How to calculate the depreciation rate of the shilling
The Sunday Nation
Nairobi,
02 October 2011
This week, our currency crossed the psychological significant Sh100 per dollar mark. From an average of Sh80.80 to the dollar in the first week of this year, it had moved steadily to around Sh102 at the time of writing this article. An interesting question arises: what is the percentage change in value during the last nine months?
One might be tempted to proceed as follows: Start by subtracting Sh80.80 from Sh102 and get Sh21.20; then divide the difference (Sh21.20) by the original value (Sh80.80) and express the result as a percentage; that is, 26.2 per cent. However, that would have overlooked the all important negative sign which tells us whether the value has increased or decreased.
When doing the math this way, we must note that the final value (Sh102 to the dollar in September) is larger than the initial one (Sh80.80 in January). Therefore, the change is positive and, as a result, the percentage will also be positive.
Now a positive change means an increase in value; but “we all know” that our shilling has been depreciating against the dollar. Therefore we should expect a negative percentage. So something must be wrong with that calculation.
The correct way of doing the math is to start by establishing “the value” of the shilling. That is what one can buy with it. In the case of foreign exchange transactions, we are buying other currencies; dollars, for example. Thus we should ask ourselves how many dollars we can get with one shilling.
To avoid dealing with very small fractions, let us change things a little. If we had Sh1,000 in January 2011, we would have bought about US$12.38 from the foreign exchange market.
Today, the same Sh1,000 will buy us only US$9.80. Therefore, the value of Sh1,000 has dropped from US$12.38 to US$9.80. Since last number is smaller than the first one, the difference between the two will be a negative quantity – just as we expect! The change is -US$2.58.
To find the percentage change, we divide the difference (-US$2.58) by the initial value (US$12.38). The answer is -0.21, or -21 per cent.
But why are we dividing by the initial value (US$12.38) instead of the final one (US$9.80)? Is it an attempt to make the depreciation look smaller? No: the answer is that this is the only sensible way to do it.
To illustrate: suppose you had 12 goats in January and the 3 died as a result of the drought and you are left with 9. What would say was the percentage reduction in your stock? Isn’t it 3 divided by 12? Surely, you can’t say 3 divided by 9, can you? Now instead of goats, let’s suppose they were dollars: the math shouldn’t change, should it?
Apart from banks and forex bureaux, the only other group that is not feeling the pain of the weakening shilling are exporters: or aren’t they? I saw a story in the newspapers this week where an exporter was complaining that her company was also hurting because the prices of imported inputs had shot upwards.
Now that got me wondering: can an exporter lose money as a result of the weakening of the local currency? Well, that’s a story for another day…
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