All entries for Friday 18 March 2011
March 18, 2011
Writing about web page http://www.bbc.co.uk/news/education-12767850
According to a new report on the BBC website, headlined in last night's BBC TV and Radio news, "Graduates 'could pay back double their student loans."
It sounds scary. I can see another few hundred families around the country listening to the news and deciding university sounds just too expensive.
That would be a shame. There is a story here, but it is not the story on the surface. It is a deeper story, one of distortion and misrepresentation.
- First: There is nothing new in this "news."
Anyone who borrows will eventually repay more -- mechanically adding up the cash amounts, year after year -- than they borrowed. Interest charges ensure this result. Moreover, the longer is the period over which you borrow, the greater is the excess of cash repayments over the initial loan.
But why do borrowers pay interest? Because not having to wait is valuable. This has an important implication. A pound today is worth more than a pound next year or the year after. When you take out a loan, you've made the calculation that it's better to have the house or car now than wait for years in rented accommodation or sharing public transport while you save up. It's better to borrow and buy despite the fact that, having borrowed, you will have to repay more later.
By the same argument, the money you will have to repay next year should be considered worth less than the same money now. This is called discounting: we discount the future compared with the present.
Because future money has to be discounted to find what it is worth today, it is wrong to add up money in different periods without adjustment. Rather, the future values should be discounted, year by year, before they are added up.
Imagine the following scenario. In the BBC's story, the graduate has a debt of £43,000. In my scenario, you decide to borrow the same sum, but as a fixed rate mortgage, not a student loan. Suppose the lender's interest rate is 3 percent a year. Suppose you repay the debt in full, in equal annual instalments over 30 years.
On these assumptions, the sum of your undiscounted cash-out repayments will be a little over £67,000. But, if we revalue your payments in every year by discounting them back the present at 3 percent annually, the present value of the sum of your discounted repayments will fall to ... oh, £43,000.
The present value of the repayments is the same as the value of the loan!
- Second, therefore, there is no story. You repay -- in present value -- exactly what you borrowed.
But wait. That leaves a puzzle in the BBC account.
Remember that, in my example, you repaid everything at the market interest rate, and yet the undiscounted sum of your cash-out repayments was just £67,000, compared the £43,000 borrowed.
Compared with that, under the government's student finance proposals, graduates will enjoy three concessions. They'll repay nothing, and accrue no interest, while their salaries remain below £25,000. Between £25,000 and £41,000, they'll pay a reduced interest rate. And anything outstanding after 30 years is forgiven. Under those assumptions, surely, graduates should end up repaying less than you?
Yet, in the BBC version, graduates have to repay much more than you. The BBC puts the sum of undiscounted repayments at sums varying between £72,000 and £84,000, depending on the income of the graduate. It's the latter figure that lets them claim: "Graduates 'could pay back double their student loans."
What's going on?
The BBC commissioned "leading accountants," including the firm Baker Tilly, to support this story. It's based on a spreadsheet, available from the BBC website, "showing the calculations." The spreadsheet shows that the BBC's accountants sneaked in a hidden assumption, not reported in the story.
They built in 2 percent yearly inflation. In each year, they added 2 percent inflation to the repayment thresholds, 2 per cent inflation to the graduate's salary, and 2 percentage points to the interest paid.
What's wrong with that? Nothing -- except this: The 2 percent inflation assumption also pumps up the nominal undiscounted cash sums that their graduate repays every year. That was how they made the figures support that scary headline: "Graduates 'could pay back double their student loans."
Inflation is a further reason why it's wrong just to add up the column of annual cash repayments. Except in the first year, the annual payments are not in present-day prices. They are in different prices of different years, all of them higher than today's and some of them much higher. It's just plain wrong, and misleading, to lump them all together.
The BBC's calculation should have been done throughout in constant prices, so that the purchasing power of £1 would be the same in every year. But, if done at constant prices, there would have been less of a story. After proper discounting, there would have been no story at all. In fact, it would have emerged that:
- Most graduates will repay less, in present values and constant prices, than they borrow at the outset.
This brings us back to "the leading accountants." Given who they are, I guess they know their stuff. But do they? The mess behind this story leaves only two possibilities. They understood these issues perfectly well when they made their calculations -- or they didn't.
Either way, it looks bad for the accountants. Incompetent, or colluding with a misleading agenda? I'll leave it to you to decide on that.
It looks bad for the BBC, too. Remember, this is not the BBC reporting the news. It is the BBC inventing the news.
- Finally, a note for readers interested in open-source data.
The BBC website provides the spreadsheet with the figures, in their words, "showing the calculations." That's good.
The problem is that, before uploading the spreadsheet, they converted all the spreadsheet formulae to values. It is the formulae that enable to user to track the links from one number to another, and see at a glance how the calculations were made. The truth is that the spreadsheet does not show any calculations at all, only numbers. That's bad.
I can see no purpose in it, except to make checking more difficult.