Expert: Lynn Houston - 9/25/2008

Question
QUESTION: 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, in trying to answer an important question that I need to know.

My job is a Chauffeur and I do a substantial amount of business miles in the UK in a company vehicle supplied to me to do my job. I am also given a BP Fuel Card to fill up the vehicle with diesel whenever my tank runs low. However, I have a big query regarding fuel re-imbursement as the company uses a particular methodology which I will endeavour to explain.

I only get reimbursed the BUSINESS MILES I do every month via a Pence Per Mile System (PPM) and GPS Tracking – the monthly total business miles figure is generated automatically via a GPS tracking system that records all the business miles in a month and reimburses monthly using a system of PENCE PER MILE (PPM). The PPM rate is currently about 14 pence to 15 pence. The PPM rate changes monthly, slightly up or down depending on the constant changing fuel price in the UK.

METHOD USED TO CALCULATE PPM RATE SYSTEM

1. Total Fuel Purchase by ALL the company’s chauffeurs
2 Total Gallons bought by ALL the company’s chauffeurs)
3. MPG (i.e. the company REQUIRES us to achieve 35mpg with the vehicle) = PPM

Calculation = (1/2)/3

( i.e. Total Fuel of Everybody / Total Gallons of Everybody) / MPG figure company expects from Everybody )

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, as mentioned, 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 also tracked via the GPS tracking system and I am NOT reimbursed this PPM rate so if I use the vehicle privately, I similarly pay a 14 pence PPM rate out of my pocket although no “credit” at 14 PPM is given for non business miles. Obviously using the vehicle heavily for NON business miles will create a deficit in itself as we are not being reimbursed for this at all – so for this query let us completely IGNORE use of the vehicle privately.

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. A ‘credit’ is given to me for business miles by this PPM method and then the my personal BP Fuel Card Monthly Bill is charged against this credit leaving me in a surplus / deficit – whichever may occur)

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 QUESTION

My main and important query is – Does it make a difference if I actively seek to buy the cheapest fuel? Does this benefit me financially via the ‘surplus’ system or does it benefit the business and not me?

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, FYI, 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 at all 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’s tank at a particular month’s end (i.e. no one knows exactly how may litres sit in a vehicle at any one time?

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 in 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 benefit to continue finding the cheapest fuel or whether I have been and will be wasting time by doing so


ANSWER: Ok.  I think the answer to your question is yes, it would benefit you to buy cheaper gas.  If they "charge" your gas purchases against your credit and you pay less for gas, then your credit will be larger. However, the question is, will the company allow you to buy gas wherever you want or do they require you to purchase BP? And, do you go out of your way to fill up at a cheaper rate or do you find the cheapest rate on your "on duty" path?  If you go out of your way, it's probably considered personal miles, therefore, offsetting any benefits you might see from the lower fuel cost.  However, either way, depending on the number of miles you put on per month and the cost difference in the BP to cheaper fuel, you're probably only talking about a few dollars a year.

As far as your second question, actually, I think they can tell how much fuel you have left (the rental car companies do it all the time, I believe, via the car computer.  But, it should have no bearing on your on your overall credit, because as you said, what goes down one month, goes up the next.

---------- FOLLOW-UP ----------

QUESTION: Thanks for your answer - the company allows us to buy gas whereever my BP card is accepted (All BP stations which all have different prices (i.e. It really does vary), and my BP card is also accepted at "TOTAL" gas stations (which is usually cheaper than any BP) - I dont go out of my way to fuel up, I always fuel up on route and make a point of keeping an eye on gas prices as I drive. I alway fuel up "on duty" so I never pay personal miles to gas up and I get paid by the hour on my salary so it makes sense to fuel up when I am on duty and passing a cheap gas station. The differential between the CHEAPEST £1.18 per litre for diesel and the AVERAGE is £1.25 so it is about £0.07 a litre of diesel and I fill up to 60 / 70 litres per filling (tank capacity).

What I dont know is whether it is worth my while doing this at all, as so many friends and work colleagues (fellow chauffeurs) have argued that it doesnt make any difference where you fuel up and what the price is?

In fact, I had one very close friend who is fairly brainy and educated tell me that it is actually in my interest to find the MOST EXPENSIVE fuel and fill up (as with BP I can also collect "Nectar Points" - a UK Loyalty reward scheme so the more I spend the more I can claim back in points. As he tells me it doesnt make any difference according to him, so why should I not find the most expensive and collect the Reward Points along side ??!!!)

Others tell me that I do personally benefit financially buy filling at the cheapest and so I must try to get the cheapest. I have never asked an expert, and never asked anybody in the company as the average intelligence of those in the office is not the greatest and again you get different accounts and stories.

All I want to know is which is it? Am I wasting my time and not benefiting, or is the company getting the benefit and not me.

Basically should I bother or care as I do not know the "scientific mathematical" answer as to whether I am gaining by doing so and so many debates amoung friends and work colleagues - everybody comes with different views but I have never asked an expert.

It has been bothering me for so long now that I decided to ask an expert as I do make every effort (so far that is) to fill up cheapest but dont know if it is working FOR ME and MY PAY?

