Double changeover – has refund been calculated correctly?

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SandsofEss

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I've just done a changeover on a season ticket with Southeastern, and I think they’ve calculated it incorrectly.

The base rate they’ve used doesn't appear to be 1/365th of the annual cost, but I can’t work out what it does relate to. What complicates matters is that this is the second changeover I've done on this ticket (and they’ve used different base rates each time).

Below I’ve noted down what I’ve been charged for each changeover, and then after that what I think I should have been charged based on the base rates for 2020 fares.

Can anyone shed any light on this? Is my understanding incorrect, or has Southeastern overcharged me by £70?

What Southeastern has done

ORIGINAL TICKET
Staplehurst to Frant
Purchased 01/09/2020
12M validity
Amount paid: £1,460

CHANGEOVER ONE
Ryde Esplanade to Ryde St John's Road
'Purchased' 01/01/2021
08M00D validity
Price of new ticket: £126.36
Amount refunded: £845.64
(Southeastern base rates used: 4.00 Staplehurst to Frant, 0.52 Ryde Esplanade to Ryde St John’s Road)

CHANGEOVER TWO
Staplehurst to Frant
'Purchased' 18/05/2021
03M14D validity
Price of new ticket: £495.02
Amount charged: £438.84
(Southeastern base rates used: 4.67 Staplehurst to Frant, 0.53 Ryde Esplanade to Ryde St John’s Road)

TOTAL AMOUNT PAID FOR TICKET: £1,053.20

My calculations

Staplehurst to Frant base rate = (£1,460/365) = £4
Ryde Esplanade to Ryde St John’s Road base rate = (£190/365) = £0.52

First ticket = £4 x 122 days = £488
Second ticket = £0.52 x 137 days = £71.24
Final ticket = £4 x 106 days = £424

TOTAL TICKET COST BY MY CALCULATIONS: £983.24
 
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CyrusWuff

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By my reckoning, you're correct and the second changeover should simply be the reverse of the first, giving a net charge of £368.88 for the period from 18/05/2021 to 31/08/2021.

Calculations in Full:

Staplehurst - Frant from 01/09/2020 - 31/08/2021 : £1460.00
Ryde Esplanade - Ryde St Johns Road from 01/09/2020 - 31/08/2021 : £188.00

Divide both by 365 to get the "base rate":

Staplehurst - Frant : £1460 / 365 ≈ £4.00
Ryde Esplanade - Ryde St Johns Road : £188 / 365 ≈ £0.52

Number of days from 01/01/2021 to 31/08/2021 : 243
Number of days from 18/05/2021 to 31/08/2021 : 106

Don't panic, I'm not about to go delving into simultaneous equations, it's just so everything's in one place!

Changeover 1:

Credit due on original ticket for 01/01/2021 - 31/08/2021 : £4.00 x 243 = £972.00
Charge for new ticket from 01/01/2021 - 31/08/2021 : £0.52 x 243 = £126.36
Refund due to customer : £972.00 - £126.36 = £845.64

Changeover 2:


Credit due on "original" ticket for 18/05/2021 - 31/08/2021 : £0.52 x 106 = £55.12
Charge for new ticket from 18/05/2021 - 31/08/2021 : £4.00 x 106 = £424.00
Payment due from customer : £424.00 - £55.12 = £368.88

What Southeastern have done, however, is treated the changeover as if it was a "new" season ticket (as opposed to the original Annual from last September) and used the current fares to calculate the second changeover, though I suspect this is due to the way their Ticket Issuing System handles changeovers (i.e. without taking into account the possibility of multiple changeovers) rather than deliberate overcharging.
 
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SandsofEss

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11 May 2014
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83
By my reckoning, you're correct and the second changeover should simply be the reverse of the first, giving a net charge of £368.88 for the period from 18/05/2021 to 31/08/2021.

Calculations in Full:

Staplehurst - Frant from 01/09/2020 - 31/08/2021 : £1460.00
Ryde Esplanade - Ryde St Johns Road from 01/09/2020 - 31/08/2021 : £188.00

Divide both by 365 to get the "base rate":

Staplehurst - Frant : £1460 / 365 ≈ £4.00
Ryde Esplanade - Ryde St Johns Road : £188 / 365 ≈ £0.52

Number of days from 01/01/2021 to 31/08/2021 : 243
Number of days from 18/05/2021 to 31/08/2021 : 106

Don't panic, I'm not about to go delving into simultaneous equations, it's just so everything's in one place!

Changeover 1:

Credit due on original ticket for 01/01/2021 - 31/08/2021 : £4.00 x 243 = £972.00
Charge for new ticket from 01/01/2021 - 31/08/2021 : £0.52 x 243 = £126.36
Refund due to customer : £972.00 - £126.36 = £845.64

Changeover 2:


Credit due on "original" ticket for 18/05/2021 - 31/08/2021 : £0.52 x 106 = £55.12
Charge for new ticket from 18/05/2021 - 31/08/2021 : £4.00 x 106 = £424.00
Payment due from customer : £424.00 - £55.12 = £368.88

What Southeastern have done, however, is treated the changeover as if it was a "new" season ticket (as opposed to the original Annual from last September) and used the current fares to calculate the second changeover, though I suspect this is due to the way their Ticket Issuing System handles changeovers (i.e. without taking into account the possibility of multiple changeovers) rather than deliberate overcharging.
Thank you CyrusWuff, especially for taking the time to run the numbers yourself.

