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Cedi Depreciation: A Primer for Computation

By Desmond A. Nartey

In principle could the cedi, and for that matter any currency, depreciate by 100 percent, or more? If it could, what would be the consequences for the legal tender of the currency? What sorts of monetary policy issues would be spawn by such an event? Or is such a situation the outcome of a computational error? The methodologies for computing currency depreciation may be simple to apply but the process is fraught with pitfalls, which require that sufficient care is taken during the computation exercise to ensure that the methodology is well understood and the underlying theory correctly applied.

In an article credited to the Centre for Policy Analysis (CEPA) titled “Election Year Excesses, Cedi Depreciation & Inflation: The Current Experience”, the rate of depreciation, in year 2000, of the cedi against the US dollar was stated as 100 percent. Furthermore, the depreciation rate for the period June 2008 to June 2009 was stated as 43.0 percent. For the benefit of readers the relevant portion of the article is reproduced below:

“Every election year in the Fourth Republic, especially the hotly contested ones, has been associated with excesses (in spending and behavior), rapid depreciation of the cedi, and accelerating inflation. The most recent to such years is election year 2000 when the excesses led to an exchange rate depreciation (number of cedis per US dollar) of 100 percent from 3,500 old cedis at the beginning of the year to 7,000 at the end of the year”.

“The next after that was election year 2008 when election year excesses led to a fall in the value of the cedi from 1.0152 cedis/dollar in June 2008 to 1.4524 cedis/dollar in June 2009 a year on year depreciation of about 43 percent which was halted only by the stabilization program agreed with the IMF”.

“The current situation has seen the cedi depreciate by about 17.3 percent in the first half of the year and by about 20.5 percent, year-on-year, from June 2011 to June 2012”.

The more accurate rates of cedi depreciation for the two periods indicated in the article quoted above are 50.0 percent and 31.1 percent in year 2000 and June 2008 to June 2009 respectively, rather than the 100 percent and the 43 percent indicated in the article. Using the methodology adopted and the exchange rates quoted in the cited article, the rate of depreciation of the cedi against the US dollar from the beginning of year 2000 through June 2009 would be about 315 percent instead of the more accurate rate of 76 percent. Indeed, using the article’s cedi/US dollar exchange rates for the beginning of year 2000 (GH¢0.35) and that of June 2012 (GH¢1.91), the methodology implied in the article would suggest a period depreciation rate of about 446% rather than the more accurate depreciation rate of about 82%. Since no exchange rates have been provided for the first half of the year and the one year through June 2012, I am unable to comment on the accuracy of the stated depreciation rates for those two periods.


In fact and in theory no currency can depreciate by 100 percent as long as the currency continues to be legal tender. Conceptually, to suggest that a currency has depreciated by 100 percent is to say that it has lost its entire value and, as such, is no more legal tender. The only time a currency can be said to have depreciated by 100 percent (lost 100 percent of its value) is when the currency ceases to be legal tender. As long as the currency continues to be recognized as legal tender it continues to retain some value albeit the value will continually approach zero as the currency continues to depreciate. The value NEVER gets to zero until the legal tender conferment is withdrawn. The most revealing case that readily comes to mind is the Zimbabwean dollar, which was replaced by the US dollar and the South African rand, quite recently. At the time the Zimbabwean dollar was virtually worthless, depreciating by over 99.9%, not 100%.

Just as the devaluation of a currency, which is a deliberate policy action, is often confused with depreciation of a currency, which is the effect of market forces, the computation of the depreciation of the cedi against the US dollar, is also often confused with the appreciation of the US dollar against the cedi. Lately, this confusion has been exhibited considerably on the airways and in the print media by policy analysts as well as political commentators. The value path of the cedi in relation to the US dollar can be defined by a simple function such as this:

f(x) = 1/x
for x › 0
Where x is the amount of cedis exchanged for one US dollar.

