the true economic cost of financial decisions. I promised my students that I would make the simple analysis we did a little more realistic, so today’s post is really a public service announcement on the different costs of paying university fees. There is however a clear winner and it appears not many people are aware this. Those who use the HECS loan for university fees are at least $1980 better off than those who pay the fees upfront. What I haven’t figured out however, is why anyone pays upfront. What is net present value? When costs (or benefits) accrue over a long time frame, it can be difficult to compare their true values. For example, one would expect that a$100 fee today would be less preferred to a $100 fee next year. Among other reasons, this is because if you choose to pay the$100 fee next year, you can save the $100 in a bank today, receive an interest payment on that money and pay the fee next year, leaving you with the interest for beer and skittles. More generally, to compare costs that occur in the future with those today, we need to discount the value back according to the interest rate we can receive. This gives us what we call the net present value – a measure of the costs of a particular decision in “today’s dollars”. So let’s calculate the net present value of the two choices before us: when Australian students attend an Australian university they can either pay the fees upfront and receive a 10% discount, or defer the payment via the HECS scheme which offers a 0% real interest rate loan (i.e. the real value of the loan doesn’t appreciate over time). Consider a typical 3 year undergraduate degree – for the representative example we will use the prestigious ANU Bachelor of Economics. This costs a student$5132 per semester for the four courses required. For the interest rate, I think 3% per annum (1.5% per semester) is a reasonable, lower bound on the interest rate you can find, whether it be in a savings account, a trust or even stocks, all of which will should yield higher returns. This gives us enough information to find the discounted cost of paying upfront:

$C_{U} = 0.9 \times 5132 + \frac{0.9 \times 5132}{1.015} + \frac{0.9 \times 5132}{(1.015)^2} + \ldots + \frac{0.9 \times 5132}{(1.015)^5}$

$C_{U} = 26708.88$

The slightly more difficult calculation is the cost of HECS scheme. The loan is paid back from taxable income when the student graduates and begins to earn over $54000 per year. If we assume the student is offered a graduate job in their fourth year paying a salary of$70000, this means they will forgo 5.5% of their income each year until the debt is repaid – $3850 a year for seven years and a final payment of$3842. Note that if we reasonably alter this assumption by delaying their employment or lowering their expected salary, this will only benefit the HECS scheme, and thus we have an effective upper bound for the cost of deferral. The net present value of this bound is then:

$C_{H} = \frac{3850}{(1.03)^{4}} + \frac{3850}{(1.03)^{5}} + \ldots + \frac{3850}{(1.03)^{10}} + \frac{3842}{(1.03)^{11}}$

$C_{H} = 24726.67$

Clearly it is far cheaper to pay through the loan in today’s dollars (we could equivalently find net future value which wouldn’t alter the findings of this analysis). Another way to read these values is to interpret them as the amount you need to invest on day one to pay for your university fees. Paying upfront is equivalent to putting $26710 in a bank account and taking out of that account at the beginning of each semester; repaying the HECS loan is equivalent to putting only$24730 in the same account and only being taken out of when you begin to earn over $54000 per year. That is almost a$2000 – 7.5% – saving by taking the loan rather than paying up front. And this is a lower estimate; if you think you think it will take longer to find a job, if you predict your won’t be paid $70000 straight out of university or if you think you can get more than a 3% return on your savings, then you stand to save much more by taking out a HECS loan. Typically, upfront payments are paid by parents, wanting to give their children a debt free future. But those parents can do much better – if they set up a trust that their children can use to pay back their loan when they begin to earn income, they would be$2000 wealthier. They could then give that cash to their children, put it in the trust for future use, or better still, spend it on themselves when the kids move away to uni.

This should be intuitive – a 0% loan is a massive hand out from the government especially if this loan isn’t paid back for a long time. The 10% discount sounds attractive, but it would need to be at least 5 percentage points higher to make upfront payments even mildly reasonable. For me then, the decision seems simple; choose the HECS scheme and save a couple of grand. Have I missed something?

EDIT (20.07.15): Reading back over this, a month later, I realise I may have been a little melodramatic. Perhaps a bigger take home from this discussion is how a simple analysis, involving a pencil, calculator and a rudimentary understanding of net present value, can save you a lot of money.