Complex Refund Puzzle

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barrykas

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Good afternoon,

It being a slow day at work, I've come up with a fiendish change-over related refund situation for folks to have a go at...if you dare. <D

Just to make life a bit easier for those who don't have access to old NFMs, I'll use current fares, though it'll make the dates look a bit silly.

Passenger A buys an Annual Season ticket between London Terminals and Banbury, valid from 02/01/2013 to 01/01/2014, at a cost of £5028.00 (7 day rate: £125.70).

On 28/03/2013 the passenger requests a change-over to a London Terminals - Princes Risborough ticket, effective from 02/04/2013. The Annual for this would have been £3280.00 (7 day rate: £82.00). As such, they receive a refund of £1317.25.

On 28/06/2013, they request a further change-over to London Terminals - Gerrards Cross, effective from 02/07/2013. The Annual would have been £2360.00 (7 day rate: £59.00). They received a refund of a further £463.68.

The question is this: Suppose our passenger then hands the last of the three tickets in for a refund on 01/08/2013, having used the ticket on that day (i.e. an overall validity period of exactly 7 months). What refund would they be entitled to?

And if you feel like a second challenge, what if the tickets were the other way round? So they started with London - Gerrards Cross, then upgraded to Princes Risborough and finally to Banbury? Assume the same dates.

Cheers,

Barry
 
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transportphoto

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"Passenger A buys an Annual Season ticket between London Terminals and Banbury, valid from 02/01/2013 to 01/01/2013, at a cost of £5028.00 (7 day rate: £125.70)." - I make that a season ticket with a validity of -1 day, is this correct?

(Edit, if it is, I concur with Harlesden in post #3...)

TP
 
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Harlesden

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No. Not one day. He's been sold a ticket with an expiry date that has already passed (I don't believe the ticket machine would issue such a ticket no matter how determined the operator eas.)
 

wintonian

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I'm too tired to play today but is this one of those trick questions and there is no refund due or something? <D
 

barrykas

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Expiry date for the original ticket should, of course, have been 01/01/2014, not 2013 as I originally wrote. My bad. Must try harder.

And I haven't come up with a figure as yet, I just wanted to see what other people thought.

Though there definitely will be a refund due, given the ticket's only been used for seven months.
 

hairyhandedfool

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I'd have to check what the manual says exactly, the recollection of the rules I have makes this a very long calculation and I hate to do it all and then find the rules have changed at some point.
 

barrykas

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I've just realised exactly how evil a query this is, thanks to the involvement of the double change-over in each case, as it involves working out four change-overs as part of the refund process.
 

barrykas

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A spreadsheet should be relatively easy...You just have to remember to take a couple of things into account:
  • Relevant prices depend on the period of the original ticket, you can't always use the figures for an Annual
  • For base rate purposes, a year is always 365 days and a month is always 30 days.
--- old post above --- --- new post below ---
Assuming my Maths is correct (which it probably isn't), I think the gross refund due in example 1 is £526.15, and in example 2 it's £1699.72.

That's only a guess though, as it's a purely hypothetical example and I haven't had to do such a refund as yet.
 

hairyhandedfool

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Lets just say I get a different figure for the initial question....a very different figure........
 

bb21

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Using the season ticket prices quoted in the OP, I get very different refund amounts for the changeovers.

For the first changeover,
  • base rate per day for Banbury ticket: £13.78
  • base rate per day for Princes Risborough ticket: £8.99
  • days remaining: 270
  • refund on Banbury ticket: £3720.60
  • charge for Princes Risborough ticket: £2427.30
  • refund: £1293.30
 

hairyhandedfool

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Minor error in your maths bb21, there are 275 days (9 months 5 days) left on the original changeover, though I admit I got a different figure for the second changeover refund (£466.20), though this could be accounted for by how the number of days remaining is calculated.
 
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bb21

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Minor error in your maths bb21, there are 275 days (9 months 5 days) left on the original changeover, though I admit I got a different figure for the second changeover refund (£467)

Yes, I think I got the definition of a "month" mixed up with base rate calculations.
--- old post above --- --- new post below ---
though I admit I got a different figure for the second changeover refund (£466.20), though this could be accounted for by how the number of days remaining is calculated.