As x gets larger and larger the value of the function becomes smaller and smaller, meaning that as the amount of cedis needed to buy one US dollar increases, the amount of US dollars that can be obtained with one cedi decreases and vice versa. Consequently, as x approaches infinity the value of the function approaches zero and the rate of depreciation approaches 100 percent; but it never reaches 100% until the cedi loses its legal tender, as did the old cedi when its legal tender conferment was withdrawn and the currency taken out of circulation.

Liberalized (floating) currencies are, basically, just like commodities and trade as such, in liberalized markets. As such, you may pay GH¢10.00 for four tubers of yam or for five US dollars. What defines your purchasing power in these instances is the quantity of the commodity you obtain per unit of the cedi (GH¢1.00). Consequently, if prices were to rise such that GH¢10.00 could buy only two tubers of yam or two and a half US dollars, the rate of decline in the purchasing power of the cedi in each case would be 50 percent. Another way to put it is to say that it would require GH¢20.00 to obtain the quantity of commodities in the latter situation, as in each of the former situations. Because currencies are commodities an exchange rate communicates two pieces of information – price and value – which are two different concepts. Fundamentally, since the basic principle of pricing entails relating value to a unit of an item, to say that the exchange rate between the Ghana cedi and the US dollar is USD 1.00 to GH¢1.95 implies that the price of US$1.00 dollar is GH¢1.95 and the value of GH¢1.95 is US$1.00. Conversely the price of GH¢1.00 is US$0.571 and the value of US$0.571 is GH¢1.00. Understanding this relationship is at the very heart of understanding the concepts of currency depreciation and appreciation, and the associated rates of change over time.
The basic formulae for calculating cedi depreciation against the US dollar (or any other currency) are as follows:

Cedi Depreciation: (a) [(X0/X1) – 1] * 100%

Where X0 and X1 are the former and latter amounts of cedis required to purchase one (1) US dollar.
(b) [(Y1 – Y0)/Y0] *100%

Where Y0 and Y1 are the former and latter amounts of US dollars required to purchase one (1) Ghana cedi.

Also, the basic formula for calculating US dollar (or any other currency) appreciation against the Ghana cedi is as follows:

US Dollar Appreciation: [(Z1/Z0) -1] * 100

Where Z0 and Z1 are the former and latter amounts of cedis required to purchase one (1) US dollar.

The table below shows the depreciation rates of the Ghana cedi against the US dollar and the corresponding appreciation rates of the US dollar against the Ghana cedi for hypothetical periods and exchange rates.
Period
US Dollar Ghana Cedi GH¢/USD USD/GH¢ Ghana Cedi Depreciation (%) US Dollar Appreciation (%)
0 1.00 1.00 1.00 1.00 - -
1 1.00 1.05 1.05 0.95 4.76 5.00
2 1.00 1.10 1.10 0.91 9.09 10.00
3 1.00 1.25 1.25 0.80 20.00 25.00
4 1.00 1.45 1.45 0.69 31.03 45.00
5 1.00 1.60 1.60 0.63 37.50 60.00
6 1.00 1.75 1.75 0.57 42.86 75.00
7 1.00 1.90 1.90 0.53 47.36 90.00
8 1.00 2.00 2.00 0.50 50.00 100.00

As can be observed from the last two columns, at low levels of the US dollar-Ghana cedi exchange rate movements the rate of depreciation of the cedi and the rate of appreciation of the US dollar are pretty close. However, the gap between the cedi depreciation rate and the US dollar appreciation rate widens as the exchange rate movement becomes sharper.

Since the beginning of the Fourth Republic, save 1992, the party in power has lost every election in the year when the rate of depreciation of the cedi has exceeded the rate of inflation – 2000 and 2008. While the data may be too scanty to allow any causal link to be established, the phenomenon, however, does suggest the influence of the state of the cedi in shaping the socio-economic conditions of the citizenry, and the consequences of such conditions for political outcomes. As such, it is extremely important that policy analysts and advisors take sufficient care in accurately computing the rate of change of the cedi’s purchasing power, at any point in time, so as to diminish any ambiguity about the value of the cedi and minimize any policy slips that may arise as a result of computational errors.

E-mail: danartey@hotmail.com

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