ANSWER: Bottom line, as far as I can see from your explanation, is yes, you would be saving by buying the cheapest gas because 1), if you fill up with cheaper gas, there is less to offset your PPM and you get more of your PPM in the long run and 2) because when you're driving personal miles, you're using cheaper costing gas.  Again, IF I understand your explanation and there is a .07 difference in price per litre and you filled up 3 times per week (just a guess on my part), the savings for the gas would be 764 (pounds?) for the year.  So, I guess, now the question is, what is the value of the Nectar points that you could get by filling up at a higher rate?

Or, maybe I don't really understand your companies system and you don't actually get your excess PPM?  My evaluation is based on the assumption that you get the excess PPM.  If that is the case, then no, there is absolutely no reason to seek out the cheapest gas and I'd go with the nectar points.

---------- FOLLOW-UP ----------

QUESTION: I think that your reason 1.) sounds like the way I have been thinking, but I do not know for a fact as I really am not fantastic at the maths side of it which is why I have asked someone like you who may be better at seeing waht I can't see or understand. I really need to understand mathematically that it is beneficial for me financially.

Your point number 2.) I do not drive the vehicle for personal miles (very rare) and I avoid using the vehicle other than for business miles - I do the odd few miles for personal use. Plus the business charges a car hire charge of £32.50 per day for personal use if not on duty PLUS the PPM miles (i.e. for every mile we do we pay 14pence per mile)

So using the car for personal use is BEST AVOIDED, plus it adds to the "deficit" in the company's fuel re-imbursement system as we are not "credited" the PPM for personal miles (thats how we end up paying for it by not getting the 'credit' back).

For example, if I were to use the vehicle HEAVILY for personal miles my build up of "Non-credits" on the PPM would be so huge that there would definately be a deficit when they offset the Business Miles PPM credit they give against the BP Fuel Card Bill (as personal miles have been driven using the fuel I have filled using the company's BP card).

The differential is definately about 0.07 pence per litre usually and I fill up about 1-2 times a week - Nectar points are ONLY given at BP stations which are usually always more expensive, there is NO nectar or similar reward scheme at TOTAL stations which are usually the cheapest.

I am banking on the fact that I get a "physical cash financial reward" through the company's fuel re-imbursement system (i.e. by 'building a surplus when the offset the business mile PPM credit against my BP bill') by filling at the cheapest station - but I am?????? That is what I need to know?

Nectar points are granted for every litre you fill (i think 1 point for £1) but you need thousands of points for it to mean anything i.e. money off shopping etc. Nectar's website is - http://www.nectar.com/NectarHome.nectar).

So actually it is by litre, and not the higher £ value rate - if that makes any difference? Does it? i.e. If i filled up 60 litres at £1.189 at TOTAL that would be = £71.34 BUT NO REWARD POINTS and if I filled up 60 litres at £1.259 at BP that would be = £75.54 BUT 60 NECTAR POINTS

Like I say in the above example, I would have chosen TOTAL "HOPING" that I am getting "CASH CREDITS / SURPLUS" via my company's fuel re-imbursement system - but am I???

I dont understand your last paragraph at all, the one beginning "Or,maybe I......." - could you please re-explain it again??? We get any "excess" if what you mean by this if there is a surplus (or deficit which gets DEDUCTED FROM PAY) created by my own Business Miles PPM CREDIT that give to me, offset by my BP Fuel Card Bill (bearing in mind we MUST also do 35mpg on the car otherwise that is ALSO DEDUCTED SOMEHOW)

Hope it all makes sense. You may be a bit confused just as I am on whether I am GAINING by filling up cheaper.

Please, you have really been really very helpful but I need a definitive answer otherwise I will be in bewilderment forever !!!. May I urge you to re-read all the 3 responses I have sent and maybe it will be a bit clearer for you to re-assess how the scheme works because whilst I understand stand it fairly well, I cant see if I am personally gaining.

My company has 500 cars and 500 chauffuers and we do roughly 1200 individual pick ups (passengers) a day between all of us and we drive hundreds and hundreds of miles a day - I can easily do 350 miles today, 265 to-morrow and then 397 miles the day after.

So it is a big, complicated Chuaffeur Drive business and I sometimes end up in deficit on fuel, sometimes in surplus - I find it hard to do 35mpg on the car although I really try as I dont want the company to deduct my pay for anything below 35mpg via our fuel re-imburesent system that I have explained to you (I think thats through the PPM formula they use that I gave you in my first message to you)

Hope it all makes sense. May I urge you just to re-read the whole lot again to see if it makes more sense to you as to how it works and whether you can help me with my main question - i.e. am I wasting my time or benefiting.

Like I say, I have had debate over debate but no one has a defintive answer and on one has been an expert either. But I really need to know now as it is bugging me greatly!!!!!!!!!! I need to know how it is benefiting me financially if it does work!!!But does it?  

Answer
Ok.  Hopefully this will be the last response and things will be clear for both of us.  If (and I wasn't totally clear about this from all your responses, that's what I meant from the last paragraph in my last answer), if you receive the surplus each month and/or have to "pay" the deficit, then you are absolutely better off finding the lowest fuel prices (for the first reason I stated last time).  Let's say you fill up on average twice a week and you said that the fill ups are 60-70 liters, so we'll use 65 as an average.  With a .07 difference, you'll save approx £40/month.  Or, approx £473 per yr.  You're correct about the nectar points, those systems in general, require you to have so many points for "prizes" that you're better off buying the same thing with real money and use the £473 extra per year that you'll have by filling up at a lower rate.