Does size matter?

Reed_Richards

I've sat down with a spreadsheet and convinced myself that a flaw in my initial assumptions made my previous calculations completely wrong.  The easiest explanation without resorting to a spreadsheet goes like this:

You have £4000 and you want to use it to generate an income of £550 per year.  550/4000=.1375 or 13.75%

At the present time you won't find an investment that can guarantee you as 13.75% return so the best you can do is to invest at a lower interest rate.  Say you could get 10%, that would give you £400 and you would have to withdraw £150 to make it up to £550.  So next year you will have £3850 invested, your interest will be only £385 and you will have to withdraw a further £165 to make this up to £550.  Keep doing this and your money runs out after about 14 years  (okay, I cheated and used a spreadsheet to work that out).  But the point is, the longer you want to keep your investment going and taking out £550 a year, the nearer your interest rate has to be to that figure of 13.75%.  That's why the calculated IRR figures for 20 or 30 years are not too far off 13.75%.

Exiled_Tyke

Reed_Richards said:

I've sat down with a spreadsheet and convinced myself that a flaw in my initial assumptions made my previous calculations completely wrong.  The easiest explanation without resorting to a spreadsheet goes like this:

You have £4000 and you want to use it to generate an income of £550 per year.  550/4000=.1375 or 13.75%

At the present time you won't find an investment that can guarantee you as 13.75% return so the best you can do is to invest at a lower interest rate.  Say you could get 10%, that would give you £400 and you would have to withdraw £150 to make it up to £550.  So next year you will have £3850 invested, your interest will be only £385 and you will have to withdraw a further £165 to make this up to £550.  Keep doing this and your money runs out after about 14 years  (okay, I cheated and used a spreadsheet to work that out).  But the point is, the longer you want to keep your investment going and taking out £550 a year, the nearer your interest rate has to be to that figure of 13.75%.  That's why the calculated IRR figures for 20 or 30 years are not too far off 13.75%.

You are simply working an IRR calculation 'backwards' here. i.e. starting with the interest rate. 

However, I don't think it's helpful to start with the aim of making 13.75%. Rather it's better to use IRR to work out what the effective interest rate is and ask whether that is acceptable or not. 

QrizB

I'm glad that we've all found a way to look at the question that gives a similar answer, even if our ways to get there differ 😉

I would however caution that the assumed Octopus Flux tariff of 20p export 25p import, cannot be guaranteed for the life of the system. If energy prices fall back to more normal levels you'll be looking at perhaps 7p export, 17p import and your £550 per year will be more like £300.

The government is forecasting that prices will fall significantly in the mid to late 2020s. See Annex M here:

https://www.gov.uk/government/publications/energy-and-emissions-projections-2021-to-2040

(Historically government projections have not been very accurate but they're still the best we have.)

Screwdriva

QrizB said:

If energy prices fall back to more normal levels you'll be looking at perhaps 7p export, 17p import and your £550 per year will be more like £300.

You really believe energy prices are going to go to 7/17p again after the geopolitical mess we find ourselves in? If so, more power to you!

Martyn1981

Reed_Richards said:

I've sat down with a spreadsheet and convinced myself that a flaw in my initial assumptions made my previous calculations completely wrong.  The easiest explanation without resorting to a spreadsheet goes like this:

You have £4000 and you want to use it to generate an income of £550 per year.  550/4000=.1375 or 13.75%

At the present time you won't find an investment that can guarantee you as 13.75% return so the best you can do is to invest at a lower interest rate.  Say you could get 10%, that would give you £400 and you would have to withdraw £150 to make it up to £550.  So next year you will have £3850 invested, your interest will be only £385 and you will have to withdraw a further £165 to make this up to £550.  Keep doing this and your money runs out after about 14 years  (okay, I cheated and used a spreadsheet to work that out).  But the point is, the longer you want to keep your investment going and taking out £550 a year, the nearer your interest rate has to be to that figure of 13.75%.  That's why the calculated IRR figures for 20 or 30 years are not too far off 13.75%.

Yep, that's another approach. But as ET says, the IRR calc is probably the simplest and best.

For your example here though, you may have gone a bit too far the other way, as you need to consider annual costs, against the annual revenue/savings, to get a 'profit' figure.

So let's depreciate the PV system over 20yrs, which gives us an annual depreciation cost of £200 (£4k / 20yrs), and also allow another £100pa for maintenance and the replacement inverter cost (the annual consumed cost). So that's about £300 in costs. [Not sure if I should only be using a £50pa cost for the inverter, as it won't need replacing at yr20, if we are only considering a 20yr period, so inverter costs over the 20yr period would only be £1k, as the initial inverter is included in the £4k investment. In that case the return may be 7.5% (£550-£250)/£4k.]

Take that from the £550, and we have a 'profit' of £250, or 6.25% net return on our £4k.

If the system is depreciated over 30yrs, and we assume the inverter lasts 20yr, then a lower cost figure may be around £183pa, giving us a 'profit' of £367 pa, or 9.18%. [But I'm way out of my depth now, relying on some accounting lessons I had back in the late 1980's.]


