PCP Calculation

[Manks]

Hi All

I have been discussing buying a new car because my local dealer is offering high guaranteed future values. However I am unable to get my calculations to coincide with theirs.

To my mind a PCP deal is just a finance deal with a deferred final payment, the magnitude of which is fixed. So an example deal would work like this:

Car price £10000

Deposit £1000

Balloon £5000

Term 3 years

Rate 5% flat.

So, interest is payable on £9000 at 5% per annum for 36 payments. = £37.50

Capital to be repaid is £4000, so 4000 divided by 36 payments = £111.11

So total monthly payment is £148.61

However their figures are working out about 25% higher and they cannot explain why. Their printed quote just says "additional charges" for the interest figure.

Can anyone point out whether I am missing something please?

Manks

[Manks]

RS6 see you said:

PCP agreements work off a yield not a flat rate although it is the flat rate which calculates the yield, that is why your unable to work it out.

on the figures quoted
9000 borrowed
5000 gfv
payments on a pcp would be 170.70 per month over 36 months

Can you explain that a little more fully please?

What do you mean it works off a yield and how is the flat rate used to calculate it?

[Manks]

audi321 said:

How many times on this forum do we have to say FORGET THE FLAT RATE AND FIND OUT THE APR!

I don't know, but you can say it a lot if you like.

What would be more helpful if if you'd answer the bloody question. Assuming that you know the answer of course, which I suspect you don't.

The APR of the deal in question is about 8.8%, but that is a completely useless piece of information.

APR is just something introduced so that your average numpty buying on tick can work out whether he is being shafted more by one lender than another. It doesn't help you calculate exact loan repayment costs.

Manks

Edited by Manks on Friday 5th March 16:10

[Manks]

audi321 said:

Manks said:

audi321 said:

How many times on this forum do we have to say FORGET THE FLAT RATE AND FIND OUT THE APR!

I don't know, but you can say it a lot if you like.

What would be more helpful if if you'd answer the bloody question. Assuming that you know the answer of course, which I suspect you don't.

The APR of the deal in question is about 8.8%, but that is a completely useless piece of information.

APR is just something introduced so that your average numpty buying on tick can work out whether he is being shafted more by one lender than another. It doesn't help you calculate exact loan repayment costs.

Manks

Edited by Manks on Friday 5th March 16:10

LOL. The APR takes into account the charges, and rather than try to belittle me, I was actually trying to point out that this is probably where you are going wrong (i.e. hidden charges!). I won't bother trying to help in future you ignoramus

It's not the charges, which are just a few pounds and itemised separately. Or at least it isn't what one would normally refer to as charges.

Who are you calling an ignoramus when you're the one that thinks APR is all you need to know about finance.

Now collect up your toys and behave ;-)

Manks

[Manks]

CaptainSlow said:

Manks said:

So, interest is payable on £9000 at 5% per annum for 36 payments. = £37.50

OK this is where you are going wrong. Remember when you are paying your monthly installment you are paying off an element of the capital balance of the vehicle, this reduces the balance interest is charged on. With this in mind and using the APR of 8.8% to take into account charges and then adding VAT on this (but not the £4,000 depreciation) I get to a monthly amount of circa £171.

Anymore clues and I'll start charging my consultancy fees

The car price already includes VAT

Furthermore my example assumes that the capital does not reduce, so the cost should be more, and yet their figures are still higher.

Don't get the invoice book out just yet ;-)

[Manks]

sidicks said:

Ok, as has already been posted previously (hundreds of times), flat rate is meaningless, you need to use the APR to calculate the monthly payments, as this takes into account all fees etc.

With a £10k car and £1k deposit, there is £9k to finance. Effectively there are 2 parts to this agreement:
- A £5000 loan (residual) on which interest is paid but no capital
- A £4000 loan which is re-payable over 3 years

Using an APR of 8.8% (equivalent to a monthly rate of 0.71%):
The interest on the £5k loan is £35.27 per month
The interest and capital repayment on the £4k loan is £126.20

This leads to a total premium of £161.47

Easy!

Sidicks

Nope, that's not the explanation. What you have done there is exactly the same as I did in the OP but used the APR instead of the flat rate, which is why your calculation is wrong.

