## Analysis of Second Hand Car Prices in Bangkok

Depreciation of Private Vehicles in Thailand

Duncan Williamson

March 2013

Introduction

Over the last few years I have used the prices of second hand cars in the United Kingdom to demonstrate how to derive a depreciation schedule from them. I have demonstrated the various calculations needed on a black/white board and in a spreadsheet.

Initially, I used the prices of a Range Rover and a Rolls Royce car for demonstration and then used those cars for several years. In summary, what I found was that one of the cars seemed to depreciate in accordance with the straight line method whilst the other car seemed to depreciate more along the lines of the reducing balance method.

The cases I built, including later revisions, were not rigorously scientific in that I did not carry out any detailed analysis of the cars, where in the country, precise ages, modifications or customisation or anything like that. I didn’t carry out any blind tests or control tests either. I was just collecting and using readily available data, processing it according to the rules of mathematics and depreciation and drawing the conclusions I drew.

See http://www.duncanwil.co.uk/costbeh.htm for much more discussion on my previous work. There is a sister page on this blog that shows summary data for three new cars from the UK: https://excel2007master.wordpress.com/depreciation-schedules-bmw-volvo-and-porsche/

In the current case, I did almost the same: I went to what appears to be a very well known car price web site in Thailand and chose two cars, almost at random, to analyse. I then prepared graphs of what I found for each car. I derived the price function by using Add Trendline in Excel: this gave me an estimate of the price of a new car and the annual provision for depreciation for that car.

Here are my findings and conclusions.

The Data

I used the web site www.thaicar.com to gather my car price data and the two cars I chose were

• Toyota Soluna 1.5
• Nissan Navarra 2.5

I chose the Soluna essentially at random: I had no preconceptions of the cars generally available in Thailand although I searched for and used prices relating to Bangkok and surrounding areas.

I chose the Nissan Navarra, a pick up truck, after reading that approximately 50% of cars bought in Thailand are pick up trucks! I made no analysis at all of the sales mixture of manufacturers of pick ups, or the models available and sold. That is, I chose the Navarra almost at random having decided to analyse pick up trucks.

First ten of 63 values for the Soluna:

 Make Model Age (years) Year Date of Price Value (Baht) Toyota Soluna 1.5 7.96 01/07/2004 14/06/2012 388,000 Toyota Soluna 1.5 6.92 01/07/2005 01/06/2012 428,000 Toyota Soluna 1.5 4.90 01/07/2007 23/05/2012 495,000 Toyota Soluna 1.5 5.74 01/07/2006 26/03/2012 419,000 Toyota Soluna 1.5 5.02 01/07/2004 07/07/2009 375,000 Toyota Soluna 1.5 8.17 01/07/2004 30/08/2012 345,000 Toyota Soluna 1.5 4.52 01/07/2006 05/01/2011 395,000 Toyota Soluna 1.5 7.19 01/07/2004 07/09/2011 399,000 Toyota Soluna 1.5 8.03 01/07/2004 11/07/2012 368,000 Toyota Soluna 1.5 7.05 01/07/2005 17/07/2012 429,000
• As far as the Age (years) of the vehicle is concerned, all I could find was the year of manufacture: I assumed that every vehicle, therefore, was six months old by assuming it had first been sold on 1st July in its year of manufacture.
• The Date of Price column refers to the date when the advertisement showing the vehicle for sale had been published

First ten of 27 values for the Navarra:

 Make Model Age (years) Year Date of Price Value (Baht) Nissan Navarra 2.5 3.74 01/07/2008 26/03/2012 639,000 Nissan Navarra 2.5 0.74 01/07/2011 26/03/2012 699,000 Nissan Navarra 2.5 5.16 01/07/2007 26/08/2012 540,000 Nissan Navarra 2.5 1.90 01/07/2010 25/05/2012 595,000 Nissan Navarra 2.5 3.11 01/07/2009 08/08/2012 729,000 Nissan Navarra 2.5 1.17 01/07/2011 30/08/2012 620,000 Nissan Navarra 2.5 3.65 01/08/2008 26/03/2012 699,000 Nissan Navarra 2.5 2.17 01/07/2010 30/08/2012 645,000 Nissan Navarra 2.5 3.90 01/07/2008 23/05/2012 650,000 Nissan Navarra 2.5 4.05 01/07/2008 18/07/2012 669,000

The graphs I prepared are as follows:

 Price Function: Y = 540,605 – 20,461Xr2 = 0.58483 Price Function: Y = 703,103 – 24,905Xr2 = 0.16008

We can now see that the provision for depreciation of

• the Soluna is 20,461 Baht per year, based on a “new price” of 540,605 Baht: that is, 3.78% of the new price … this assumes a useful economic life of 26.5 years
• the Navarra is 24,905 Baht per year, based on a “new price” of 703,103 Baht: that is, 3.54% of the new price … this assumes a useful economic life of 28.2 years

Should we use the Straight Line Method?

