I have been asked to investigate factors that affect the depreciation of cars.

I have been asked to investigate factors that affect the depreciation of cars. To do this I would ideally like to collect my own data about used cars. This would be called primary data. I would have collected data on the make, model, mileage, engine size, age, price and price when new of several hundred used cars. Unfortunately this would have taken a lot of time, but the advantage would have been that it would have been reliable data which I could trust, and I could have found out exactly the information that I wanted.

It would have been impossible for me to do such a large survey, however, so I had to use secondary data that I got from the CCEA website. The advantage of this was that it was quick, cheap and easy, but I can’t be sure of the accuracy of these results and I don’t know if any bias was involved when it was being collected. I have also found that many of the results are incomplete.

From the very start, I am sure that two of these results are wrong – a Renault Laguna which costs £50,000, and a Renault Clio that increases in value. I have deleted these results straight away.

Hypothesis 1

My first hypothesis is that cars depreciate more as they get older. I used the spreadsheet on the computer to test this hypothesis, but first I had to get the age and percentage depreciation for each car, neither of which are recorded in the table.

Firstly, to get the age of the cars, I subtracted the year in which they were made from 2002, the year when the data was collected. I first created a new column on the spreadsheet and called it age. Then I typed into the first box under the title the formula for age-

=2002-F2

where F2 is the column for the year the car was made. This filled the box with the age of the car. I then highlighted the box, right clicked and selected copy, before highlighting all the boxes below and selecting paste special, formula. This filled in the ages for all of the cars.

Next, to get the percentage depreciation, I made another column and filled it with a more complicated formula-

=(I2-H2)/I2*100

where I2 is the price when new and H2 is the price now. This filled the first box in the percentage depreciation column with the appropriate value, and I copied the formula into the other boxes as before.

I then highlighted these two columns and copied them into chart 2. I then changed all the values to 2 significant figures, highlighted the two columns, and made a scattergraph using the computer. When I saw the graph, I noticed that some of the values formed a straight line across the top of the graph. This was because some of the prices were missing, and the percentage depreciation had been calculated as 100%. I decided to delete these values, as they were incorrect. The scattergraph now looked more like my hypothesis had predicted.

The graph shows a positive correlation, which means that, as I had predicted, the cars had depreciated more as they got older. The graph did not form a straight line, however. The points formed a curve that got less steep as the age increased. This indicates that the cars loose more value numerically in the first year than they do in the second, and that they loose a smaller value each year than they did the year before. This could be caused by the cars loosing a certain percentage of their value each year. For example, if a £10,000 car looses 10% of its value each year, in the first year it will lose 10% of £10,000. This means it will lose £1,000, making its value £9,000. The next year the car will lose 10% of £9,000. 10% of £9,000 is £900, so the car will now be worth £8,100. Since the slope of the graph is equal to the percentage of the original value lost per year, the graph will form a curve, similar to an upside down exponential.

I can use this graph to make comments about used cars taken from a copy of an auto trader magazine. For example, I found an advert for a Ford fiesta that was made in 1996, priced at £1,275. This is a 6-year-old car, and when I look at my graph I can see that the percentage depreciation of most 6-year-old cars is between 65 and 85 %. If I take the middle of this group to be 75%, and assume that this car has depreciated by 75%, this means that the price stated above is 25% of the price when ...

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100/25 x £1,275 = £5,100

This means that the price when new would have been roughly £5,100, but this is a very rough answer as there is a wide range of values within each age group, and the graph can only be used as a guide. The price that was quoted in the magazine could also be unreliable, as the owner may have raised his asking price in case the buyer wanted to haggle the price down.

Within each age group there is a wide range of values for the percentage depreciation. This suggests that there may be other factors that affect the depreciation of the car.

Hypothesis 2

From looking at my graph for hypothesis 1, I have decided that there must be another factor that affects the depreciation of cars, and that this factor must be responsible for the wide range of values that were seen in each age group of the scattergraph. I think that this factor is likely to be mileage. My hypothesis is that the higher the mileage of the car, the higher the percentage depreciation.