I have now found out the reason why PCP works out the way it does and it is this:

There is a flat rate at that is applied to the repayment element of the loan AND the balloon. But then the same rate is applied to the balloon again.

So, the repayment element of the loan carries a true interest rate of approximately twice the flat rate (because the capital is decreasing but the payments aren't). The bubble carries twice the flat rate.

The PCP lenders (as far as I have seen anyway) don't make it clear that they are actually charging interest twice on the bubble. But that's what they are doing. Basically they are deriving interest on the loan and a yield on the balloon, one of which is about double the flat rate and one of which is double the flat rate.

And that is partly why APR is useless. It doesn't explain any of that, all it does is provide a comparative measure to compare loans. APR is also useless, however, because it is allowed to be rounded down and also because different elements of the loan have a different bearing on how the APR rate appears.

So, this is far more complex a question than it appears. "Look at the foookin APR mate" is not the answer and what happens when you create a simple comparative measure that everyone understands - they think it's the answer to everything. To a man with a hammer, every problem looks like a nail.

ItaI'm afraid there is only one numpty here and it isn't audi321.......

Wrong again Sidicks, you've obviously used APR in your calculations. There are in fact two of you.;)

Manks

Edited by Manks on Saturday 6th March 11:09

[Manks]

sidicks said:

Manks said:

Nope, that's not the explanation. What you have done there is exactly the same as I did in the OP but used the APR instead of the flat rate, which is why your calculation is wrong.

Given the cashflows you have described, my calculation is 100% correct. That's what the APR is - it is the effective interest rate that is used to equate the cashflows back to the initial loan amount.

Manks said:

I have now found out the reason why PCP works out the way it does and it is this:

There is a flat rate at that is applied to the repayment element of the loan AND the balloon. But then the same rate is applied to the balloon again.

So, the repayment element of the loan carries a true interest rate of approximately twice the flat rate (because the capital is decreasing but the payments aren't). The bubble carries twice the flat rate.

I'm afraid that is rubbish. That is not how it works, but maybe that's how it was described to you!

Manks said:

The PCP lenders (as far as I have seen anyway) don't make it clear that they are actually charging interest twice on the bubble. But that's what they are doing. Basically they are deriving interest on the loan and a yield on the balloon, one of which is about double the flat rate and one of which is double the flat rate.

Wrong!

Manks said:

And that is partly why APR is useless. It doesn't explain any of that, all it does is provide a comparative measure to compare loans. APR is also useless, however, because it is allowed to be rounded down and also because different elements of the loan have a different bearing on how the APR rate appears.

APR is rounded down to the lower 0.1% (or at least it used to be), for simplicity, but that has little practical difference.

Manks said:

So, this is far more complex a question than it appears. "Look at the foookin APR mate" is not the answer and what happens when you create a simple comparative measure that everyone understands - they think it's the answer to everything. To a man with a hammer, every problem looks like a nail.

The flat rate is a meaningless measure as a comparator as it does not take into account the timing of cashfows. Obviously you can use the flat rate to derive the payments, just as you can with the APR but the APR actually means something!!

Manks said:

Wrong again Sidicks, you've obviously used APR in your calculations. There are in fact two of you.;)

That's because that is exactly what the APR is designed for!!

You lose....

Sidicks

You should probably read this:

http://www.oft.gov.uk/shared_oft/business_leaflets...

You need the section marked "An option hire purchase agreement". That will explain it to you.

On the subject of double interest on the balloon, see this bit:

"An option loan of the type described in this example is a mixture of an
instalment loan (because of the credit repaid by the 36 monthly instalments)
and a single repayment loan (because of the lump sum paid at the end) and
the lender’s return on the part of the credit repaid by the lump sum is about
half that on the rest of the loan. To counteract this, the lender applies the 5%
rate to both the amount originally borrowed and again to the lump sum paid
at the end (in effect, applying the rate twice to the lump sum amount to
obtain the expected level of return)."


Now, would you like to apologise or email the OFT and call them numpties who don't understand what they are talking about?

Manks

[Manks]

Dr Jekyll said:

Manks said:

[Sidicks

You should probably read this:

http://www.oft.gov.uk/shared_oft/business_leaflets...

You need the section marked "An option hire purchase agreement". That will explain it to you.

