In ancient Athens it was fashionable among the wealthy political classes to take debating lessons from tutors known as Sophists.

Despite their apparent wisdom, the Sophists gained a reputation as slippery intellectual mercenaries who would use their skills to make the bogus appear reasonable. In the 5th century BC, Aristophanes took the mickey out of the Sophists in a play called The Clouds, in which a debtor seeks to defeat his creditors by learning dodgy arguments at The Thinkery.

Arriving at The Thinkery, debtor Strepsiades learns how Socrates reasons that a gnat's buzzing is generated by air passing through the narrows of its anal sphincter.

"So a gnat's arsehole is a giant trumpet!" cries Strepsiades. "O triply blessed man who could do this - anatomise the anus of a gnat! A man who knows a gnat's guts inside out would have no trouble winning lawsuits."

Strepsiades ultimately learns his lesson in the play, but after reading the latest report from the Electricity Authority more than 2000 years later, Chalkie reckons anal anatomy is back in vogue with a vengeance.

To recap, this report aimed to analyse historical electricity costs to see why household power prices had risen so much over the last couple of decades. It concluded that although households were paying a lot more, they were still not paying enough to cover the actual cost of providing the electricity.

"This finding is contrary to claims that consumers have been over-charged for electricity for more than 30 years and they have already paid off past investments," the authority said.

With that, the government organisation is wading with considerable weight into politics in opposition to the "single buyer" power policy proposed by the Labour and Green parties. And the general election is about 10 months away.

Chalkie is no natural friend of the Labour/Green scheme, being a power company shareholder and supporter of the mixed ownership model for state-owned enterprises. However, it is important that these policies are discussed with due respect for reason and fact.

Sadly, the authority's report does not meet the mark. Indeed, Chalkie reckons it is clever, fallacious and deceptive - in modern parlance, sophistry.

The report's goal is admirable. Going back to 1907 to tot up the total cost of our electricity supplies is a great idea. With those numbers we could end once and for all the tedious debate over whether prices are too high.

The authority usefully lists every power station built since Waipori in 1907 along with its construction cost and power output. Waipori near Dunedin cost $70,000, or $2.6 million in today's money, for an output of 2MW.

Unfortunately, those are about the only actual historical figures the authority uses.

Rather than use the actual operating costs, which for the state-owned years are surely still in a filing cabinet in Wellington and for the privatised companies are in published accounts, the authority uses "figures published as part of the grid planning assumptions work carried out by the Electricity Commission".

Fuel costs are "based on information from the MBIE Energy Data File publications", rather than the actual fuel costs paid by the power companies.

Retail marketing costs are "estimated by the authority"; metering costs are "estimated by the authority".

It's hard to say how much these estimates differ from the actual costs, but it is unfortunate that non-facts have been used in an analysis presented as fact-based.

However, this expedient pales beside the authority's nutty decision on the cost of capital.

Clearly, money used to invest in something has a cost because those providing the money require compensation for giving up the use of it. The authority has decided that the capital cost for every year since 1907 was 10.1 per cent - a choice justified by analysis from the NZ Institute of Economic Research.

(Coincidentally, the authority's report was found to be "fit for purpose" in a peer review by NZIER, whose former senior fellow and chief executive, Brent Layton, is now chairman of the authority.)

The cost of capital process used by NZIER is conventional - for commercial investment - in that it takes account of the cost of equity and debt used to finance a project.

If you have to pay 6 per cent to borrow $1 million, and equity investors won't provide a further $1m for less than 10 per cent, your weighted average cost of capital (WACC) is 8 per cent. Simple.

Let's remember at this point that the WACC is not some theoretical ideal but a measure of how much your money actually costs every year.

And let's also remember that to calculate your WACC you have to know how much debt and equity is being used for each investment.

So how much equity was invested in building power stations before the first state-owned enterprise was formed in 1987?

Er, let me see, that would be, um, actually, it must be, hmmm . . . Yes it's tricky, because the notion of equity capital for the government's investment in power stations before 1987 makes no sense. The closest we can get to the cost of that money is the cost of sovereign debt, also known as the risk-free rate, for which the numbers are readily available to a government entity such as the authority.

Yet the NZIER model assumes all debt cost 2.7 percentage points more than the risk-free rate.

It also assumed gearing - the ratio of debt to debt plus equity - was always 25 per cent. Yet when Contact Energy became the first privatised SOE it had a gearing ratio of 37.4 per cent.

The relevance of the NZIER's assumption is that, within certain limits, a lower gearing means a higher cost of capital.

By no means are these the only criticisms you can make of the NZIER's choice of WACC, but Chalkie reckons you could drive a bus through the holes in its logic.

According to the report, the reason for NZIER's approach was that there wasn't enough time and resource to do it properly so "it makes sense to keep things simple". Yes, and stupid.

There are other questionable assumptions in the authority's efforts to establish that it costs more to provide electricity to households than to commercial and industrial users. The idea is that households' demand is more "peaky" than others and therefore more costly to serve.

"Generation suitable for meeting fairly constant levels of consumption over time (baseload generation) is generally cheaper to run than generation that is more suited to ramping up-and-down in order to meet variable demand (peaking generation)," says the report.

This sounds reasonable, until you note that low cost hydro generation, which provides about two-thirds of our power, is good at both. At even a venerable station such as Benmore the time taken to ramp up for power peaks can be measured in seconds rather than minutes.

With a whole battery of generators required to meet our national power demands, Chalkie reckons it is hard to say which ones are providing power to who.

Anyway, having designed a model to estimate the cost differences across consumer types, the authority concedes that its model shows no difference before the year 2000.

"Prior to 2000 there was little or no difference in costs between consumer types because of the excess hydro capacity available to the model," it says.

It then ignores the finding and applies the cost differential to its estimates all the way back to 1974.

It's almost as if the study was trying to produce a particular result.

Strangely enough, an alternative analysis in the report, not mentioned in the executive summary, comes up with a different answer.

This one measured the actual wholesale price of electricity from 2005 to 2013 and used the average as a proxy for the wholesale cost of power for all consumers.

After adding its other cost estimates, the authority found consumers were collectively paying a bit more than cost for their power - the opposite of its main finding.

Applying the average generation cost across a model of consumer types came up with the answer that residential consumers were paying considerably more than cost, while industrial consumer were paying below cost. Woops, wrong answer.

There are obvious flaws with this analysis too, but Chalkie is not sure they are worse than the howlers in the methods the authority chose to highlight.

Chalkie reckons what we have here is an attempt to justify the huge price rises for households in a politically led effort to discredit the Labour/Green policy.

But the upshot is that the authority has discredited itself.

Chalkie is written by Fairfax business bureau deputy editor Tim Hunter.