Guidelines on Interest Rates for Borrowing

Eng. Dr. Paul Sagala

Phantom Solutions, Ltd

Background

There is need to endeavour to present issues surrounding 'borrowing' money for all. For short-term 'business' purposes, a number of critical issues many a manufacturer face are not apparent, as repayment periods are pretty short.

Industry on the other hand, has on the whole, much longer periods to 'spread' repayments in. Given the rather high interest rates that have prevailed in this country, there is a great need to have a better understanding of 'fundamental' issues relating to 'time value of money' concepts if an enterprise is not to run into a 'risk' of 'going under' from the burden of borrowing.

It is our intention to start to address salient issues, in a piecemeal fashion, hoping to look at other issues progressively.

We start off with a 'hypothetical' situation, looking at how a 'unit now' changes in 'worth' with time, given varying interest rates and duration between now and the time the future worth is determined. We hope this series will, with time, bridge that critical gap between now and the 'grey' areas of what could become of a loan prospect in future.

Future Value, F of Principal P at time t = 0,

The formula F = Peⁱⁿ can easily be demonstrated for continuous compounding at an interest rate (i) per cent on an annual basis. This gives us one 'first' formula below:

FORMULA 1:

Future Value, F of Principal P at time t = 0,

F = Peⁱⁿ - Principal P compounded continuously at interest i after n years

In order to demonstrate the impact of such a formula on borrowing in any context, we will need to apply some interest rates over varying durations in order to get a 'feel' for what is possible.

It is important to observe that, what formula 1 says is that,

"anyone with a unit P (P = 1) at time 't = 0' will have it grow to a future value, F (F = Peⁱⁿ)".

That expression is valid in a situation where there may be one or two different 'entities', the term entity possibly representing a person, persons or organisation(s). In other words, a person can deposit P in a bank, or, lend it to another entity. Conversely a bank or organisation can lend an individual, a company or another bank.

Why do I pose the above statements? The main reason is to say that, the principles about 'time value of money' have been acceptable as valid, irrespective of any parties involved. We will take these further later on.

It should also be said that while one may use 'discrete' or 'continuous' compounding, the trends / implications / lessons are 'similar'. Hence, we will look at continuous only for now.

There are also alternative considerations of 'stream' payments versus 'future' sums. For now, we will look at 'present, P' and 'future, F' sums. 'Equivalences' will be demonstrated in future.

Case I: Longer Duration, n

One approach we would like to take is to look at this picture on a relatively longer time horizon:

Note: 'Pe**in' in chart represents the expression 'Peⁱⁿ'

Observations

The following emerge from above:

The higher the interest rate, that 'faster' F grows with time, 'exponentially and in combination' for interest and time.;
Conversely, if one were to look at the time it would take F to equal 2 (double), 5% interest pa would take longer than 13 years, 10% interest pa would take just under 7 years, while 20% interest pa would require just over 3 years. This in fact works out to be 'inversely proportional'

Case II: Wider Range of i, Interest Rates

The second variable to stretch, is interest rates, see below:

Observations

Clearly, with much higher interest rates, F 'spirals away faster' with time, still 'exponentially and in combination';

Note: 'Pe**in' in chart represents the expression 'Pe ⁱⁿ'

Conversely, if one were to look at the times of after 3 and 7 years, F would grow to 3.32 and 16.445 at 40% interest pa, as opposed to 'doubling' for interest at 20% and 10% respectively.

Lessons

To those to whom F is 'due to be paid back', increasing interest rates mean better 'gains'
To those to pay back, higher interest rates and longer 'time delays' are a big cost;
One needs to borrow at as low interest rates as possible, and, pay back as soon as possible; and,
The higher the interest rate, the shorter should the repayment period be, beside others.

Implications

Try as much as possible to minimise borrowing when interest rates are too high;
Any delays to pay on schedule, can be viewed as borrowing 'P' with 'F' to be repaid back, depending on delay and value;
As much as possible, avoid late repayment;
If possible, pay back earlier than scheduled, reduce borrowed sum, or, do not borrow at all;
Use internal funding whenever possible;
Whenever possible, sell shares to raise capital, especially funding long-term investment;
If you must borrow, profits should exceed 'due repayment sums' on a period-by-period repayment basis, the considered norm for repayments in a 'going concern', probably twice or higher if the enterprise is to benefit from the exercise.

Several economies the world over have been able to grow under a set of ideal conditions, including but not limited to:

Interest rates below 5% per annum (pa);
Years of interest free period;
Abundant and cheap raw materials;
Readily available local and export markets;
A less competitive environment; and,
Exporting to markets without protective subsidies.