Nominal interest rates and the cost of electricity (continued)

I wrote a blog about how higher nominal interest rates won’t necessarily result in higher real electricity tariffs from renewables projects. I got this response:

Which is a good question. I am going to try to answer it using simple numerical examples, but in what follows you are likely to discover that either I don’t understand how the “levelized cost of electricity” (LCOE) is calculated, or I don’t understand how project finance works, or possibly both.

If you are thinking “this guy works at DFI that invests in renewables, why doesn’t he go talk to the project finance team” you are correct, and I shall.

My initial response was to model a simple project where capital is the only cost, and the “tariff” is the interest charged on the outstanding principal plus a principal repayment. This is modelling a solar plant as if it was a loan, and the tariff you pay for electricity is the similar to a loan repayment (and the project developer is the same as a lender). In this very simple model the cost of supplying electricity is the same as the cost of repaying the loan that paid for the solar plant to be built, with interest.

Obviously, this excludes a lot, but I think it’s enough to illustrate the point. People are concerned that higher interest rates will hurt investment in renewables because they are capital intensive compared to fossil generation, meaning that all the costs come from initial construction and very little from operations and maintenance (unlike fossil generators, which must pay for fuel). In this example, the project is so capital intensive, there is nothing else.

Here’s what that looks like. This is the “low interest rates, low inflation” regime — the tariff is calculated by adding together a principal repayment and interest rate charge. I then divide the tariff by the economy’s “price level” to get a real cost. The numbers here are arbitrary — you can think of the real cost of the tariff as being measured in quantities of goods instead of dollars. If your economy consisted only of apples and electricity, this is how many apples you are giving up paying for your electricity. The tariff is in dollars — the “real cost” those dollars represent something like an index which tells you what those dollars can buy [1].

Now, what happens if we move to a high interest rate, high inflation environment?

What you can see here is that the interest charge doubles, but the tariff only goes up by about 15% and the total real cost over four years — which is the number in the green rectangle—is unchanged. But notice how the timing has changed — the real cost is now higher in early years and lower in later years. I think that means if you are impatient (if you discount the future) then you are worse off. That is a point I omitted from my initial blog.

But why does my little model suggest such a small change in tariff, when LCOE calculators imply such a large change, when interest rates double?

My first thought was that because I modelled the debt as being repaid over only four years, principal repayments make up most of the tariff and interest payments little. What if the power purchase agreement / loan is over 20 years?

Yes, that changes things. It does not change the fact that moving from a low interest, low inflation environment to a high interest, low inflation environment leaves the total real cost unchanged, but it does imply a much larger initial change in the dollar tariff. In these examples, I have hidden the years 3- 18 to make things legible. Ignore the inflation-linked tarriff shown in the bottom three rows for now. Here is a 20-year PPA with low interest and inflation:

And here is it is with high interest and inflation:

You can see the tariff jumps from 10 dollars in the first year, in the first case, to 15 in the first year, in the second case — a 50% increase. If you add up the total dollar cost over the 20 years, it’s 147.3 under the low interest and inflation regime and 199.5 under the high interest and inflation regime — a 35% increase.

Now for those new rows showing an “inflation-linked” tariff. These represent an alternative pricing scheme. There is no need to structure tariffs like a loan, with regular principal repayments and interest charged on the principal outstanding [2]. What you could do instead, for example, is charge an inflation-linked tariff, so that the dollar tariff rises over time but stays constant in real terms, rather than shrinking in both nominal and real term like payments under a loan-like structure do.

To make a like-for-like comparison, I keep the lifetime real cost of this alternative inflation-linked tariff unchanged from the original “loan” tariff, by setting its initial level equal to the original lifetime real cost divided by 20, and then increase the tariff by inflation each year. Important caveat: I don’t know how developers actually calculate inflation-linked tariffs! That results in a tariff with a annual fixed real cost, and the same total real cost over 20 years as the loan-like structure. It is shown in the examples above in the row labelled “constant real tariff”.

This results in a tariff that is initially lower — looking at the example above, the tariff in the first year with a loan-like structure is 15 dollars and it’s just 5.5 dollars for the inflation-linked tariff. But looking ahead to year 20, the original loan-like tariff has shrunk to 5.5 in nominal (dollar) terms whereas the inflation-linked tariff has risen to 33.6 dollars, which is what it takes to keep up with inflation.

Now, comparing the low interest and inflation regime against the high interest and inflation regime, looking at the “constant real tariff”, the initial dollar change is very small — from 5.3 to 5.5 in the first year — but the difference between the two regimes grows over time. By year 20, the inflation linked tariff is 13.3 dollars in the low inflation regime and 33.6 in the high. If you add up the dollar cost over the 20 years, it’s 160.3 in the low inflation regime and 281.4 in the high inflation regime (although, of course, the real cost is the same under the two regimes.

This gets us closer to the large percentage increase in dollar costs that LCOE calculators imply when interest rates rise, although the point that real costs don’t change of course remains. What I want to do next is understand how LCOE calculations work in more detail, to understand how they compare to these tariff structures.

[1] If it is not obvious to you why project developers and governments buying electricity would care about real income and real costs, think about how inflation is said to erode the value of savings.

[2] In earlier drafts I described this as similar to a mortgage, but repayment mortgages are designed to keep your monthly payments constant, rather than having them shrink over time as the principal is paid down. When monthly payments are fixed, what happens is that the proportion of the payment that is going towards interest charges shrinks over time, and the proportion that is repaying the principal rises. This would be another possible tariff structure — a fixed nominal (dollar) payment each year.