In order to prove my hypothesis, I have decided to draw another scattergraph, but this time I will take a stratified sample of the cars. I have decided to stratify on ages and I will take a stratified sample of 40 cars. The first thing that I must do if I want to stratify on ages is to put the cars in ascending order of age. Thankfully the computer can do this for me in an instant. Next I must decide on the groups that I will separate them into. I have decided to put them into three roughly equal groups, and boundaries of 0-3, 4-6, and 7+ fit this quite well. I now have to decide how many cars I will take from each group. To ensure that every car has an equal chance of being chosen the number of cars taken from each group must be proportional to the size of the group. This means that the number of cars taken from the group is found by

Cars taken = (Cars in group / Total no of cars) x 40

When worked out to the nearest whole number, group 1 will have 14 cars selected from it, group 2 will have 17 cars selected from it, and group 3 will have 9cars selected from it. I will use the random number generator on my calculator to select the cars at random as follows.

Place in group of car selected = Random number x No. of cars in group

I will use this formula and select the nearest whole number to my answer until I have selected the required number of cars from each group. When I have selected the 40 random cars, I will plot their mileage against their percentage depreciation in a scattergraph. (See scattergraph)

The graph shows a definite positive correlation, meaning that as the mileage of the car increases, so does the percentage depreciation. This time the best-fit line is not curved, suggesting that the two values are directly proportional – as mileage doubles, so does percentage depreciation. There is again a large variation in the percentage depreciation, as the values form a wide band across the axis. This is due to the effect of age on the percentage depreciation.

These results agree with my hypothesis and show that the mileage must have an effect on the percentage depreciation.

This graph can also be used to make predictions about used cars. For example, I have found an advertisement for a 1.2 litre ford fiesta made in 1999. All of the 1.2 litre fiestas made in 1999 on the spreadsheets were priced at £9,020, so I will assume that this was the original price for the car in question.

The advertisement says that the car has a mileage of 34,000 miles, and states a price of £2,100. From looking at my scattergraph, I can see that a car with this mileage should have depreciated by roughly 60%. If this car was worth £9,020 when new and had depreciated by 60%, it should now be worth

£9,020 – (60/100) x (£9,020) = £3,608

This price is significantly more than what the owner is asking for, so if I was going to place an offer on this car, I would place a bid slightly higher than the price quoted. This would increase my chances of being successful, but I would know that I would still be getting a good deal.

Hypothesis 3

I think that different makes of cars depreciate at different rates. I decided to draw a box-whisker diagram of the data to test this theory. These diagrams allow me to look at the middle 50% of each group and the median, but allow me to ignore any unusually high or low results, although they are there if I need them.

The first thing that I had to do was to sort the data into four separate sheets, one for each make, and then arrange each sheet in order of ascending percentage depreciation. I then used these four sheets to locate the highest, lowest, and median values, as well as the first and third quartiles (the boundaries of the middle 50%) for each make. I then combined this information in four diagrams on one page so that I could compare them. From this information I was able to come to some conclusions-

∙The four makes all have a similar range. Their highest values are almost identical. This means that the highest depreciation for each make is very similar.

∙The spread of the middle 50% of three of the groups are similar sizes and in similar positions, but the fourth make, the Vauxhalls, have a much smaller range for this middle section, and the lower bound of this section is much higher than that of the others. This means that more of the Vauxhalls will have a high depreciation rate than for other makes. The tight spacing of the group shows us that there isn’t much variation within the middle 50% of the Vauxhalls.

∙The median of three of the groups is closer to the top of the group than to the bottom. This is especially true for the Renaults. This means that for these three groups the values are negatively skewed, or squashed towards the top of the group. If a histogram were drawn, its peak would be towards the right of the group. The exception to this rule is the Peugeot diagram. The median for this set of values is situated in the middle of the group. This means that the data is almost symmetrical and that a histogram of this data would peak in the middle.

This information can be used to make predictions about how the value of different makes of car will change. Judging by this diagram alone, if I was going to buy a new car, I would buy a Peugeot. This is because they seem to keep their value better than the other makes of car that have been sampled, and I would get a better price if I was to sell it again. I definitely wouldn't buy a Vauxhall as they seem to lose their value the quickest.

However, all of this information depends on the assumption that the sample was unbiased. It could be that Vauxhalls depreciate more than the Peugeots, or it could be that the Peugeots sampled were from a used car dealer and therefore in decent condition, and the Vauxhalls were sampled from the Auto Trader and in relatively worse condition. It could also mean that the Peugeots were on average younger than the Vauxhalls in the sample. This shows how important it is to avoid bias when collecting data for a study such as this.