In the previous section I referred to the annual rate of depreciation and that was assuming the straight line method was being used. Is that fair: do we see a straight line relationship between the assumed age of the vehicle and the annual provision for depreciation?

• Toyota Soluna: on the face of it, I would say that an assumption of the straight line method seems reliable.
• Nissan Navarra: the sample size for this vehicle is just 27 and the relationship between assumed age and the annual provision is not so clear cut.

Take a look at this web page on my web site for further discussion here, if you are new to the accountant’s view of depreciation: http://www.duncanwil.co.uk/deprgr.html

Let’s take a look at the residuals to try to resolve this matter.

Analysis of Residuals: the appropriate depreciation method to use is … ?

In statistics we use the term residuals to mean the difference between the actual value and the value predicted by the regression equation.

In the case of the Soluna, the first five results, together with predictions and residuals are:

 Make Model Age (years) Year Date of Price Value (Baht) Predict (Baht) Residuals Toyota Soluna 1.5 7.96 01/07/2004 14/06/2012 388,000 377,761 10,239 Toyota Soluna 1.5 6.92 01/07/2005 01/06/2012 428,000 398,951 29,049 Toyota Soluna 1.5 4.90 01/07/2007 23/05/2012 495,000 440,377 54,623 Toyota Soluna 1.5 5.74 01/07/2006 26/03/2012 419,000 423,167 -4,167 Toyota Soluna 1.5 5.02 01/07/2004 07/07/2009 375,000 437,911 -62,911

Plotted on a graph, the residuals look like this:

Statisticians like to see a random pattern of the residuals since that shows the results are healthy with no cross references or leads and lags and goodness’ knows what else (see below for the discussion of the normality of the variance). However, a further analysis of the residuals shows this:

This second graph, in which the ages of the vehicles have been sorted from smallest to largest, demonstrated what is called drift: that is, in this case, the older the vehicle the smaller the residual.

A further step in the analysis of the residuals of the Soluna shows this:

That is, when we plot residuals (t-1) against residuals t, we see there is also a pattern in that generally, the data move upwards from left to right: as the value of the residual from t-1 increases, the value of residual t also increases. That’s a pattern and it shows the model we have built may be unreliable.

Nissan Navarra Residuals Analysis

Without comment, here is the same information for the Navarra as for the Soluna:

 Make Model Age (years) Year Date of Price Value (Baht) Predict (Baht) Residuals Nissan Navarra 2.5 3.74 01/07/2008 26/03/2012 639,000 610,033 28,967 Nissan Navarra 2.5 0.74 01/07/2011 26/03/2012 699,000 684,748 14,252 Nissan Navarra 2.5 5.16 01/07/2007 26/08/2012 540,000 574,620 -34,620 Nissan Navarra 2.5 1.90 01/07/2010 25/05/2012 595,000 655,749 -60,749 Nissan Navarra 2.5 3.11 01/07/2009 08/08/2012 729,000 625,727 103,273

Normality of the Variance

The most important point of the analysis of residuals is that it is really testing for the normality of the variance of the model we are considering. If we prepare a histogram of the residuals, we can see visually whether the variance is normal or not. Here is the result for the Soluna and then for the Navarra:

We can see that the frequency distribution of the Soluna shows a more near normal distribution for the Soluna than for the Navarra and we might have been able to suggest that had our sample size been a lot bigger, we might have proven normality here.

As far as the Navarra is concerned, the frequency distribution of the residuals is nowhere near as clear cut, is it? Again, however, a much larger sample size might prove helpful here.

Discussion of the Findings

Finally, what do we think of our findings?

On the one hand, it seems clear to me that a lot more data collection is needed to provide much larger sample sizes and a reliable data set. This would not be difficult to do. It might also be interesting to add two or three more vehicles to the analysis, although I used only two car types in my original UK work.

On the other hand, both sets of data have shown consistent results in the following way:

• a very low annual depreciation rate, therefore
• very long useful economic lives

These results are rather unusual and I am sure, if I were to analyse the financial reports of the average Thai company and how they depreciate their vehicles over, it would be much less that 26 – 29 years!

What can we conclude, then?

Conclusions

This preliminary and unscientific analysis of second hand car prices in Thailand has shown one interesting conclusion, even though the overall models we have derived may not be statistically reliable.

It seems that the second hand car market in Thailand is such that vehicles are virtually stores of wealth in that they seem to depreciate at around 3.5 – 3.7% per year as opposed to the 15 – 25% we might have expected. We should ask why this might be the case: why do cars in Thailand hold their values? We can suggest supply and demand, we can suggest that Thailand is a rapidly growing and developing economy which exerts pressure on manufacturers and buyers of cars. About half of all cars manufactured in Thailand are sold for export: could this be causing an imbalance in the local market?

Time permitting I will work on this case and will provide my updated findings once I have done that!