Email Conversation with Kimathi Mwiricia

Following is a raw and unedited conversation I had with a reader of my column “The World of Figures” – complete with all the typos!

 We are in a deadlock.

Please read through and make your judgment. I would be happy to hear from finance professionals. Send your comments to info@figures.co.ke with a copy to Mr Mwirichia via Kimathi.mwirichia@gmail.com

 From: kimathi.mwirichia [mailto:kimathi.mwirichia@gmail.com]
Sent: 30 October 2016 10:49
To: Sunday Nation
Cc: Public Editor; Mungai Kihanya Training
Subject: "The Link Between Loan Instalments and Change in Interest Rate":A Critique.

I have just read an article by your columnist  Mr Kihanya in today's issue of the Sunday Nation and wish to offer a reasoned  critique.

His assertion that loan instalment is not directly proportional to interest rate is not based on facts and sound reasoning and appears hinged on a gross failure of appreciation of the issues at play.

Loan instalment is a function of interest rate,r, and the period loan is repayable,n.

However,the two variables move in opposite directions.Whereas loan instalment is directly proportional to interest rate,the latter is inversely proportional to the period of the loan,n.

Take a loan of she.1,000,000,n equals 60 months and r equals 20%.Using a Financial Calculator,the payment per month is kshs.26,493.88.

If the interest rate is reduced to 14.5%,the period,n should be increased to 60×20÷14.5=82.76 months.

Again, using a Financial Calculator payment per month becomes shs.19,187.89.

Thus a reduction of interest rate by 27.5%(20% to 14.5%) results in a reduction of monthly payment roughly by an average of 27.5%(26,493.88 to 19,187.89).

Thus,interest rate is directly  proportional to the loan instalment,Ceteris Paribas!

It is incredibly important that columnists have a grasp of topics they write about lest the readers ,many of whom have a smattering knowledge of finance theory and practice, will be misled big time.

From: kimathi.mwirichia [mailto:kimathi.mwirichia@gmail.com]
Sent: 30 October 2016 12:03
To: Sunday Nation
Cc: Mungai Kihanya Training; Public Editor
Subject: Fwd: "The Link Between Loan Instalments and Change in Interest Rate":A Critique.

I have noticed a typo in my piece...In the sentence starting with "whereas "...where I wrote "latter"....that word should be sustituted with the word "former".

The typo is greatly regretted.

From: Mungai Kihanya - Figures Consultancy <info@figures.co.ke>
Date: 2016/10/30 17:58 (GMT+03:00)
To: "'kimathi.mwirichia'" <kimathi.mwirichia@gmail.com>, 'Sunday Nation' <sundaynation@ke.nationmedia.com>
Cc: 'Public Editor' <publiceditor@ke.nationmedia.com>
Subject: RE: "The Link Between Loan Instalments and Change in Interest Rate":A Critique.

Dear Kimathi,

 See my comment inside you original message.

 Regards,

Mungai Kihanya

From: kimathi.mwirichia [mailto:kimathi.mwirichia@gmail.com]
Sent: 30 October 2016 10:49
To: Sunday Nation
Cc: Public Editor; Mungai Kihanya Training
Subject: "The Link Between Loan Instalments and Change in Interest Rate":A Critique.

I have just read an article by your columnist  Mr Kihanya in today's issue of the Sunday Nation and wish to offer a reasoned  critique.

His assertion that loan instalment is not directly proportional to interest rate is not based on facts and sound reasoning and appears hinged on a gross failure of appreciation of the issues at play.

Loan instalment is a function of interest rate,r, and the period loan is repayable,n.

However,the two variables move in opposite directions.Whereas loan instalment is directly proportional to interest rate,the latter is inversely proportional to the period of the loan,n.

Take a loan of she.1,000,000,n equals 60 months and r equals 20%.Using a Financial Calculator,the payment per month is kshs.26,493.88.

If the interest rate is reduced to 14.5%,the period,n should be increased to 60×20÷14.5=82.76 months. {A change in the interest rate does NOT result in a change in the period of the loan. The period remains 60 months as per the contract. The instalments are therefore changed. Repeat the calculation with 14.5% and 60 months}

Again, using a Financial Calculator payment per month becomes shs.19,187.89.