Hypothesis 4

I think that diesel cars depreciate less than petrol cars. To test this theory, I decided to take a random sample of 35 diesel and 35 petrol cars, and I found the mean of each sample and compared them.

The first thing that I did was to separate the cars into two sheets, one for petrols and one for diesels, and arrange these into order of age. I then took a random sample of 35 cars from each group using the random number generator on my calculator.

When I found the average depreciation of these two samples, I was surprised to find that the diesels had an average depreciation of 70.20%, but the petrols had an average depreciation of 63.86%. This was the opposite of what I had expected. I thought that my stratified samples could have accidentally picked up a range of diesel cars that were on average older than the petrol cars that were sampled. This would be a possible explanation for the unexpected averages that I had calculated.

In order to test this theory I drew a varying width histogram of each of the two stratified samples showing the ages of the cars and compared them. When I did this, I found that the histogram of the petrol cars began to peak slightly earlier and more dramatically than that of the diesel cars. This means that there were more older diesels than petrols, although the difference wasn’t very much. This could be the reason why the average results were not as I had expected.

There were two possible reasons for this difference in the average ages – either my stratified samples had been accidentally biased, and were not representative of the original data, or the original data itself had contained a difference in the average ages of petrol and diesel cars. In order to determine which of these it was, I drew two more varying width histograms, but this time I used all of the cars in the original data.

When I compared the sample of petrol cars to the complete set of data, I found that their histograms were very similar, although the original histogram peaked slightly before the stratified one, so the stratified sample that I took must have been fairly representative of the original data. I then compared the original diesels with the stratified sample of diesels, and I found that the two histograms were almost identical to one another. This means that my two stratified samples must have been accurate enough to be representative of the entire data. If my stratified sample was accurate, then the diesel cars must have been on average older than the petrol cars. There could be several reasons for this – perhaps the original data was biased, and therefore unrepresentative of the population of petrol and diesel cars nation-wide. Another possible explanation is that diesel cars could be more reliable than petrol cars, and therefore people like to keep them for longer before selling them. If this was the case, it would mean that the original data was in fact representative of the population.

All this tells us that the average percentage depreciation of the diesels was higher than that of the petrols, either because for some reason the diesels tended to be older than the petrols, or it could just be that the diesel cars really do depreciate more than petrol cars do.

Conclusion

During this investigation, I have identified several factors that affect the depreciation of cars.

Age

The first factor that I identified was age. I found that as the age increases, so does the percentage depreciation. I think that age has the greatest influence on the depreciation of the car, as the points on my scattergraph form a very obvious pattern. This could be because age not only affects the condition of the car, but also its style and desirability, as older cars may not have certain features such as airbags or power steering.

Mileage

Mileage was the next factor that I identified, and I think that it is the next most important factor after age. I think this because the scattergraph again shows an obvious pattern, but it isn’t as uniform as the scattergraph for age. This could be because the mileage can affect the condition of the car, but it doesn’t necessarily affect the desirability of the car. A car can have a high mileage but still be relatively new and have features like airbags.

Make

I found that make had a small effect on the percentage depreciation. I found that Vauxhalls depreciate the most and that Peugeots depreciate the least. However, the difference was less than 20%, so make has a smaller effect on the depreciation than age or mileage.

Petrol/Diesel

I found that the fuel on which a car runs has a small effect on the depreciation on the car. I found that diesel cars depreciate more than petrol cars do. However, the difference was very small - less than 7% - and I was unable to determine whether this difference was caused by the fuel used or by bias involving age in the original sample.

All of the data that I have collected can be used to make decisions when buying a new or used car.

If I was buying a new car, I would buy a Peugeot that runs on petrol, because the data suggests that this sort of car would be likely to depreciate the least, and therefore be worth more when the time came to sell it. I would definitely not buy a Vauxhall as they depreciated more than the other makes in the survey.

If I was buying a used car, I would buy a Vauxhall, because they have depreciated more than any other type of car in the survey and should therefore be the cheapest. I would try to buy one that was less than 5 years old, however, because of the way that the graph of depreciation against age curves. After 5 years old, the slope of the graph becomes very gentle. This means that the cars are getting older, and therefore in worse condition, but the price is falling very slowly, so you will get less value for money as the cars get older.