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Maths expert needed to help solve real life mystery?

December 3rd, 2009 | by admin |

I have a real life maths problem scenario but I need a maths expert to help me as I cannot get my head around the conceptual maths part of it.

I get reimbursed business miles I do every month – the monthly total business miles figure is generated via a GPS tracking system that records daily business miles and reimburses monthly at a PENCE PER MILE (PPM) rate of about 14 pence. The PPM rate changes monthly, slightly up or down depending on the constant changing fuel price in the UK.

This figure is calculated by the Business as follows:-

(Total Fuel Purchase / Total Gallons) / MPG (i.e. expected to get 35mpg) = PPM

Example;-

Total Fuel Purchase = £563.76 Total Gallons = 115 thus MPG = 35mpg

563.76 / 115 = 4.90

4.90 / 35 = 0.14ppm

(I do not suspect that knowing how this is derived is relevant to the question I will pose shortly apart from the fact that we are expected to achieve 35 miles per gallon on the vehicle and if we under achieve on this target we pay for it ourselves somehow and if we over achieve they give a credit for this somehow).

For NON business miles that is tracked via the GPS tracking I am NOT reimbursed this PPM rate so if I use the vehicle privately, I similarly pay a 14 PPM rate out of my pocket although no “credit” at 14 PPM is given for non business miles.

Therefore, I get a “credit” for all business miles only monthly at this 14 pence (PPM) rate but the business also give me a BP Fuel Card (relevant to this query as BP is by far, not the cheapest fuel to purchase in the UK) which they charge against the “credit” they have given me for business miles (i.e. Credit given for business miles and then the BP Fuel Card Monthly Bill charged against this credit)

So in an example they may give me £300 credit for business miles but my total fuel card bill may be £350, therefore I am in DEFICIT or I could be in SURPLUS if my total fuel card bill came to £280.

My main and important query is – Does it make a difference if I actively seek to buy the cheapest fuel? Does this benefit me or the business? If so, can you please explain how this benefits me i.e. does it make any difference to me financially to seek the cheapest fuel which I have been doing as a general principle in the expectation that I AM PERSONALLY BENEFITING financially by doing so.

This has lead to heated debates between colleagues and friends where some have argued it is in my financial benefit to seek cheap fuel whereas others have said it makes no difference at all and that I should fill up anywhere?

My secondary query which is not as important as the first – The business works STRICTLY on a monthly basis for fuel calculations but obviously no one can be exactly sure of how much fuel is in the car at a month’s end?

Some argue that I should aim to run the tank down at month end not to end up in a bad “deficit” position, and, or, not to fuel up at all on the last day of the month as this will ‘create’ a deficit. Is there logic in this as any deficit at a month’s end would be a credit in the new month following, wouldn’t it so you maybe worse off at one month but be in a recovered position the next?
Please help as this has been bewildering me for quite some time, especially whether it is in my own financial interest to continue finding the cheapest fuel or whether I have been and will be wasting time by doing so.

Let me answer the easier part first:
You are right, creating a deficit (if it does so) near the end of the month is balanced out by the fact that you don’t make that fuel purchase in the following month, and therefore attract a credit (or a smaller deficit) for the following month.

The first question depends on how much you can save by buying the cheapest available petrol. (sorry, I’m drinking brandy and getting a bit foggy). In which state it seems to me that the "no difference at all" crowd are correct: If the full price of the fuel bought on the BP card is charged against your credit, then it’s better to chase the lowest fuel price.

e.g. If you buy £220 on the BPcard against your £300 allowance, you have £80. If instead of this arrangement, you buy the fuel for a total of £190, you get the full £300 having spent £190, so effectively you have received £110 — rather better than using the BP card.