Student loan repayments & ‘present value’

Say you want to borrow a tenner from me. I agree, but you can either repay £11 in two years or £13 in ten. Which would you choose?

If you choose the first because it’s a lower total amount, then you may not have considered the ‘present value’ of the deal – how to calculate what a future payment, or flow of payments over time, is worth in today’s terms.

The above example is trivial but let’s add a few zeros to those figures and a few years. What’s preferable repaying £110 000 in 22 years or £130 000 in 30? Bit trickier? Especially if you have to make a series of fluctuating (income-contingent) monthly payments rather than a one-off lump sum at the end of the period.

Unfortunately, a report published by Political Quarterly and covered by Times Higher Education (£) and the Daily Mail ignores this whole aspect, with headlines reading respecively ‘Poor to face bigger student loan bill than rich’ and ‘Middle-class women face unfair tuition fees burden: Squeezed graduates face paying more than highly-paid peers or low earners’.

Here’s some figures quoted:

In banking, finance and insurance, for example, women’s starting salaries are around £22,500 compared to £29,000 for men. Based on a debt of £43,500, the woman would repay £131,416 over 30 years, after which £31,796 would be written off. But male peers would pay £109,766 and be debt free after 21 years and ten months.

Which brings us back to the opening questions: which is ‘more’, £130 000 over 30 or £110 000 over 22 years?

Perhaps the first question is: what’s inflation predicted to be? The official ‘ready reckoner’ model, on which the research is based, has been built with an assumption of RPI running at 2.75% each year (and earnings growth in excess of that so that in 2041 the repayment threshold is £70 000 compared to £21 000 in 2016).

These figures should make one pause and ask what does repayment measured at £100 000+ over 30 years even mean? Especially as the assumptions in this model – put together in 2009/10 – have since diverged from economic reality.

One way is to do a crude calculation to factor out that inflation figure of 2.75% (as if it were a lump sum rather than the aggregate of a stream of payments), when you  find that the ‘present value’ of £130 000 over thirty years is less than        £110 000 over 22 years: £58 235 to £60 432. At an inflation of 2% it might be more      (£72 550 to £71 000), but it’s the former figure that’s been used in the generation of those numbers in the first place.

All a lot trickier than the headlines and the study suggest. If you want a more informed analysis on these distributions then I can recommend that Institute for Fiscal Studies’s analysis, The distributional impact of the 2012-13 HE Funding Reforms (July 2012).