@ QrizB - I did start to wafle about index linking, with regard to the PV returns, but it was getting too complicated, largely because leccy prices may see a negative inflation rate (as you mention) for a few years. But then if energy costs fall, so might general inflation, and then so might interest rates for investments.  I finally gave up and deleted it, but I think many other people have used the far simpler and straightforward term (v's my waffling) of 'hedging', against future leccy/energy bills, which zxzxzx suggests (I believe).

Reed_Richards

Martyn1981 said:

Yep, that's another approach. But as ET says, the IRR calc is probably the simplest and best.

No, my approach is undoubtedly far inferior to an IRR calculation but I thought it was useful as a very quick estimate which could also be used as a sanity check of any IRR results.

Exiled_Tyke

Martyn1981 said:

Reed_Richards said:

I've sat down with a spreadsheet and convinced myself that a flaw in my initial assumptions made my previous calculations completely wrong.  The easiest explanation without resorting to a spreadsheet goes like this:

You have £4000 and you want to use it to generate an income of £550 per year.  550/4000=.1375 or 13.75%

At the present time you won't find an investment that can guarantee you as 13.75% return so the best you can do is to invest at a lower interest rate.  Say you could get 10%, that would give you £400 and you would have to withdraw £150 to make it up to £550.  So next year you will have £3850 invested, your interest will be only £385 and you will have to withdraw a further £165 to make this up to £550.  Keep doing this and your money runs out after about 14 years  (okay, I cheated and used a spreadsheet to work that out).  But the point is, the longer you want to keep your investment going and taking out £550 a year, the nearer your interest rate has to be to that figure of 13.75%.  That's why the calculated IRR figures for 20 or 30 years are not too far off 13.75%.

Yep, that's another approach. But as ET says, the IRR calc is probably the simplest and best.

For your example here though, you may have gone a bit too far the other way, as you need to consider annual costs, against the annual revenue/savings, to get a 'profit' figure.

So let's depreciate the PV system over 20yrs, which gives us an annual depreciation cost of £200 (£4k / 20yrs), and also allow another £100pa for maintenance and the replacement inverter cost (the annual consumed cost). So that's about £300 in costs. [Not sure if I should only be using a £50pa cost for the inverter, as it won't need replacing at yr20, if we are only considering a 20yr period, so inverter costs over the 20yr period would only be £1k, as the initial inverter is included in the £4k investment. In that case the return may be 7.5% (£550-£250)/£4k.]

Take that from the £550, and we have a 'profit' of £250, or 6.25% net return on our £4k.

If the system is depreciated over 30yrs, and we assume the inverter lasts 20yr, then a lower cost figure may be around £183pa, giving us a 'profit' of £367 pa, or 9.18%. [But I'm way out of my depth now, relying on some accounting lessons I had back in the late 1980's.]


@ QrizB - I did start to wafle about index linking, with regard to the PV returns, but it was getting too complicated, largely because leccy prices may see a negative inflation rate (as you mention) for a few years. But then if energy costs fall, so might general inflation, and then so might interest rates for investments.  I finally gave up and deleted it, but I think many other people have used the far simpler and straightforward term (v's my waffling) of 'hedging', against future leccy/energy bills, which zxzxzx suggests (I believe).

You are correct that other potential costs needs to be considered. Although  I can't see maintenance being an issue myself as I've never needed maintenance.   We don't need depreciation in the calculation.  This is already taken into account in the IRR calculation. Also we don't need an annual allowance for the inverter replacement. It is more accurately accounted for at the time it is needed. (I put every 10 years in my calculations).  This is all about pure cash: what cash goes in and what cash goes out. 

Finally we don't even need to worry about index linking and inflation if we assume that PV returns will move broadly in line with inflation: which is probably the best estimate we have for the longer terms.  If we want to take inflation into account then we need to flex the PV returns (and any future costs) as to how we think they will move. We then calculate IRR but then remove from it the general rate of inflation (i.e. to account for the general reduction in overall spending power of the £ because of inflation) 

ka7e

Thank you all for your detailed input!

I have had my first quote back from So Energy (Octopus have no installers in my area) -

6 x 400W Eurener monocrystalline panels

"Suitable inverter and all associated equipment"

5 year warranty on work

15 years manufacturer's warranty 

25 year performance warranty?

Scaffolding, etc

£5563

Optional Puredrive 5kWh DC battery + £3539

Ovo would like to do a remote survey before they quote, but I will need help to facilitate loft access.

Martyn1981

Immediate gut response is that it is quite a bit too high. Smaller systems are proportionately more expensive (more £'s per Wp installed), but even being generous I'd hope for sub £4k. Especially this time of year, when business should be a bit slow.

Recent inflation has thrown things out, and pushed some costs up. But the panels themselves continue to get cheaper (per Wp), so maybe keep looking. No need to rush atm since generation is poor this time of year, so you won't miss out on much.

zxzxzx

Seems high.

When I said ‘a good installer’ in my post above, perhaps I should have added ‘local’. 

Maybe knock on a few doors near you that have had solar installed? Word of mouth is valuable imho.