Endowment Pricing: A Better Way of Pricing Projects

A particular amount of assets earns a certain cashflow in each year. A particular cashflow is equivalent in value to a certain sum of assets. If 100$ in a bank account earns 5$ forever, then a bond earning 5$ forever is equal in value to 100$ in a bank account. In this way, all recurring incomes and expenses can be made commensurate with one-time investments, while being consistent with the more "correct" yet complex LCOE calculations. This principle lets us make a simple system for calculating the costs, both upfront and long-term, of some investment or project.

The cost of an upfront investment, is simply what you pay for it. The formula for handling recurring costs is slightly more subtle. What we need is a start amount that we set aside, \$s\$, a multiple of how much that money grows while we wait, \$m\$, and the cost we’re ultimately having to pay, \$c\$. We have to know how much money we have to put in start with, and set aside that much money to pay the recurring cost.

\$sm = c\$

However, this is still not enough. If we start with s = 500, m = 2 and c = 1000, then we end up starting with $500, waiting for it to double in value, paying the cost, and ending up with 0$ at the end of it. We need to end up with s, so that we’ll have s after paying the cost, which is enough money to replace it again and still have s left over next time, as well.

\$sm = c + s\$

We want to have s as a fraction of c. To do this, we have to solve this equation:

\$c/{(m-1)} = s\$

m is simply your total return while waiting, when you earn a return of \$r\$ over the lifespan of your investment, \$l\$. The formula thus becomes:

\$c/{(1+r)^l-1} = s\$

The end result is a simple process for calculating how big an endowment you’d need, such that you’d be able to enjoy a particular asset perpetually into the future. You’d need to pay the cost to buy it to begin with (\$c\$), replace the original investment at the end of its lifespan (\$l\$), discounting your original investment its discount rate (\$r\$), and repeating this process with every cost that you’re paying. We can put all this into a single, simple equation:

\$Endowment C\ost = c + c_r/{(1+r)^{l_r}-1} + c_1/{(1+r)^{l_1}-1} + ... c_n/{(1+r)^{l_n}-1}\$

Let’s try this with a few actual numbers, from Lazard’s most recent round of LCOE calculations. I took the most optimistic estimate in each of the categories from their site.

Source: Lazard LCOE Plus

My findings are that endowment pricing achieves results quite similar to that of the LCOE calculations. Solar and wind are near-identically priced, with nuclear being 5.4 times more expensive. The Lazard study found that nuclear energy, at an LCOE of 141$ in their optimistic case, was 5.875 times more expensive.

I suspect that the difference comes down to differences in rounding on both ends. When comparing my endowment costs to their LCOE estimates per MWh, I found that the ratio was quite consistent:

My conclusion is that endowment pricing is a simple tool for comparing the costs of different potential investments. It uses a very simple and direct method of making upfront and recurring costs commensurable: it calculates how much money you need to invest as an extra upfront cost, such that all recurring costs are paid in advance. It makes estimating the potential value of savings due to new technology, and the appropriate level of spending on R&D, as simple as comparing it to the endowment cost already invested.

Given its simplicity of calculation, its ease of interpretation, and how it inherently treats long-term and short-term expenses equally, endowment pricing is an accounting technique that’s uniquely useful for public accounting. Putting all the expenses for any project or investment upfront, leaves no room for dishonest politicians or deceptive accounting to underestimate the cost of their new policies. Switching from a system of invisible liabilities slowly building up, to one where costs must be written down and paid for on day one, is both more honest and more understandable. That’s why I think it’s ultimately a superior accounting method that should be used by anyone wanting to compare the costs of different technologies, or wanting to find an honest estimate of the cost of a given government program.