Thus a reduction of interest rate by 27.5%(20% to 14.5%) results in a reduction of monthly payment roughly by an average of 27.5%(26,493.88 to 19,187.89).

Thus,interest rate is directly  proportional to the loan instalment,Ceteris Paribas!

It is incredibly important that columnists have a grasp of topics they write about lest the readers ,many of whom have a smattering knowledge of finance theory and practice, will be misled big time.

From: kimathi.mwirichia [mailto:kimathi.mwirichia@gmail.com]
Sent: 30 October 2016 20:01
To: Mungai Kihanya Training
Subject: Fwd: RE: "The Link Between Loan Instalments and Change in Interest Rate":A Critique.

Mr Kihanya,your thesis was that loan instalment is not directly related to the change in interest rate.That is what I set to disabuse and debunk.The issue of stipulation in loan contract is thus very tangential.

The point is that if , for instance,you reduce interest rate by 27.5% and make the appropriate change to the period of the loan,there is a direct correlation(and coefficient of correlation is +1) between interest rate and the amount of instalment thereof.Do you know that loan instalment can have more that one explanatory variables?

I do not see why you can't get simple things  and are bent on sticking to your position.

I would want to know,most respectfully,your level of education and what your specialisation is to enable me know how I can relate with you intellectually.

Finance is not like politics where every opinion is valid depending on where you belong to.

You need to appreciate knowledge and apply it in the right way.You should understand that what you write is subject to critical thinking and analysis by we the readers.

I am ready that we involve independent  professionals and intellectuals in the field to vouch the veracity of my critical analysis because I have done it objectively with a view to correcting you.I also get corrected but do not take umbrage at the critique.

Lastly,do you think that your position can stand scrutiny and pass in master's finance class?I know you write very interesting things when the topic is on mundane matters but when it comes to finance it appears you have serious knowledge gaps,in my respectful submission.

From: Mungai Kihanya - Figures Consultancy <info@figures.co.ke>
Date: 2016/10/30 22:03 (GMT+03:00)
To: "'kimathi.mwirichia'" <kimathi.mwirichia@gmail.com>
Subject: RE: RE: "The Link Between Loan Instalments and Change in Interest Rate":A Critique.

Dear Kimathi,

See my comments {in red} in your mail below

Regards,

Mungai Kihanya

From: kimathi.mwirichia [mailto:kimathi.mwirichia@gmail.com]
Sent: 30 October 2016 20:01
To: Mungai Kihanya Training
Subject: Fwd: RE: "The Link Between Loan Instalments and Change in Interest Rate":A Critique.

Mr Kihanya,your thesis was that loan instalment is not directly related to the change in interest rate. That is what I set to disabuse and debunk.The issue of stipulation in loan contract is thus very tangential.

The point is that if , for instance,you reduce interest rate by 27.5% and make the appropriate change to the period of the loan, {You are shifting the goalposts to get the result you desire. Proper analysis of anything – financial or otherwise – requires that you hold everything constant, then change ONE parameter and measure another ONE. Changing two parameters distorts the situation and yields misleading results. This what you are doing when you change the interest rate AND the term of the loan simultaneously.} there is a direct correlation(and coefficient of correlation is +1) between interest rate and the amount of instalment thereof.Do you know that loan instalment can have more that one explanatory variables?

I do not see why you can't get simple things  and are bent on sticking to your position.

I would want to know,most respectfully,your level of education and what your specialisation is to enable me know how I can relate with you intellectually.

Finance is not like politics where every opinion is valid depending on where you belong to.

You need to appreciate knowledge and apply it in the right way.You should understand that what you write is subject to critical thinking and analysis by we the readers.

I am ready that we involve independent  professionals and intellectuals in the field to vouch the veracity of my critical analysis because I have done it objectively with a view to correcting you.I also get corrected but do not take umbrage at the critique.

Lastly,do you think that your position can stand scrutiny and pass in master's finance class? I know you write very interesting things when the topic is on mundane matters but when it comes to finance it appears you have serious knowledge gaps, in my respectful submission.

From: kimathi.mwirichia [mailto:kimathi.mwirichia@gmail.com]
Sent: 30 October 2016 22:17
To: Mungai Kihanya Training
Subject: Fwd: RE: RE: "The Link Between Loan Instalments and Change in Interest Rate":A Critique.

