VAT calculations and a mathematical method of determining World Cup winner

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

02 July 2006

Several people have written to me asking why computer dealers have not reduced their prices even after the value added tax was removed on these items. Well the prices have dropped but not by 16 percent. This is not because the traders are greedy but a result of the arithmetic.

If the price of a machine (inclusive of 16 per cent AT) was say, Sh 50,000, what would be the price without tax? It is tempting to calculate 16 per cent of 50,000 which is 8,000 and the to remove this from the initial price giving Sh 42,000. But that would be wrong.

The reason is that if we now try to work backwards, we get: 16 per cent of Sh 42,000 equals Sh 6,720. And on adding the two values the total comes to Sh 48,720 – Sh 1,280 short of the original Sh 50,000. Clearly something is wrong.

To get the right answer, we need to ask ourselves what price gives Sh 50,000 when we add 16 per cent to it? Now when we add 16 per cent to anything, the result is 116 per cent of the starting amount. Thus to get the required result we should divide the Sh 50,000 by 116 per cent (or 1.16). The answer is Sh 43,103.45. Try it out – add 16 per cent to this and you will get Sh 50,000.

Therefore, the prices will go down by about 13.8 per cent and not 16 per cent. But still, many of the traders did not change their prices at all. The reason is that the dealers usually quote the cost excluding VAT. So all they did after the budget was to remove the note stating, “Subject to 16 per cent VAT”.

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Now let’s turn to something more interesting – football. Bookmakers are doing good business taking bets on who will win the on-going World Cup. But Evans Gichuhi believes he has worked out the winner mathematically. He says:

“Brazil won the world cup in 1994. Before that, the last time they had won this title was 1970. If you add 1970 + 1994 = 3964. Argentina won the world cup for the last time in 1986. Before that only in 1978. Add 1978 + 1986 = 3964. Germany, won the world cup in 1990. Before that, Germany won in 1974. 1990 + 1974 = 3964.”

“This could lead us to guess the winner of the World Cup in 2002, it should be the winner of the 1962 World Cup (since 3964 - 2002 = 1962). And, yes, Brazil won in 1962 and 2002. This numerology seems to work...”

“And now, who would be the winner of the 2006 world cup? Let's see, 3964 - 2006 = 1958. And who won in 1958? Oh, Brazil did!!!”

Well by the time you read this, Brazil will have played their quarterfinal match against France. So, are they still in the tournament? I wouldn’t know, I don’t watch football!