The unorthodox model of risk pricing behind the UK EMR #3: toss out the principle of value-additivity

This post takes up the core theoretical issue behind the EMR’s advocacy for having public authorities assume risk from low carbon generators. The White Paper claims that the profit margin of a gas-fired generating station is naturally hedged because the price of electricity moves in line with the price of gas. In contrast, the profit margin of a low-carbon technology generators is exposed to electricity price risk, since the operating costs of a low-carbon generator does not fluctuate with the electricity price. Consequently, the White Paper claims,

(i) even if the levelized cost of electricity were approximately the same for gas-fired and low carbon technologies,

(ii) nevertheless, investors would prefer the former over the latter.

Can (i) and (ii) be true at the same time?

No. Not if we are operating in an orthodox model of risk pricing. Not if there are robust capital markets where each risk has a unique price. Not if the principle of value additivity applies — “If we have two streams of cash flow, A and B, then the present value of A+B is equal to the present value of A plus the present value of B.” (Brealey, Myers and Allen, Ch. 17).

To examine claims (i) and (ii) more carefully, I constructed the two figures below based on Newbery (2008) which is one of the background papers underpinning the EMR’s White Paper. Similar figures have been used in other academic papers underpinning the EMR’s White Paper.

This first figure is a stylized graph of the volatile revenue stream, volatile cost stream and riskless profit margin on a gas-fired generating unit. The volatile revenue stream reflects primarily fluctuations in the wholesale price of electricity. The volatile cost stream reflects primarily fluctuations in the market price of natural gas. A key premise of the argument in the EMR White Paper is that the price of natural gas determines the price of electricity, and therefore these two cash flows move together. Hence, the profit margin is constant. The gas-fired generator will therefore discount its profit margin using the riskless discount rate.

Now let’s turn to a low-carbon technology, such as wind or nuclear. The revenue, cost and profit margin are shown in the figure below. The revenue stream for the low-C generator is the same as for the gas-fired generator, exhibiting the same volatility. However, the costs of the low-C generator are independent of the price of gas. In this stylized representation, they are shown as constant for the purpose of keeping things simple. Consequently, the profit margin reflects the volatility from the revenue. The low-C generator will therefore discount its profit margin using something larger than the riskless discount rate.

Note that the cost lines for the two different technologies are centered around the same average level. One has a volatile cost cash flow, the other a constant cost cash flow, but both at the same average level. Since the average cost is the same, the average profit margin is also the same across the two technologies. Since the investor discounts the low-C profit using a higher discount rate than when discounting the gas-fired generator, the value of the low-C profit margin must be less than the value of the gas-fired profit margin. This establishes claim (ii).

So far, so good. Now comes the tricky part. How do we establish claim (i)? It is here that the logic of the EMR White Paper breaks down.

The EMR White Paper implies that the fact that the two average costs are the same establishes claim (i). But that’s not true. Average cost is not the same thing as levelized cost. Levelized cost takes into account risk. In order to establish (i) it is necessary to evaluate costs after discounting for risk, just as in order to establish (ii) it was necessary to evaluate profits after discounting for risk.

Assuming that we evaluate costs using the same risk discounting used to evaluate profits, then if (ii) is true, (i) MUST BE false.

The original source for these two diagrams doesn’t include any actual explicit risk discounting calculations, so I have added that myself. To each of the cash flow line items I have added a present value figure based on discounting the cash flow streams using a consistent risk pricing model. I used the CAPM, but any model will do. If we do this, we find that because the low-C technology’s cost is riskless, the discounted value of that cost cash flow stream is GREATER than the discounted value of the gas-fired generation cost cash flow stream.

Therfore, claim (i) does not hold. The two technologies do not have the same levelized cost.

The only way to rationalize the White Paper’s claims (i) and (ii) with one another, using any model with real numbers and actual risk discounting, is to use an unorthodox model of risk pricing. This will have to abandon the principle of value additivity. It will have to abandon the notion that the capital markets have established a unique price for each risk.

This is exactly what the academic work underpinning the EMR’s White Paper has done. More on that in future posts.

One Trackback

  1. […] an earlier post I showed a stylized graph of a low-C generator’s revenue, costs and profit margin, all […]

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