I need a mathematical thinker.

[ss]

This is not exactly an excel issue but I am trying to enrole the
expertise and mindset of you guys as you all seem to display greater
levels of logic than average and have a greater understanding of
mathematics than I could dream of. This for me is difficult to explain
but will try.

The issue is to do with my gas company (uk) the figures themselves are
not that important as I am just trying to figure out if I am right or
wrong. I have tried to replicate some of this in a spreadsheet so I can
introduce variables to answer my question but so far have not made much
progress. I am not looking for a formula or someone to do the
spreadsheet really just want confirmation one way or the other then I
can plod on on my own.

This is the conundrum:-

The deal I am on is a tariff as detailed.(figures made up for ease of
explanation)
Year is in 4 quarters
Each quarter I am charged for gas as follows...
1st 631kwh charged at 30p per kwh
After 631 kwh I am charged 15p per kwh
Each quarter should be approx 91 days with adjustment for weekends.
And the above figures reset at the start of each quarter.

This far I am ok with. Now last quarter was only 80 days

So because they have cut short one quarter they have now put me on the
more expensive initial charges sooner (by about 10 days) than they
would normally, now that means (in my head) that when I hit the less
expensive charges I will be using less gas as the weather will be
possibly warmer, so in theory my gas bill will be slightly more. So
they are manipulating the bill so that I pick up the more expensive
initial charges while the weather is colder. At least thats what my
brain is saying but I cant get the figures to stack up.

Any thoughts on this?

 

[joeu2004]

Year is in 4 quarters
Each quarter I am charged for gas as follows...
1st 631kwh charged at 30p per kwh
After 631 kwh I am charged 15p per kwh
Each quarter should be approx 91 days with adjustment for weekends.
And the above figures reset at the start of each quarter.
This far I am ok with. Now last quarter was only 80 days

First, how do you figure that the last quarter has 80 days?

365 - 3*91 = 92.

(In a leap year, the quarters might be 91, 91, 92, 92 instead of 91, 91, 91,
93.)

So because they have cut short one quarter they have now
put me on the more expensive initial charges sooner (by
about 10 days) than they would normally
now that means (in my head) that when I hit the less expensive
charges I will be using less gas as the weather will be possibly warmer,
so in theory my gas bill will be slightly more.

Yes, __if__ one quarter were significantly fewer days than the other
quarters, your __daily_average__ cost would be higher because the divisor is
smaller.

But the total cost for the quarter would be the same, regardless of the
number of days in the quarter. Arguably, that is what matters.

As for the daily average cost....

It has nothing to do with __when__ the gas is used ("initial charges sooner
by about 10 days").

It simply has to do with the __total__ kwh of gas in a quarter divided by
the number of days in that quarter.

But as I asserted above, not only is one quarter __not__ significantly
smaller, it is longer. And the difference of dividing by 91 v. 92 is less
than 1.1%: 92/91 - 1.

(In contrast, if you were right, the difference of dividing by 91 v. 80 is
13.75%: 91/80 - 1.)

Moreover, there is nothing to say that the 92-day (or "80-day") quarter is
the last quarter when you are "using less gas as the weather will be
warmer". It might be the first quarter; or it might be a middle quarter.

 

[joeu2004]

Year is in 4 quarters [....]
Each quarter should be approx 91 days with adjustment for weekends. [....]
Now last quarter was only 80 days

First, how do you figure that the last quarter has 80 days?
365 - 3*91 = 92.
(In a leap year, the quarters might be 91, 91, 92, 92 instead of 91, 91,
91, 93.)

Of course, the quarters are the days in each 3-month period, which is not
necessarily 365/4.

The typical quarters are Jan to Mar, Apr to Jun, Jul to Sep, and Oct to Dec.

In 2012, the number of days in each of those quarters are indeed 91, 91, 92
and 92 respectively. In 2013, there are 90 days in the first quarter.

But you wrote "with adjustment for weekends". That might make sense if you
are business operating Mon through Fri (typically), and you want to compute
the average cost per __workday__.

