Understanding break-even period and the correct way to calculate loan payments

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

29 September 2019

After reading last week’s article about the returns expected from buying a house, some readers have raised a few questions. The first one is about terminology: why did I refer to “break-even period” while the common phrase used is “break-even point”?

My first thought was: isn’t a period in American English the same thing as a point in British English? Any way; suppose you buy goods at Sh100 each and sell them at Sh150. If the cost of running the shop (rent, salaries, etc.) is a fixed Sh10,000 per month, how many pieces do you need to sell in order to meet these expenses?

The answer is 200 (do I really need to explain how I got that?). This can be referred to as the “break-even volume”. One might go further and work out the “break-even sales turnover” (Sh30,000 – again, no need to explain the math!).

Whichever value is used (be it volume or turnover), it is commonly called “break-even point”. Notice, however, that in this case, the cost is constant and the cumulative sales turnover is increasing day-by-day.

In the case of a house bought on a loan, the monthly sales remains constant over several years – at least two years in most cases. However, as the loan is paid back, the interest component (which is the biggest cost) decreases every month.

For that reason, it is reasonable for the house owner to ask this question: how long will it take for the rent I am getting going to be greater than the interest I am paying? For that reason, we are justified to refer to a “break-even period”. After all, we are looking for a duration of time. However, …

Another reader was confused by the way I calculated the monthly instalment. For a loan of Sh8 million payable over 15 years at 14 per cent interest, I found the payment to be about Sh106,500 per month. But his calculation yielded Sh137,000.

Naturally, I asked him how he had arrived at his answer. He explained that he first divided the Sh8 million by 180 months (15 years) to get the monthly principal payment. Then he worked out the monthly interest on the loan amount (14 per cent of Sh8M divided by 12) and got Sh93,000. Adding these two yields over Sh137,000.

This is a fundamental error. It assumes that the interest will be charged on the entire amount throughout the loan period. After the first payment of Sh137,000, the money owed reduces instantly to Sh7.955M. And every month thereafter, it goes down by Sh44,000.

It would be criminal for the lender to charge you interest for money that you don’t owe! Nevertheless, some banks do work it out in this manner, but they reduce the interest accordingly with every payment. This the instalments keep reducing: by the final month, you would pay just Sh45,000.

Most banks, however, work out instalments using a formula where the interest amount reduces and the principal component increases, but the total remains constant. This helps borrowers in planning future payments.