On the subject of double interest on the balloon, see this bit:

"An option loan of the type described in this example is a mixture of an
instalment loan (because of the credit repaid by the 36 monthly instalments)
and a single repayment loan (because of the lump sum paid at the end) and
the lender’s return on the part of the credit repaid by the lump sum is about
half that on the rest of the loan. To counteract this, the lender applies the 5%
rate to both the amount originally borrowed and again to the lump sum paid
at the end (in effect, applying the rate twice to the lump sum amount to
obtain the expected level of return)."


Now, would you like to apologise or email the OFT and call them numpties who don't understand what they are talking about?

Manks

Surely that is just explaining the contortions you have to go through when you use flat rate instead of APR.

Suppose you pay £5000 over 12 months, followed by a £5000 balloon, all at 10% APR.

Looking at the instalment loan the APR enthusiast says the average amount outstanding is about £2500 so the interest is about £250. The flat rate fan says that if the interest of a £5000 loan comes to (approx) £250 that must be a 5% rate, he doesn't care when the money is paid.

Looking at the lump sum the APR enthusiast says that £5000 was outstanding over 1 year at 10% a year so that's £500 interest.
The flat rate fan says that £500 for a £5000 loan is 10%, so he regards the lump sum as attracting double the fat rate as the instalments.

Far simpler to use APR.

That isn't correct. I would caution anyone borrowing significant sums (eg car sized sums) not to rely on APR. It is a comparative measure only. You cannot calculate loan payments from it.

There's another big problem with APR as a sole measure too. I have on my desk several quotes with similar APRs. One of them though has a big bubble and lower repayments. But it is the worst deal for most people because it has the lowest capital repayment over the term and the borrowed may well be underwater for most of the loan term, and unable to return the car if they needed to.

But the single biggest problem with APR is that too many people have begun to think it's all you need to know. And it isn't. Far from it.

Manks

[Manks]

sidicks said:

Dr Jekyll said:

Surely that is just explaining the contortions you have to go through when you use flat rate instead of APR.

Exactly!!

Sidicks

No, not exactly. You got it completely round your neck, you stated quite categorically that my explanation was incorrect and you were completely wrong. So either apologise or go and sit in the corner with your numpty hat on.

Incidentally, if you want to know how the original example works out it's like this. Someone (not I) has bothered to get the pocket calculator out:

Assuming that the borrower meets all his obligations under the credit agreement and ultimately purchases the car by making the final lump sum payment.

The amount of credit provided under the agreement is the cash price less the deposit (£10,000 – £1000) = £9000.

The interest charged on this is calculated as (£9000 x 5% x 3yr) + (£5000 x 5% x 3yr) = £2100 and, as there are no other charges, this is the Total Charge for Credit.

The 36 regular instalments repay the interest and the part of the credit which is not repaid in a lump-sum. The instalments are therefore (£2100 + £9000 – £5000) ÷ 36 = £169.44. The Total Amount Payable is (£1000 + 36 x £169.44 + £5000) = £12,099.84.

The APR would be calculated as a loan of £9000 repaid by 36 monthly instalments of £169.44 and a 37th of £5000.

The APR result is 8.8% when rounded down to next decimal place below the true rate - as the regulations permit.

A system generated PCP quote coomes out at £170.70, which is probaably because the true rate is nearer 5.1% and it too has been rounded down to "5%" for the quote.

Joking aside though Sidick, don't get hung up on APR it is only a guide. It doesn't tell you everything and sometimes the things it doesn't tell you are well worth knowing.

Manks

Edited by Manks on Saturday 6th March 18:01

[Manks]

sidicks said:

Manks said:

There's another big problem with APR as a sole measure too. I have on my desk several quotes with similar APRs. One of them though has a big bubble and lower repayments. But it is the worst deal for most people because it has the lowest capital repayment over the term and the borrowed may well be underwater for most of the loan term, and unable to return the car if they needed to.
Manks

That comment shows a huge lack of understanding!

Sidicks

Why is that then?

[Manks]

sidicks said:

Manks said:

Why is that then?

(copied from above)
The lower APR is always the better economic deal because it represents the true interest being charged.

What you are saying is that the £ amount (i.e. the total cost for credit) might be higher on such a loan, because of the deferred amount. That is not the same thing - put it this way if you borrowed twice the amount, but with the same interest rate, you'd pay back twice the £ amount in 'charges' but this wouldn't be a better or worse deal!!

