How to work out the rate of return for an investment

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

10 June 2007

I was offered an “attractive” offshore investment recently. According to the brochure, the scheme has earned 450 percent in the last five years. The sales rep tried to convince me that this translates to about 90 percent annually. She arrived at this figure by simply dividing 450 by 5. Is that the correct way to do it?

Suppose I invested Sh10,000: at 90 percent per annum, my account would have Sh19,000 the end of the first year. In the second year, this Sh19,000 would earn another 90 percent to bring the total to Sh36,100. This would then grow to Sh68,590 in the third year and so on until the fifth year when my balance would be Sh245,600.

Now that is a 2,356 percent growth! Not the 450 in the brochure. So the question arises: what annual earning rate would translate to 450 percent in five years?

If an investment earns 450 percent, it means that its value is 5.5 time then initial amount. That is, my Sh10,000 will grow to Sh55,000. To get the annual rate, the first step is to get the fifth root 5.5. In other words, we ask ourselves, what number would be multiplied by itself five times to give 5.5. The answer is 1.406 – punch 1.406 x 1.406 x 1.406 x 1.406 x 1.406 into your calculator and see.

A multiplication factor of 1.406 is equivalent to an increase of 40.6 percent. That is, if the investment grows by 40.6 percent annually for five years, it will accumulate to 5.5 times the initial amount. This is the 450 percent growth that we desired.

This is not an attempt to belittle the investment; 40.6 percent is a huge return by any standards. The aim is only to demonstrate that it is not the 90 percent presented by the sales rep. The analysis will also help illustrate another point…

The government recently unveiled its 25-year vision for the country – the so called Vision 2030. The plan is to accelerate economic growth to 10 percent per year and maintain it at that level for 25 years. If this is achieved, the economy will grow by a factor of 11 (1.1 x 1.1 x 1.1 x 1.1 x ….. 25 times) in the period – from the current average national income of $540 per person to about $5,940. This would be greater than the present values of South Africa, Malaysia, and Brazil, to name a few.

 However, when launching his election manifesto, Langata MP Raila Odinga said that he will implement programmes that would achieve the same goals in ten years.  We may want to know the rate of economic growth that would be required to meet that target.

That is, what annual multiplication factor would increase our income from $540 to $5,940 in ten years? The answer is the tenth root of 11, or 1.27. That is an annual economic growth of 27 percent!

Clearly, that is an unrealistic goal.