A note on discount rate changes

I promised a short note on IFS’s analysis of discount rate changes. I have previously offered a brief explainer here on how discount rates work to convert a projected stream of cash payments – that come in over several years  – into a net present value today (or 2016).

The basic idea is that £1 000 received or paid in ten years’ time is not worth £1 000 today. Think about swapping some cash in your pocket for a promise from me to pay you £100 in 2025. How much might it be worth? A number of factors obviously come into play here, but when we are talking about the government and student loans a rate of RPI plus 2.2 per cent is used to discount all future repayments.

If RPI  is projected to be 1.8%, then the government discounts a payment made a year in the future by roughly 4% (1.018 * 1.022 – that ‘plus’ is a 2.2% increase on top of one of 1.8%). So a repayment of £1.04 made in 2017 is worth £1 in 2016 NPV terms. And so on – the rate is applied to a repayment received for each year away from 2016 that transaction is projected to occur (e.g. for five years away the rate would be 1.04 to the power of 5 – so £1.22 then would be worth £1 today).

It is this idea that underlies all discussion about how much the government ‘loses’ on student loans: it sends money out into the world today and repayments come back over the next few decades; how do you compare what is issues compared to what it gets back? What sum today (or in 2016) would be the equivalent of all the associated repayments generated over the lifetime of the loans?

Similarly, if we are discussing the impact of government changes to borrowers then the sums expressed, say £13 000 worse off, are also discounted in this way in reach an NPV figure using the government’s preferred measure.

In its analysis from Tuesday, the IFS considered a fourth measure proposed by government (subject to Treasury review). The discount rate would be brought into line with the government’s cost of borrowing. IFS suggest this might be around RPI plus 1.1%.

No change to projected repayments occurs here, only how those repayments are to be valued. Lowering the rate by which future payments are discounted would improve the overall value of the cohort’s aggregated repayments such that the government ‘contribution’ to HE drops dramatically from £7bn (after the other three changes) to £4.6bn. You can see how this presentational effect might alter the rather ill-informed debate we currently have around the sustainability of English HE (a drop in the resource accounting and budgeting charge or 15 percentage points according to IFS!).

Using a discount rate of RPI+1.1% (instead of RPI+2.2%) would increase the value of repayments from an average of £30,700 per student to an average of £37,900 per student in 2016 money when looking at the three policies combined.

That is, an additional £7 000 in value is recognised by altering the discount rate.

In many ways, this would merely be a presentational matter that improves the figures in the debate. No extra repayments come in and BIS’s departmental budget would be revised down accordingly to accommodate the change. Lower losses, so less budget is needed to cover those losses.

But you might already have noticed something – the government’s discount rate may not tally with your own. Using something closer to RPI plus 1.1% may better reflect how repayments are felt as an impact on individuals. Alternatively, simply factoring out graduate earnings growth from the repayments model (which IFS assumes to be RPI plus 1.5% after 2020) may give an indication of what future payments represent in relation to earnings.

From that perspective, the costed impacts of the government’s proposals on individuals which we looked at in the previous two posts may be too low.

On a very simplified illustration, say you are required to pay £1 000 every year for thirty years starting next year.

That would be £30 000 in cash terms but with a discount rate of RPI plus 2.2% those repayments would be worth about £16 800 NPV.

Using RPI plus 1.1% would instead value those repayments at the equivalent of £19 300 today. At RPI plus 1.5% we’d be looking at a little more than £18 300.

If then the government told you that your repayments had to increase by £500 per year, then using their current discount rate the new level of repayments would be worth £25 185 to them, an increase of nearly £8 400.

But if you use the lower two discount rates, then that increase would be £10 620 at the RPI plus 1.5% rate and over £14 000 at RPI plus 1.1%.

Whatever your preference, you would be wrong to consider the government’s proposals as having minor implications. In return for increased cash while studying (£766 if away from home in London), the government’s proposed changes to the loan scheme may leave you facing much, much higher repayments.