Hello, can of worms fans. In this piece, we're going to discuss the various ways one might compute the present value of an amount of money, when it was originally valued in a foreign currency. We'll propose an algorithm, and work some examples.
The transformation of money through time is well known to economists, and any decent measure of inflation can be used - retail prices, consumer prices, GDP deflator. Transforming money from one currency to another is more difficult, because it's necessary to convert between one currency and another, and the date of change can be critical. Get it wrong, and you'll have nonsensical results.
For instance, someone who believes that the USD is the industry standard would take €21m from 2005, and convert it to USD 27.5m. Increase that by three years inflation, call it USD 29m. Now take €20m to-day, we find it's valued at USD 31.7m (or whatever the exchange rate is). So, if we're to believe this metric, €20m now is more valuable than €21m three years ago. It's an answer that we find to be ridiculous.
Our preferred method is to convert between currencies only during periods where they're relatively stable. The most recent period of stability seems to have been between mid-2003 and mid-2007, when a pound bought €1.50 and USD 1.90. For more recent sums of money, we must use the conversion rate that's closest to a stable point. However, it's only in retrospect that we'll be able to determine when a stable rate was reached. Until that time, the least awkward approach is to convert at the date in question. For instance, a work of art sold for GBP 10,000 in 2005 is converted to €15 000; one sold for the same price to-day would convert at the current rate, €13 000 (or whatever it is).
Inflation should be applied at the appropriate rate for the currency that is being counted at a particular date. If the money is in pounds, use UK inflation; if it's in euro, use euro-zone inflation, and so on. The best rate of inflation is a difficult decision: retail prices are an approximation of how much a given currency will buy, while GDP / GNP deflators will approximate to how much of the economy's growth is due to changes in prices. Our preference is to use GDP / GNP deflators where they are easily available, and RPI or national equivalent where not. Usually, GDP deflators for the UK and certain other countries are implicitly available, including explicit figures for the eurozone.
Eventually, one has to make a decision as to which currency to be the currency of record. This is a nakedly political decision: our preference is for the euro, as the nascent international reserve currency.
The algorithm we adopt is as follows:
- For amounts awarded prior to 1 July 2005, use the appropriate national inflation figure to increase the amount.
- Convert to euro at the ruling rate (£ 1.50 = €1 = USD 1.20)
- Then apply a further inflation, currently 6.1%, to achieve a final figure. (We use here the final consumption of households deflator.)
- For amounts awarded between 1 July 2005 and 1 July 2007, convert at these rates, and apply the appropriate eurozone inflation figure.
- For amounts awarded since 1 July 2007, convert at the rate applicable on the day of award, and apply the inflation.
This discussion was sparked by various contributions at Bother's Bar; we can use this conversion algorithm to determine if 20 really is greater than 21...
Beat the Star
, Germany, 2008: €2 000 000.
Pasaparabala
, Spain, 2006: then &euro2 190 000, now €2 280 705.
Thank goodness for that! 2.1 > 2.0, and we can sleep soundly.
Jeopardy!
, Brad Rutter, 2001-5:
2001 - USD 55,102
2002 - USD 1,100,000
2005 - USD 2,115,000
After USD inflation to 2005, this totals to USD 3,365,852.88 = €2 807 377,40
After euro inflation to the present: €2 978 627
Jeopardy!
et al, Ken Jennings, 2004-7:
2004 - USD 2,520,700
2005 - USD 500,000
To convert: USD 3,102,195.34 = €2 585 162,78, which inflates to €2 742 857,71
13.10.06 - USD 714.29 = €571,52, which inflates to €580,09.
18.12.07 - USD 100,000 = €69 490.
Grand total: €2 812 927,80
Millionaire
, 2001: USD 2,207,000, which ends up at €2 153 378.
Millionaire
, 2000: £1,000,000, which finishes as €1 813 911.
What, people have to pay taxes on their winnings? That's a whole other argument...
