Tag Archives: maths

Chop off the tail?

The cost of installing a PV system has fallen dramatically since the introduction of the Feed-in Tariff for the UK three years ago. With some very serious wobbles, the FIT rates are now low but crucially relatively predictable and still high enough to give a good rate of return.

Still, with the FIT rate for a domestic (<4kW) system now down to 13.9 p/kWh (effectively 16.2 p/kWh including the 4.64 p/kWh export payment on 50% of generated electricity) the annual FIT payment is no longer such a head-turning amount for what is quite an intrusive installation. If you were to install a 3 kW system now, you would get back on the order of £500 per year for 20 years.

Given that you might be dead in 20 years (let’s hope not) or more likely you’ve moved house, you really don’t care about the money in the last 5 years. Economists call the time-value of money the discount rate,  basically ‘a bird in the hand…’ which for most people shakes out at around 10% per year. So what if we change the game? Let’s still give you the same amount of money (net present value or NPV – everything in the future is translated back into ‘today money’) but let’s do it over a shorter period so you get a bigger annual payment.

As an aside, The Stern Review on the Economics of Climate Change was a ground breaking work and argues that the rationale for higher discount rates is the expectation that things can only get better. If you take climate science as a given (for the purposes of the review, Stern took the prevailing scientific view, mostly from the IPCC at face value), this presumption may not hold and so a much smaller discount rate is necessary. Of course, the effect of this is to raise the significance of long-term elements in your economic model so that, for example a climate-induced London flood in the 2050-2060 period actually has does some economic damage instead of being discounted away to almost nothing. Besides ‘Climate change is a scienco-communist hoax perpetrated on the world’, this is one of the main criticisms of Stern from the laissez-faire types at the GWPF etc.

So anyhow, the reason for this front loading of the FIT scheme idea is to make it more attractive to consumers and drive uptake. All well and good, more solar, lovely stuff but playing devil’s advocate for a moment let’s look at it from the point of view of the Treasury or the Daily Mail. Here’s where things get trickier.

Germany has started to get into quite large problems with the scale of the payments they are making over the odds for the electricity delivered through their FIT which got underway just over ten years ago. By some estimates, the cost of FIT electricity is around 20 billion euros where wholesale electricity would have been down around the 3 billion euro level. This is causing quite a lot of carping about paying over the odds for energy, having some of the highest prices in Europe etc etc. What this doesn’t acknowledge is that once the FITs expire and systems are still running (PV will certainly outlast the FIT in many cases) the cost of this electricity will drop to almost zero giving Germany a tremendous competitive advantage over rival countries still doing the burning old dead things game.

Now what we want is to have similar levels of renewable power to the Germans, but for less money. Well, we will get it for less money automatically because we’ve delayed for around a decade during which prices fell sharply, allowing us to introduce FITs at lower levels of support from the outset. Using a 10% discount rate and a few other assumptions – 3% inflation, a fixed 15p/kWh for grid electricity and a 30% annual reduction in PV costs (reflected in falling FIT rates), the peak in the total annual cost of a PV FIT scheme comes in around year 5-6. after that it starts to fall away with a reasonably long tail until the year zero systems reach the end of their payment period when there is a second, sharper drop off in FIT payments. Looking at this keeping the NPV steady and changing from 25 years (the original scheme length in the UK) to 15 years, the peak in the total costs for a single year increased by around 25% which, given 2 GW of installed PV per year would mean that every household would be paying £45 instead of £33 per year for PV electricity. I played around with these figures in an Excel spreadsheet, trying to find a way to make my idea of bringing forward the payments into a shorter window work, both for the consumer and for the scheme as a whole. Needless to say, this was a futile venture, no matter how you cut it, front loading the tariffs is always a winner for the consumer and a loser (in terms of peak payments) for society.

It was only after going away and thinking about it some more did I realise that I was thinking along the right lines but wasn’t quite there. My first postulate was that nobody cares about the final years of their FIT installation. I stand by this. My second was that by paying out the same amount of money over a shorter period to sustain higher annual payments would make the scheme more desirable. It would; if you are the one getting the payments. If you are making the payments, you might prefer not to raise the maximum outlay for a single year which this approach undoubtedly would. Which brings us back to the original postulate which I believe is correct…

Nobody cares about the last few years FIT money, it probably won’t go to them anyhow. So why not do away with them. The FIT will still drive interest, you could even put a small bump on the FIT rates though not enough to cover the loss of the money from the final years, lowering the NPV of the FIT scheme while maintaining the attractiveness of the scheme overall. It means that we can get to the nirvana of FIT-free PV faster and steal a march on the Germans who are still going through the FIT time-bomb.

We can chop off the tail. We’re apes after all, we don’t need it.

Advertisements
Tagged , , , ,