Whether the car is worth more and less than the deferred amount is irrelevant as to whether the loan represents a good deal or not. Whether a PCP is the best means of financing the car is not under discussion.

I refer to my previous post - why won't you respond to my question about the different loan options??


Sidicks

What previous post? What different loan options? Must have missed that one. If you mean are the quotes on my desk different types of loan then yes they are. They have similar APRs but they are not economically similar. The one with the lowest payments is in faact the worst deal for most people. This is because if they wanted to take advantage of the one month interest and exit facility they would have begative equity to cover in all probability.

I will say this once more because you don't seem to be getting the point. APR is a crude measure designed to make it easier for Joe public to compare loans. Outside of that it is of little use and you most definitely cannot calculate loan repayments from it.

And by the way, if you have FIA after your name why is it that you don't understand how PCPs work?

Manks

[Manks]

sidicks said:

I know exactly how they [PCPs] work - this is a discussion about APR v Flat rate.

Sidicks

Well apparently not.

On page 1 of this thread, we had the following exchange:

Manks: I have now found out the reason why PCP works out the way it does and it is this:

There is a flat rate at that is applied to the repayment element of the loan AND the balloon. But then the same rate is applied to the balloon again.

So, the repayment element of the loan carries a true interest rate of approximately twice the flat rate (because the capital is decreasing but the payments aren't). The bubble carries twice the flat rate.

Sidicks: I'm afraid that is rubbish. That is not how it works, but maybe that's how it was described to you!

Manks: The PCP lenders (as far as I have seen anyway) don't make it clear that they are actually charging interest twice on the bubble. But that's what they are doing. Basically they are deriving interest on the loan and a yield on the balloon, one of which is about double the flat rate and one of which is double the flat rate.

Sidicks: Wrong!

I then provided you a link to the OFT website which confirms that PCP works exactly as I explained it. Thus demonstrating that you don't (or at least you didn't yesterday) know how PCP works.

This isn't a thread about flat rate it is about how PCP works. We have been dragged off topic by a discussion about APR because a couple of people didn't understand the question and think that APR is the cure all for everthing including the common cold. Which it isn't.

Now, it's time to open a bottle of wine.

Manks

[Manks]

sidicks said:

Manks - did you enjoy your wine?!


How a PCP works?
A PCP works by deferring part of the total cost of a car until a later date. The borrower pays off part of the finance on a regular basis, typically monthly throughout the period of the finance and then needs to pay a lump sum to complete the finance deal. Normally this lump sum acts as a guaranteed minimum value for the car.

That is how a PCP works - i think we agree on that!!

Approximate pricing methodology
The approach you have set out effectively uses the 'wrong' number twice to end up with the 'right' result!

As we all know, for a normal loan, the APR (the true cost) is roughly twice the flat rate (as over the period, the outstanding balance is roughly half of the initial loan).

The approach on the OFT website that you linked to applies a flat rate of interest to a reducing loan, so this ignores the timing of repayments. The flat rate is the 'wrong' number (compared with the real cost of interest).

Similarly on the deferred value, the 'correct' value is a compound rate not a simple rate, but as there is no reducing balance these are broadly similar. Therefore using twice the flat rate is also the 'wrong' number to apply (compared with the real cost of interest).

Effectively using simple interest in this way means that, in an era before computers, given the appropriate simple formulae and a basic calculator, a car finance chap could easily produce quotes on a number of different bases.

i.e. the point I was trying to make (badly) is that the calculation methodology described above doesn't make economic sense in terms of the actual payments and the timing of them, but as APR is approximately twice flat rate, you get to the right result!

The APR is the 'right' rate!!

Sidicks

PS - Do you yet accept that in no way is an APR a 'crude' measure?!
PPS - Are we going to swap loans?

Edited by sidicks on Sunday 7th March 09:33

Sidicks

Wine was fine thank you. Cava actually, turned it into cocktails.

As for your argument above, you are still trying to suggest that black is white. The Office Of Fair trading, I strongly suspect, can be relied upon to know how PCP deals are structured. The link I provided to their site gives a full explanation which I feel sure is correct. You, on the other hand, have demonstrated that you definitely don't understand how it works, dismissing what the OFT says as "nonsense". I prefer their credentials to yours.