In 2012, the number of workdays in each of those quarters are 65, 65, 66 and
66 respectively. In 2013, there are 64 days in the first quarter. The
number of workdays in each quarter might vary each year (in a 14-year cycle,
IIRC; maybe not).

In any case, the point is: the number of days per quarter does not vary
greatly; and none is 80.

It simply has to do with the __total__ kwh of gas in a quarter
divided by the number of days in that quarter.

I meant: the total __cost__ divided by the number of days.

 

[ss]

First, how do you figure that the last quarter has 80 days?

It was the utility company that made it 80 days for reasons I cannot
understand which is what started me off on this as I am sure there will
be some financial gain for the company in doing so and thats what led me
to looking more closely at the tarriff and how the KWH charges are made.

This I received from the utility company....
"Your account is a combine billing account, so there is a single bill
for your gas and electricity. We previously billed your gas account till
15 November 2012 and electricity to 26 November 2012. Your current bill
was due by early February 2013, this is why you received a bill for less
days than the quarter. I ensure that your next bill will cover the
quarter correctly."

They are incorrect as the bill was not due for another 10 days based on
previous years dates.

 

[Alex Plantema]

ss schreef in

This I received from the utility company....
"Your account is a combine billing account, so there is a single bill
for your gas and electricity. We previously billed your gas account
till 15 November 2012 and electricity to 26 November 2012. Your
current bill was due by early February 2013, this is why you received
a bill for less days than the quarter. I ensure that your next bill
will cover the quarter correctly."

They are incorrect as the bill was not due for another 10 days based
on previous years dates.

The dates that the bills are made up possibly don't have to do with the dates that the quarters start.
But when they do, it might affect how much you pay.
You pay the most when you reach 631 kWh in each quarter.
If you would reach 631 kWh in each quarter when they are evenly long,
changing their lengths will be advantageous when as a result you don't reach 631 kWh in some quarter.
But it might be disadvantageous e.g. when you use less then 631 kWh in summer and they make the summer quarters longer.

 

[Mark F]

It was the utility company that made it 80 days for reasons I cannot
understand which is what started me off on this as I am sure there will
be some financial gain for the company in doing so and thats what led me
to looking more closely at the tarriff and how the KWH charges are made.

This I received from the utility company....
"Your account is a combine billing account, so there is a single bill
for your gas and electricity. We previously billed your gas account till
15 November 2012 and electricity to 26 November 2012. Your current bill
was due by early February 2013, this is why you received a bill for less
days than the quarter. I ensure that your next bill will cover the
quarter correctly."

It seems like the gas company wants the gas and electricity to be
billed on the same cycle and have therefore shortened the gas cycle
for one quarter to get things in synch.

You need to check that they prorated the 631 KWH break point to
631 KWH * (ND/91). ND should be about 80, which yields
about 554.7 KWH. This is how things have
worked for me in the USA for phone, cable, gas, and electric.

You may have some issues as to whether ND should be 79, 80, or
81, depending on the times of the readings.

 

[ss]

It seems like the gas company wants the gas and electricity to be
billed on the same cycle and have therefore shortened the gas cycle
for one quarter to get things in synch.

You need to check that they prorated the 631 KWH break point to
631 KWH * (ND/91). ND should be about 80, which yields
about 554.7 KWH. This is how things have
worked for me in the USA for phone, cable, gas, and electric.

You may have some issues as to whether ND should be 79, 80, or
81, depending on the times of the readings.

Thanks all for the replies , it has given me a clearer picture.
To date they have only said they will bring it into line next quarter
but no reason for why they did this. Interestingly I had the guy who
reads the meter out yesterday.... to read the meter......14 days after
they sent the Bill. Had a chat with him and he says he is given a time
window of so many days to read the meters, he was within the time window
which was outwith the end date of the last quarter.
Anyhow not come to a conclusion with the utilty company yet as they are
fudging answers at the moment so will escalate it soon if necessary.