Where a dependent  variable y is dependent on more than one independent or explanatory variables x1 and X2,you look at the values of y as they are being impacted by x1, x2.....

From: Mungai Kihanya Training <mail@mungaikihanya.com>
Date: 2016/10/30 22:34 (GMT+03:00)
To: "'kimathi.mwirichia'" <kimathi.mwirichia@gmail.com>
Subject: RE: RE: RE: "The Link Between Loan Instalments and Change in Interest Rate":A Critique.

To do that, you must hold x1 constant, vary x2 and measure y and plot the relationship; THEN hold x2 constant, vary x1 and measure y again and plot ANOTHER relationship. Thus you get TWO curves: one for constant x1 and the other for constant x2.

The question now becomes whether any of these two curves is a straight line passing through the origin. If yes, then we conclude that y is directly proportional  to that variable.

So, if you hold the term of the loan constant, vary the interest late and measure the monthly instalment; do you get a straight line passing through the origin? The answer is NO; the plot is a curve and it does not pass through (0,0). Therefore the relationship is not a direct proportionality.

Regards,

Mungai

From: kimathi.mwirichia [mailto:kimathi.mwirichia@gmail.com]
Sent: 31 October 2016 00:59
To: Mungai Kihanya Training
Subject: Fwd: RE: "The Link Between Loan Instalments and Change in Interest Rate":A Critique.

If the dependent variable y in our case is the loan instalment and the explanatory variables are the interest rate x1 and the period x2 you can use multiple regression model to test the relationship.In multiple regression we are concerned with linear relationships and not merely directly proportional relationships that are a subset of the former.

If more than one explanatory variables affect a dependent variable,we can use a tool like SPSS to analyse the relationship.We do not hold a variable constant as you state.

Y= b0+b1x1+b2x2+et

I think the mistake you made in your column is to talk about directly proportional relationships and not linear relationships.

If when X increases by 2,y increases by 2,that is clearly a directly proportional relationship.But if X increases by 2 and y reduces by 1/2,that is a linear relationship.

In statistical analysis the concern,to repeat,is on linear relationships.

But as I always say,my miraa chewing uncle in Meru cannot appreciate this and it means you have to be careful when you write for public consumption because most readers cannot see the nuances.

Brother,read a good book on econometrics and you will appreciate these intricacies.

From: Mungai Kihanya - Figures Consultancy [mailto:info@figures.co.ke]
Sent: 31 October 2016 09:52
To: 'kimathi.mwirichia'
Subject: RE: RE: "The Link Between Loan Instalments and Change in Interest Rate":A Critique.

Kimathi,

The problem is much simpler than that. It is NOT a statistical problem and so SPSS would be an inappropriate tool.

No; Let:

P = the monthly instalment Payment

L = the Loan amount

n = the Number of months of payment

r = I/1200, where I is the interest rate in per cent

It then follows that:

If there was a direct proportionality between P and r, we would expect to be able to express it in the form:

 or , where k is a constant.

Clearly, this equation for “equated monthly instalments” CANNOT be written in this form. Therefore, the relationship between P and r is NOT a direct proportion.

Furthermore, it is also NOT a linear relationship, for in such a case we should be able to express it in the form:

, where C is yet another constant – the intercept on the P-axis.

I hope you now get my point.

Regards,

Mungai Kihanya

From: kimathi.mwirichia [mailto:kimathi.mwirichia@gmail.com]
Sent: 31 October 2016 01:12
To: Mungai Kihanya Training
Subject: Fwd: RE: "The Link Between Loan Instalments and Change in Interest Rate":A Critique.

And by the way,why do you have this fascination with lines that pass thro the origin?If you analyse the relationship between interest rates and inflation rates over a ten year period in kenya,would you say there is no relationship cos graph does not pass thro the origin?

Please avoid this business about directly proportion.

Think linearity!

From: Mungai Kihanya - Figures Consultancy <info@figures.co.ke>
Date: 2016/10/31 10:23 (GMT+03:00)
To: "'kimathi.mwirichia'" <kimathi.mwirichia@gmail.com>
Subject: RE: RE: "The Link Between Loan Instalments and Change in Interest Rate":A Critique.