Your theory is helpful. Can you explain how you think Southeastern got to a base rate of 4.67 for the latest calculation of Staplehurst to Frant? Multiplying that by 365 gives £1,704.55, whereas the current annual price for that ticket is £1,496.

I don't think this is a nefarious plot by Southeastern. It's clearly a complex procedure and one the ticket office staff don't often come up against.
 

CyrusWuff

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The base rate is variable, dependent on the original period of validity of the ticket. For an Annual, this is always 365 days. For shorter validities, one month is 30 days and then any "odd" days are added on. In this case, 01/01/2021 to 31/08/2021 is 8 months, which is treated as being 240 days.

So in this case, with a weekly rate of £36.50 for the Staplehurst - Frant ticket, you multiply that by 30.72 (8 times the monthly multiplier of 3.84) to get a price of £1121.30 for the 8 months, then divide that by 240 to get the revised base rate of £4.67.

For the Ryde ticket, they've divided the price on the ticket (£126.36) by 240 to get a base rate of £0.53, whereas it should be £0.60 if based on the price of an 8 month season (£4.70 x 30.72 = £144.40 then divide that by 240).

As such, their calculation is correct based on the figures they've used but doesn't take into account the fact that the original ticket was an Annual.
 

SandsofEss

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Messages
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Thanks Cyrus,

I still don't quite understand why the weekly rate is used to ascertain the date, or why the monthly multiplier is 3.84, but thankfully I don't think I need to.

From the sounds of it, the key point is that they appear to have done the calculations based on the wrong assumptions about my ticket, so I should be due a bit more of a refund.

I'll put it in an email to their customer service team and hope it gets forwarded to someone with the appropriate time, knowledge and authority to do the sums and issue a cheque for the correct amount.
 

CyrusWuff

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Season ticket fares are all based on the Weekly rate (or what's called a "market-priced" base rate in some cases). In the fares data, actual weekly rates in most cases will have a ticket type of 7TF, 7TS, 7DF, or 7DS depending on whether they're point-to-point tickets or Travelcards and whether they're Standard or First Class. "Market-priced" tickets will have a ticket type of TRF, TRV, PSF, or PSS. Again, this will depend on Class and whether it's a Travelcard or not.

The price of an Annual season is that figure multiplied by 40, which is nice and simple. For anything shorter, there's a lookup table with all of the multiplication factors (which I've attached to this post) or there's a formula you can use to work it out.

Using that formula, each whole month has a multiplier of 3.84, each group of five days has a multiplier of 0.64 and each remaining day has a multiplier of 0.13. So, for example, if you had a ticket valid for 5 months 17 days that'd be five lots of 3.84 plus 3 lots of 0.64 plus 2 lots of 0.13, giving a factor of 21.38 (as also shown on the table).

You then multiply the Weekly figure by that amount (and round up to the next 10p if appropriate) to get the price of the season ticket for that duration.

Changeover calculations are based on a notional daily rate for each of the tickets involved. To simplify matters (as months vary from 28 to 31 days) a little, it's assumed that all months have 30 days and a year has 365 days for the purposes of working out the daily rate, but the calculation also has to take into account the fact that an Annual effectively provides 12 weeks "free", where shorter period tickets don't.

So for the original calculation, they divided £1460 (the price of the Annual) by 365 and rounded to get £4.00 as the notional daily rate, but for the second calculation, they divided the price of an 8 month season ticket (£1121.30) by 240 (8 nominal months) to get £4.67.
 

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Haywain

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So for the original calculation, they divided £1460 (the price of the Annual) by 365 and rounded to get £4.00 as the notional daily rate, but for the second calculation, they divided the price of an 8 month season ticket (£1121.30) by 240 (8 nominal months) to get £4.67.
This is, in my view, wrongly calculated. The season ticket is/was at all times an annual season and therefore the rate for an 8 month season is not relevant to the calculations - the rates used at all times should have been those relevant to annual seasons..
 

CyrusWuff

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This is, in my view, wrongly calculated. The season ticket is/was at all times an annual season and therefore the rate for an 8 month season is not relevant to the calculations - the rates used at all times should have been those relevant to annual seasons..
Glad we're both singing from the same hymn sheet and it's SouthEastern that are in error, per my brief explanation in post #2. ;)
 

SandsofEss

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An update for any future readers with similar issues...

I received a very rapid response from Southeastern acknowledging the calculation error, and promising a cheque for the difference in the post.

Thank you again for your help CyrusWuff
 
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