The difference between that and the OP's figure is one day's difference in base rates: £2.52, so presumably you are refunding one more day than the OP.
 

hairyhandedfool

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.....The difference between that and the OP's figure is one day's difference in base rates: £2.52, so presumably you are refunding one more day than the OP.

Exactly, and I think I know why, leading me to believe there are, infact, atleast four possible 'correct' answers.
 

bb21

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Exactly, and I think I know why, leading me to believe there are, infact, atleast four possible 'correct' answers.

I know what you mean, however I will just use the figures quoted in the OP for now. I get £641.60 gross refund. This is the difference between the price the passenger paid in total, £3247.07, and the price the passenger would have paid had he bought the 7-monthly ticket at the start and did two changeovers on top, £2605.47.

What the passenger paid
  • charge for Banbury ticket: £5028
  • refund on Banbury ticket for first changeover (275 days remaining, base rate £13.78): £3789.50 [1]
  • charge for Princes Risborough ticket for first changeover (275 days remaining, base rate £8.99): £2472.25 [1]
  • refund on Princes Risborough ticket for second changeover (184 days remaining, base rate £8.99): £1654.16 [2]
  • charge for Gerrards Cross ticket for second changeover (184 days remaining, base rate £6.47): £1190.48 [2]
  • total paid: £3247.07

What the passenger would have paid
  • charge for Banbury ticket: £3378.90
  • refund on Banbury ticket for first changeover (122 days remaining, base rate £16.09): £1962.98 [3]
  • charge for Princes Risborough ticket for first changeover (122 days remaining, base rate £10.50): £1281.00 [3]
  • refund on Princes Risborough ticket for second changeover (31 days remaining, base rate £10.50): £325.50 [4]
  • charge for Gerrards Cross ticket for second changeover (31 days remaining, base rate £7.55): £234.05 [4]
  • total would have paid: £2605.47

Comments appreciated. Calculation for the second scenario follows the same method and I arrive at a figure of £1815.17 gross refund.

* Of course, the differences between the two [1] figures, [2] figures, etc, are the respective charges/refunds for each changeover.
 

hairyhandedfool

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What the passenger paid
  • charge for Banbury ticket: £5028
  • refund on Banbury ticket for first changeover (275 days remaining, base rate £13.78): £3789.50 [1]
  • charge for Princes Risborough ticket for first changeover (275 days remaining, base rate £8.99): £2472.25 [1]
  • refund on Princes Risborough ticket for second changeover (184 days remaining, base rate £8.99): £1654.16 [2]
  • charge for Gerrards Cross ticket for second changeover (184 days remaining, base rate £6.47): £1190.48 [2]
  • total paid: £3247.07

I have the highlighted figures differing to those I calculated. I used 185 days for the second changeover, as that is what I had calculated the days remaining to be, giving figures of £1663.15 and £1196.95 and a total paid of £3244.45.

However the rules do actually say to use the season ticket database to check what has actually been paid, so I guess we should use the Ops figures.

What the passenger would have paid
  • charge for Banbury ticket: £3378.90
  • refund on Banbury ticket for first changeover (122 days remaining, base rate £16.09): £1962.98 [3]
  • charge for Princes Risborough ticket for first changeover (122 days remaining, base rate £10.50): £1281.00 [3]
  • refund on Princes Risborough ticket for second changeover (31 days remaining, base rate £10.50): £325.50 [4]
  • charge for Gerrards Cross ticket for second changeover (31 days remaining, base rate £7.55): £234.05 [4]
  • total would have paid: £2605.47

As above, highlighted figures differ from mine. I calculated that the first changeover period remaining [3] was 125 days (4 months 5 days) giving a changeover refund value of £2011.25 and a changeover charge of £1312.50.

I calculated the second changeover period remaining [4] as 35 days (1 month 5 days) giving a changeover refund value of £367.50 and a changeover charge of £264.25.

This leaves the total that would have been paid as £2576.90 and a gross refund due of £670.17.

....Calculation for the second scenario follows the same method and I arrive at a figure of £1815.17 gross refund....

I haven't done that one yet, my head hurts too much......
 

barrykas

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Okay...My bad. I'd failed to take all of the charges into account, having wrongly assumed that they cancelled each other out.
--- old post above --- --- new post below ---
One thing that The Manual doesn't make clear is whether the second (and subsequent) change-over should be calculated using the "new" price and validity on the ticket or the validity from the original ticket.

