## Saturday, August 20, 2011

### On Symmetry and the Rate of Return on Investment: Economics using only physical units

I'd like to join together two of the major themes in my blog:  symmetry and the rate of return on investment.
In a prior post, I mentioned that there is connection between the two:   those projects that yield higher rates of return on electrical & mechanical work invested will produce more symmetry than those processes with low rates of return on work invested.  Let me be clear here. In this case, I'm not talking about reflection, rotation, or translation symmetries. I'm talking about permutation symmetries (i.e. entropy.) Follow this link to my previous post to see how high rates of return on investment leads to more (permutation) symmetries.

Now, I'd like to discuss why I prefer using the internal rate of return on investment rather than the levelized cost of electricity when calculating the comparative economic viability of different electricity generating power plants. One advantage of the IRR is that it's units are purely physical [%/yr] (whereas the LCOE has units of [\$/MWh].) Another advantage is that the IRR is nearly-symmetry when calculated at different locations on the globe and at different times (a sort of near-symmetry in space-time translations.)

What I'm trying to do in my research is to reduce the amount of calculations required to determine which type of power plant to build and where. Is there any underlying order and structure? Or instead:  is everything local?
By this I mean,  does each location in the world have to do separate calculations to figure out what is the right type of power plant?
At each location, there will be different prices for natural gas, coal, oil, labor, materials, and taxes, as well as different wind speeds, water flow rates and geothermal resources. Then there's the problem that different countries use different currencies. And finally, you have the problem that not only are these prices changing in location, but they are also changing in time.

So, at first, you might think. Well, there are just too many variables. Let's just give up. This means that businesses need to redo their calculations for each city in the world.

But let's not get too caught up in the difference between locations. Let's now focus on what's similar between locations (similar in both time and space.)  What appears to be very similar between different cultures is the 'inflation-adjusted' yield curve.  (See the following site for a quick tutorial on yield curves if you are not already familiar.) Yield curves themselves are constantly changing in time. There is definitely no symmetry with respect to time for the yield curves themselves. But if you subtract out investor's expectations for future inflation, the yield curves are nearly always quite similar. The shape of the 'inflation adjusted' yield curve is similar both in the US and in Europe. The inflation-adjusted rate of return always increases for investments that require holding the money for longer times. In a world with zero-inflation (such as with an electricity-backed currency), we should expect the yield curves to look similar in almost every location and at almost every point in time (after implementing the zero-inflation currency.) This is due to the fact that our average level of risk aversion is nearly the same in different cultures, but not exactly the same. As Kritzman et al. stated in 2002, "There is a high correlation between the risk aversion of different countries, but there are also important country-specific effects."

What's nice about using yield curves (rather than prices for bonds) is that there are no units of currency in the graph. Yield curves only have units of time (since the units of the y-axis are [% per yr] and the units of the x-axis are [yr].)  This means that there is no need to introduce non-physical units such as \$'s or euro's. (My goal is to do economic analysis using only physical variables, such as time, length and mass. For example, work and energy have units of mass times length squared divided by time squared.)

So, getting back to the rate of return on investment, we can ask the questions: how does the rate of return on investment vary in different countries and at different points in time?

Do locations with high capital/fuel/labor costs always have high electricity prices? Do locations with low capital/fuel/labor costs always have high electricity prices?

It turns out the ratio of natural gas prices to electricity prices fluctuates greatly in the US, whereas the ratio of labor costs to electricity prices varies only slightly in the US. And now, I'd like show the advantage using the IRR by using the example of nuclear power plants built in the US vs. China. I'm using the example of nuclear fission power plants because it's a heavy up-front construction type of project. The costs are mainly local labor...and the price of local labor is largely a function of the price of electricity and the price of gasoline. This means that higher local prices of electricity will effect both the revenues and the costs associated with the plant. Using capital cost estimates from wikipedia (and from the US EIA) for nuclear power plants in China and in the US, one can see that there are huge differences in capital costs, and hence huge difference in the levelized cost of electricity between a power plant build in the US and a power plant build in China. (And because of inflation, the value that the EIA or IEA calculate for the levelized cost of electricity is constantly changing.) However, since the price of electricity in China is less than in the US, the rates of return on investment are much closer to each other. And since inflation typically effects both the capital costs and the price of electricity nearly equally, the rate of return on investment does not change significantly year to year, as would the levelized cost of electricity.

[Note: Please let me know if you have calculated the IRR of power plants in different locations or at different points in time. I am trying to build a database of such IRR's to see whether there is any near-symmetry in the rates of return at different times and locations.]

The main point here is that we should stop calculating the levelized cost of electricity. (This is what most government agencies use when comparing between different power plants.) Instead, we should be using the rate of return on investment because, like the inflation-adjusted yield curve, the IRR is more symmetric with respect to time and location because it's the ratios of the price of electricity to capital costs, the price of fuel to capital costs, and the price of labor to capital costs that determine the IRR. The ratios of these quantities fluctuation much less in time and space than do the variables themselves.

And this is ultimately the goal of my on-going research: if we can reduce the amount of effort that goes into figuring out which type of power plant to build, then this will free up people to do other things, such as actually building power plants or becoming doctors & aerospace engineers.