Should I get a more efficient X: payback times in money

I have been asked a few times why I only look at energy and carbon payback times in my book, not money payback times, since money is of more immediate concern to most people than climate change. Well, there are several reasons for this. Firstly, prices change so quickly the book would be out of date before it was published. Also the calculations are basically identical to those for energy or carbon until you take inflation into account - and then things become much more complex and I was very keen to keep the arithmetic in my book very simple. Lastly, it is extremely difficult to predict how energy prices will rise in the future, so in practice these calculations are too much like guess work for my liking.  Reducing our energy consumption is a win-win because it helps keep energy demand, and hence prices, low and it reduces our costs when prices do rise. Still, if you really want to see some illustrative calculations here goes.

Example 1 Kettle (Short payback time)

Suppose you are considering buying a new kettle. In my book I show that if you are mostly making tea for one person at a time and switch from an old kettle to a new one which allows you to boil only the amount you need, you can payback the carbon emissions from making the kettle in a few weeks. What about the money? This is what it might look like:

Price of kettle: £20
Energy use/day with old kettle: say 0.5kWh
Energy use/day with new kettle: say 0.25 kWh
Savings = 0.25 kWh/day
Price electricity 12p/day
Savings = 0.25*0.12*365  = £10.95 /year

Ignoring inflation totally, payback time = 20/10.95= 1.8 years

Taking inflation into account, the easiest way is to work all the way through in 2011 pounds, adjusting for the retail price index (RPI) as we go along. This way we only have to allow for the difference between energy price inflation and the RPI. If the RPI is 2% and energy prices go up 5% then the difference is 3% and that is what we use in the calculations.

Assuming a step change in energy price each year, to make life easy, we can calculate our profit over 2 years:

Inflation (energy over RPI)	0%		3%		7%		10%
Year	Balance	Savings	Balance	Savings	Balance	Savings	Balance	Savings
0	-£20.00	£10.95	-£20.00	£10.95	-£20.00	£10.95	-£20.00	£10.95
1	-£9.05	£10.95	-£9.05	£11.28	-£9.05	£11.72	-£9.05	£12.05
2	£1.90	£10.95	£2.23	£11.62	£2.67	£12.54	£3.00	£13.25

 
In year 0 we're £20 down, but during that year we make savings of £10.95 which means at the start of year 1 we are only £9.05 down.

In year 1, if inflation is 0%, then we save another £10.95 and we have a profit of £1.90 at the end. However, if our energy prices have gone up 10% more than the RPI, the second year we save £12.05 which means we are £3 in profit. That's not a big difference.

Example 2: Freezer (Medium term payback)

Let's imagine we are considering buying a new freezer that costs £200 and it saves us £20/year.  Ignoring inflation payback time is £200/20 = 10 years. However, over that time energy inflation at 3% over the RPI would increase energy prices by 34% (relative to the RPI ) so each year I am saving more than I would have done and the payback time is shorter. This is how the table works out:

Inflation (energy over RPI)	0%		3%		7%		10%
Year	Balance	Savings	Balance	Savings	Balance	Savings	Balance	Savings
0	-£200	£20	-£200	£20	-£200	£20	-£200	£20
1	-£180	£20	-£180	£21	-£180	£21	-£180	£22
2	-£160	£20	-£159	£21	-£159	£23	-£158	£24
3	-£140	£20	-£138	£22	-£136	£25	-£134	£27
4	-£120	£20	-£116	£23	-£111	£26	-£107	£29
5	-£100	£20	-£94	£23	-£85	£28	-£78	£32
6	-£80	£20	-£71	£24	-£57	£30	-£46	£35
7	-£60	£20	-£47	£25	-£27	£32	-£10	£39
8	-£40	£20	-£22	£25	£5		£29
9	-£20	£20	£3
10	£0

If energy inflation is only the same as the RPI then we get back our costs in 10 years. However, if energy inflation is 10% more than the RPI then we are  £29 in profit by the end of year 8.

In general, the longer the payback time the more energy inflation matters. If the upfront cost is £400 and we are still saving only £20/year then the payback time is 20 years for 0% inflation but 12 years at 10%.

What inflation figure should we use?

Well that is an interesting question. Just look at the world oil price graph on my post Demand for Oil - at any cost to see how fast prices can rise when there is a supply problem.

Over the years 2005 to 2010 the RPI rose by 16.5% overall but our petrol prices rose 34%, electricity by 55% and our domestic gas price rose a whopping 82%. The price in 2010 was actually down from before though: the  peak gas price was 102.9% up on 2005 in Q4 2008. [1]

Relative to the RPI, electricity prices rose 55-16.5 = 38.5% over the 5 years which is an average of 6.5%/year.

Of course, the price in future may rise faster or slower than this. Who knows? Personally I'm not betting on it rising more slowly.

[1] DECC Quarterly Energy Prices June 2011