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The loss on loans – errors in the media coverage

March 22, 2014

The RAB charge is meant to cover the estimated loss on the loans the government issues allowing for the fact that the cash that comes back does so over several years. The government thinks that it will receive back 55p for every £1 in net present value terms.

£1 today is not the same as £1 received next year and again those both differ in value from £1 received in ten years’ time.

The government uses a ‘discount rate’ to measure the worth of £1 received in the future.  A discount rate can cover the cost of borrowing, inflation, a risk premium or reflect the value of alternative uses to which I can put that £1. The government’s current discount rate is RPI + 2.2% per year.

In terms of student loans, the government believes that the value of all the discounted cash streams coming back related to this year’s loan issue is the equivalent of swapping £1 for 55p today. It loses 45p – hence the RAB charge.

Let me give a simplified example to show what we then mean by loss.

I agree to lend you £10 in return you will pay me £1 each year for 10 years starting next year. Nominally I have got back the same payments as I lent – £10. But I use a discount rate of 5% per year to assess the value of each payment in today’s terms.

£1 received in one year is worth 95p; £1 received in two years’ time is worth 5% less again – a little over 90p; and so on.

Year 1 2 3 4 5
Payment 1 1 1 1 1
Value £0.95 £0.91 £0.86 £0.82 £0.78
Year 6 7 8 9 10
Payment 1 1 1 1 1
Value £0.75 £0.71 £0.68 £0.64 £0.61

So £1 received in year 10 is worth 61p today.

I then aggregate all those discounted cash flows to give a total of £7.72. I have lost £2.28 on the deal. Effectively, I need a RAB charge of 23% to cover that estimated loss. (I have to find £2.28 from elsewhere to cover the deal).

So, don’t think of the number of borrowers who don’t fully repay their loans; don’t think of the face value of any account write-offs in 2046 and beyond; think of the cash flows. The government’s loss on the loans is the difference between cash outlay and cash repayments but discounted to give a value today.

The important point about the policy to write-off outstanding balances thirty years after repayments first become due is that the cashflows stop.

I extend the analysis in the next post to see what happens if we have to revise down the cashflows.

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