Going back to the original example:

Working on the basis that we use the validity of the original ticket, we get a base rate of £8.99 (£3280 / 365) for the Princes Risborough ticket and £6.47 (£2360 / 365) for the Gerrards Cross ticket. From 02/07/2013 - 01/01/2014 there are 184 days, giving a credit on the original ticket of £1654.16 and a charge for the new ticket of £1190.48, for a refund of £463.68.

If we change that to use the period of validity of the "new" ticket instead, along with the price for the "new" ticket that applied at the time of the first change-over, that's 09M00D, giving a base rate of £2472.25 (Cost of new ticket) / 270 = £9.16 for the original ticket, and £2039.10 / 270 = £7.55 for the new one.

Using these new figures gives us a credit of £1685.44 for the "new" ticket and a cost for the new ticket of £1389.20, giving a much smaller refund of £296.24.

And I've just broken my brain...more than it already was.
 

hairyhandedfool

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I honestly think that the daily rate for the ticket held is as if that ticket were always held as this is what they have paid per day for the rest of the ticket's validity and that is what the changeover charge/refund is based on.
 

DaveNewcastle

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One thing that The Manual doesn't make clear is whether the second (and subsequent) change-over should be calculated using the "new" price and validity on the ticket or the validity from the original ticket.
I can't help with an authoritative reference, but I would say that it would be common practice in commercial matters to apply any adjustments to the price which applied at the time of making the adjustment; in your words, that would be using the new price.
I honestly think that the daily rate for the ticket held is as if that ticket were always held as this is what they have paid per day for the rest of the ticket's validity and that is what the changeover charge/refund is based on.
That would be my postion too.
 

barrykas

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Whilst that is perfectly logical reasoning, if you continue with that line of thinking, then at the point of the second change-over, our hypothetical passenger would possibly lose their Gold Card, if you work on the logic that the "original" ticket for change-over purposes is now only valid for 9 months...

I suspect that, like so many things, there is no 100% "correct" answer, and it's pot luck if you end up with something that looks vaguely reasonable!
 

hairyhandedfool

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But it is a ticket that will be held for a year. It may have changed origin and/or destination, but the PoV hasn't actually changed, indeed we are not allowed to change it. The first changeover therefore gives us a yearly ticket, therefore the next changeover will give us a yearly ticket, and so on.

If this yearly ticket had been issued on or before 1st January, what fares manual would you use for the second changeover?

If you use the old one you must admit to when the original was issued, if not you are changing the value of the ticket.
 

bb21

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But it is a ticket that will be held for a year. It may have changed origin and/or destination, but the PoV hasn't actually changed, indeed we are not allowed to change it. The first changeover therefore gives us a yearly ticket, therefore the next changeover will give us a yearly ticket, and so on.

This is my understanding on this matter. The ticket has been changed over, therefore there is no alteration to the validity period of the ticket.

This is the only interpretation that makes sense to me, although I understand that it rarely goes hand-in-hand with railway ticketing.
 

barrykas

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It's my understanding as well, and what I've been doing, but a strict reading of what The Manual says about calculating the base rate is that you use the price and validity on the ticket in front of you.

And as I mentioned in post 17, that would affect the base rate you get when calculating a second (or subsequent) change-over.

Taking that to its logical conclusion, if you then proceed to use the Fares Manual that was valid at the time the first change-over was done to get the fare for the second, it's entirely feasible that the customer could end up paying more for a shorter journey!

To illustrate this: In NFM13, the 7 Day price between Beaconsfield and London Terminals was £68.40. In NFM14, the 7 Day price between Seer Green (one station nearer London) and London Terminals is £69.50.

Obviously this isn't what is intended, but it's one way you could interpret the procedure as written...

Now...To return to our second example, where we're trading up each time:

Again, I'll use current prices from WebTIS, given I know the fares were changed after the freeze for NFM14.

Original Ticket: London Terminals - Gerrards Cross Annual, valid 02/01/2013 to 01/01/2014. Price: £2360.00 (Weekly: £59.00)

First change-over: London Terminals - Princes Risborough, effective from 02/04/2013. Annual price would have been £3280.00 (Weekly: £82.00)

Second change-over: London Terminals - Banbury, effective from 02/07/2013. Annual price would have been £5028.00 (Weekly: £125.70)

What would the refund be had this been submitted on 01/08/2013, having used the ticket that day (i.e. exactly 7 months use)?

