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The loss on loans – part two

March 22, 2014

To develop the scenario in the previous post:

I have lent you £10 which you will repay in ten installments of £1 each year starting next year.

The following week you come back to me and explain that your circumstances have changed. You appeal to an income contingent clause in our original deal which means you will now end up only paying 90p each installment.

The discounted cashflows now look like this

Year 1 2 3 4 5
Payment £0.90 £0.90 £0.90 £0.90 £0.90
Value £0.86 £0.82 £0.78 £0.74 £0.71
Year 6 7 8 9 10
Payment £0.90 £0.90 £0.90 £0.90 £0.90
Value £0.67 £0.64 £0.61 £0.58 £0.55

The total value of repayments is now £6.95.

I wasn’t charging you interest so I write off the £1 outstanding balance (in nominal terms you paid £9 out of the £10 owing).

But according to how I value those payments, I have now lost £3.05 on the deal.

If you’ve been watching the BBC, you might think the RAB is 100% because you, the borrower, didn’t clear your account.

If you’ve been reading the Guardian, you might think that the loss was £1 – the nominal amount written off.

But the RAB I need to cover the estimated loss on the loan today is £3.05 (30.5%).

Now I have to go back to the person who covers my spending commitments and say, ‘I thought I was going to lose £2.28, but it’s now £3.05. Can you book me the extra 77p?’

They might agree (the discount rate may include a risk premium to cover such eventualities in the round), but they might look at some of your other spending commitments – widening participation schemes, say – and ask for a saving there to compensate.

Update – 23 March

Now that we have new budgeting guidance on the treatment of revisions to estimates of loss we can see what happens to that 77p. My paymaster asks me to make reductions to my spending commitments over the next 10 years to cover that 77p. So I cut funding to e.g. widening participation so that over the ten year period I save 77p in today’s value terms. (Roughly 10p in nominal terms each year).



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