To suggest that I am using the wrong rate twice is simply ridiculous Sidicks and you know it. You have demonstrated earlier in the thread that you've got it wrong because someone has fed the numbers into a PCP calculator and the answer is different from yours.

APR is calculated AFTER base rate has been used to perform a calculation and other factors are incorporated. It is then rounded down unless it is a whole number. For this reason you cannnot then input it in a reverse calculation and expect to get an accurate answer.

With the greatest respect I think you know you are wrong but simply won't admit it.

Manks

[Manks]

sidicks said:

What I am saying is that how they calculate the PCP premiums may well be on the basis you have supplied,

Hellelujah.

sidicks said:

but that is a 'nonsense' calculation as the interest rate used is a simple flat rate which therefore takes no account of the timing of cashflows.

It don't matter Sidicks. That's how it works. If PCP providers decide to multiply their payments by a fixed random figure, that is how it works. If they will only use odd numbers, that is how it works. Quotes only on Thurdays? That's how it works. My question was "[can someone explain] PCP calculation. You couldn't. But the ensuing argument has nonetheless been entertaining.

sidicks said:

In economic terms, a PCP does not charge double interest on the deferred amount (that is misleading as it implies that in some way PCPs are a rip off).

What do you mean in economic terms? PCP does charge interest twice on the bubble - go and read the OFT site again.

sidicks said:

What we are actually saying is that the interest rate quoted as being charged on the deferred amount is roughly half of the true rate, so you need to double it to get the right answer.

No, it is very close to the TRUE rate. It is twice the flat rate.

sidicks said:

I.e there is a significant difference between the calculation that us being done and what is actually happening from an economic perspective!

You seem to be trying to introduce a new concept of a calculation being different in economic terms to justify your argument. This isn't open to interpretation from different viewpoints, it's a mathematical calculation that is all. You'll be trying to argue it from a sociopolitical standpoint next. You'll still be wrong, but don't let me stop you from trying to wriggle out of this. Perhaps you could consider and abstract cubism explanation, or maybe argue that if you close one eye and squint a bit the numbers look altogether different.

Manks

[Manks]

sidicks said:

Manks said:

What do you mean in economic terms? PCP does charge interest twice on the bubble - go and read the OFT site again.

In the calculation from the OFT website, premiums are calculated based on charging twice the flat rate on the deferred payment.

Yes

sidicks said:

That is not the same as saying that 'interest' is charged twice on the 'bubble'.

I think it is. The flat rate is an interest rate and it is being applied twice to the deferred sum, which in common parlance is known as a "bubble".

sidicks said:

The true interest i.e. the effective interest rate is the IRR (i.e. unrounded APR) and that is only charged once on the bubble (and once on the other part of the loan)

Well I am not going to staate categorically that you are wrong. But if you are right the OFT is wrong. How confident are you that they are wrong?

sidicks said:

What about my loan question - when are you going to respond to that?

When it becomes relvant to the discussion.


Manks

[Manks]

sidicks said:

Manks said:

Well I am not going to staate categorically that you are wrong. But if you are right the OFT is wrong. How confident are you that they are wrong?

Why can't we both be right, as we are taking about different things:

The OFT is using a simple rate of interest purely used to calculate premiums which takes no account of the timing of payments.

However, because the rate is a simple rate and does not take into account the timing of cashflows and the impact of compounding it does not represent the true cost of the finance. That is why I am saying that in reality you are not actually being charged twice on the bubble, because the true rate, the IRR is only applied once.

Manks said:

When it becomes relvant to the discussion.Manks

It is relevant as it demonstrates the usefulness of APR and the huge limitations of flat rate, and why the APR is the objective, meaningful measure.

Sidicks

Sidicks

I am going to draw a line under this now.

My question was how to correctly calculate PCP finance. The answer is provided by the OFT website and using their method gives an answer that tallies with a broker's PCP quote generator.

So I am satisfied that I now have the correct answer.

Thanks for your input.

Manks

[Manks]

johnfm said:

If I could upload the excel spreadsheet, the issue woul dbe resolved once and for all.

But I don't have anywhere to host it.

If you are 100% sure it is correct (and I am sure it is) perhaps you could report your own post and ask the moderators to host it on a sticky?

Manks