I'll start by breaking this down into two main parts: Calculating the change-overs and then calculating the refund.

For the first change-over, we start by calculating the base rate for both tickets.

Base rate for original ticket : £2360.00 / 365 days = £6.47 (to nearest 1p)
Base rate for new ticket : £3280.00 / 365 days = £8.99 (to nearest 1p)

Number of days for new ticket from 2nd April 2013 to 1st January 2014 : 275

Credit due on original ticket : £6.47 * 275 = £1779.25
Charge for new ticket : £8.99 * 275 = £2472.25
Additional payment due : £693.00

Notional charge for new ticket for Section 3 of season ticket refund form : £2360.00 (Original Price paid) - £1779.25 (Credit for new ticket) = £580.75

And for the second change-over:

Base rate for original ticket : £3280.00 / 365 days = £8.99 (to nearest 1p)
Base rate for new ticket : £5028.00 / 365 days = £13.78 (to nearest 1p)

Number of days from 2nd July 2013 to 1st January 2014 : 184

Credit due on original ticket : £8.99 * 184 = £1654.16
Charge for new ticket : £13.78 * 184 = £2535.52
Additional payment due : £881.36

Notional charge for new ticket for Section 3 of season ticket refund form : £2472.25 - £1654.16 = £818.09

Moving on to the refund:

Amounts paid by customer:

London - Gerrards Cross 02/01/13 - 01/01/14 : £2360.00
Additional charge for first change-over 02/04/13 - 01/01/14 : £693.00
Additional charge for second change-over 02/07/13 - 01/01/14 : £881.36
Total Paid : £3934.36

Cost of tickets for revised period:

London - Gerrards Cross 02/01/13 - 01/08/13 (07M00D) : £59.00 * 26.88 = £1586.00 (rounded to next 10p)
London - Princes Risborough 02/01/13 - 01/08/13 : £82.00 * 26.88 = £2204.20 (rounded to next 10p)
London - Banbury 02/01/13 - 01/08/13 : £125.70 * 26.88 = £3378.90 (rounded to next 10p)

Revised change-over figures:

Base rate for London - Gerrards Cross : £1586 / 210 days = £7.55
Base rate for London - Princes Risborough : £2204.20 / 210 days = £10.50
Base rate for London - Banbury : £3378.90 / 210 days = £16.09

Number of days from 02/04/13 - 01/08/13 : 122

Credit due on original ticket : £7.55 * 122 = £921.10
Charge for new ticket : £10.50 * 122 = £1281.00
Additional payment due : £359.90

Notional charge for notional season ticket refund form : £1586.00 - £921.10 = £664.90

Number of days from 02/07/13 - 01/08/13 : 31

Credit due on original ticket : £10.50 * 31 = £325.50
Charge for new ticket : £16.09 * 31 = £498.79
Additional payment due : £173.29

Notional charge for notional refund : £1281.00 - £325.50 = £955.50

Figures for Refund Form:

Tickets bought:

London - Gerrards Cross 02/01/13 - 01/04/13 : £2360.00 - £1779.25 = £580.75
London - Princes Risborough 02/04/13 - 01/07/13 : £2472.25 - £1654.16 = £818.09
London - Banbury 02/07/13 - 01/01/14 : £2535.52
Total : £3934.36

Tickets needed:
London - Gerrards Cross 02/01/13 - 01/04/13 : £1586.00 - £921.10 = £664.90
London - Princes Risborough 02/04/13 - 01/07/13 : £1281.00 - £325.50 = £955.50
London - Banbury 02/07/13 - 01/08/13 : £498.79
Total : £2119.19

Gross Refund : £3934.36 - £2119.19 = £1815.17

And on that bombshell, I've finally worked out what needs to go where to make the whole thing work properly...fsvo "properly" equalling our understanding of it without seeking clarification from ATOC/RSP.
 
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hairyhandedfool

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....but a strict reading of what The Manual says about calculating the base rate is that you use the price and validity on the ticket in front of you....

The Manual says the base rate means the price which was, or should have been, paid for the season ticket or travelcard divided by the number of days for which the season ticket or travelcard is valid (less any lost days already included in that ticket).

It goes on to say that you would normally use the value of the ticket in front of you, this implies there are times when you don't and/or can't.
 
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