Kimathi,

In your initial email, you challenged my statement that “monthly instalments are NOT directly proportional to the interest rate”. You went ahead and attempted to prove that they are directly proportional.

I responded by demonstrating that they are not directly proportional. My proof was based on the FACT that in a direct proportion relation, the graph is a straight line passing through the origin.

Now you accuse me of having “this fascination with lines that pass through the origin”. It is not a fascination; it is a mathematical FACT: in a direct proportion relation, the line must pass through the origin!

You close by asking me to “avoid this business about direct proportionality”. Well; it is you who is insisting on saying that the relation between instalments and interest rate is a direct proportion. I am saying that it is NOT!

You have invited me to “think linearity”. Well; in a separate email, I have given you the proof that Interest rate and monthly instalment are NOT linearly related! The graph is a CURVE, not a straight line…and it does NOT pass through (0,0): BUT that does not mean that the two aren’t related. They are – when you change one, the other also changes – and I have given you the equation relating them!

Regards,

Mungai Kihanya

From: kimathi.mwirichia [mailto:kimathi.mwirichia@gmail.com]
Sent: 31 October 2016 14:04
To: Mungai Kihanya Training
Subject: Fwd: RE: RE: "The Link Between Loan Instalments and Change in Interest Rate":A Critique.

Let me repeat this for clarity:variables can exhibit linearity where there's no direct proportionality.Right?

I have a 5 year 2.5m mortgage with HFC.I have been paying shs.64,824.25 per month when rate was 17%..now the rate being 14.5% I am paying shs.62,280.

Clearly there is a linear relationship between loan instalment and interest rate Ceteris Paribas...It is not a direct proportionality but there's linearity...If period was adjusted upwards as I explained yesterday we would be talking about direct proportionality.

You should have explained to the reader that you held the period constant.

Lastly,get a Financial Calculator which assists you  vary easily variables and enables you see the effects.Using excel is not digital!

Ibrahim's supermarket near the the stanley hotel kimathi street has BA 2 plus Business Analyst calculator and it is very helpful.

Good day kaka.

From: Mungai Kihanya Training [mailto:mail@mungaikihanya.com]
Sent: 31 October 2016 14:39
To: 'kimathi.mwirichia'
Subject: RE: RE: RE: "The Link Between Loan Instalments and Change in Interest Rate":A Critique.

“You never do a calculation unless you know the answer” - John Wheeler, Physicist [1911 – 2008]

No, no, no! The relation between instalment and interest rate is NOT linear. Please put the calculator aside and look at the equations.

You don’t need a calculator to see that this equation is NON-LINEAR in r:

If your calculator is showing it as linear, then I’m afraid your calculator is wrong!

PS: The calculation about the HFCK mortgage is wrong; please check it again.

Regards,

Mungai

From: Mungai Kihanya Training [mailto:mail@mungaikihanya.com]
Sent: 31 October 2016 15:05
To: 'Mungai Kihanya Training'
Subject: RE: RE: RE: "The Link Between Loan Instalments and Change in Interest Rate":A Critique.

By the way; two points always lie in a straight line. Therefore you cannot prove linearity by considering just two points, namely, P1=(Sh64,824, 17%) and P2=(Sh62,280, 14.5%). You need at least a third point, P3, and then demonstrate that the gradient between P1 and P2 is equal to that between P2 and P3.

Alternatively, you can plot the three points and show that they lie in a straight line. And since the three are analytically determined through calculation (as opposed to experimental data), the resulting line MUST touch the line – approximations are not acceptable.

Regards,

Mungai

From: kimathi.mwirichia [mailto:kimathi.mwirichia@gmail.com]
Sent: 01 November 2016 14:40
To: Mungai Kihanya Training
Subject: Grasp of Finance theory and practice

Going through your argument,in my respectful submission,shows a serious dearth grasp of Finance Theory and Practice on your part.That is clearly evident from the cavalier matter you answer my questions.

Maths alone cannot assist you navigate through the intricate issues kaka yangu.

Arguing with you is like doing it with a first year student in a business class:a waste of time!

I am ready to take you through basic lessons of finance for free!

Otherwise I will start a blog where I will be giving a critique of your columns especially where you goof,as you normally do,so that other serious readers can see light.

Thank you.