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swampwiz_gw

My analysis of the costs & benefits of energy efficiency systems

swampwiz
14 years ago

I've just done a thorough cost benefits analysis of an energy efficient system, so I'd like to share it with the community, and get any feedback.

It seems that the financial decision to install an energy efficiency system (i.e., either insulation, or alternatively, a solar energy system, which would have the same net effect as insulation, or the difference in the capital and maintenance cost of a higher efficiency HVAC unit) is really a put option on the relative rate of energy cost increase vs. the rate of interest (i.e., either the cost to finance, or the rate or return on an investment.) There could also be the side effect of the relative rate of the cost and resale value of the installation of the energy efficiency system, and the difference in the capital and maintenance cost of a larger capacity HVAC unit.

When considering the installation, there are 2 different scenarios:

[1] Don't install the system, and just pay the extra costs of what would have been saved in the future.

[2] Install the system, and pay the interest on the costs of the financing of the installation (or forgo the return on the investment of the amount that instead was spent on the installation.

The general idea is that the savings due to the energy efficiency system must be greater than the financing cost of the installation. For example, if the system were to cost $10K, at 5% interest (tax neutral), the yearly finance cost might be something like $650. For this to make economic sense, the annual energy savings should be at least this $550, or it would have been better to simply pay the extra energy costs rather than the interest.

However, it is not the actual interest cost that should be measured, but rather the interest rate relative to the rate of increase in the cost of energy, since the savings would be worth that much more in actual terms.

So, while the interest rate and rate of return could be known and locked in (either by a fixed rate loan or bond), it is anybody's guess as to how expensive energy cost are going to be in the future. Obviously, the cost is at least going to go up with the general rate of inflation, but with the situation of Peak Oil and its side effect on the price of natural gas (which is the main way that electricity is generated for my area), and the unknown effect of mandated limiting of carbon emissions, who knows how high energy cost can go up!

I suppose that in the general, an energy efficiency system always makes sense if the savings outweigh the payments on the financing, so long as the cost of the system is not expected to go down in cost in the future (e.g., even if a solar power system makes sense now, if it is expected that the price of the system will drop significantly in the future, it may make sense to forgo the net savings to save the capital cost in the future.) If the system does not have a net savings at present, and the system does not have any extra cost for being installed after construction vs. during construction, then the proper action is to simply wait until such time in the future when there is a net savings to do the installation. For example, if a solar power system costs $20K, with a financing cost of $1010/yr, and with present reduction in energy costs being $500/yr, it would not make sense to do the installation. If however, 5 years from now, the cost were $12K, with a financing cost of $660/yr, and the reduction in energy costs being $700/yr, then it would make sense.

However, there is the situation with insulation such that the cost of installation is much higher after construction than before. In this situation, the decision to wait is not an option. A determination must be made that the current net loss (i.e., using the installation cost at construction) with respect to the installation cost at construction will be balanced by the future net gain. For example, extra insulation may cost $10K, with a financing cost of $550/yr, and only save $300/yr now, but save $700/yr in 20 years. So long as the net savings balance out over the long term (with the investment rate of return factored in, since the early savings of not installing the system could be invested to produce savings themselves), it would make sense. Thus, for this situation, the rate of interest should be modified such that it is relative to the rate of increase in energy costs.

Now for some math.

factors in analysis:

i = interest rate

f = rate of increase of energy cost

d = f - i

J = cost of system installation

E0 = current energy cost savings due to system

R0 = E0 / J

N = time period

then, for small D, a system installation system the financial equilibrium (i.e., break-even) point - i.e., where it starts to make financial sense - is, after a lot of math, and approximately:

with Y = exp(N * d) - 1 // exp(y) is the natural logarithm base e to the power of y

R0eq = d / Y

if d is negative, and d * N is large, then Y -> -1, so:

R0eq = :d:

examples:

N = 50, d = .02: Φ = 1.7, R0eq = 0.012

N = 50, d = -.02: Φ = -.63, R0eq = 0.032

N = 50, d = -.05: Φ = -.91, R0eq = 0.055

N = 1000, d = -.03: Φ = -1, R0eq = 0.03

So, in the case of this R0eq = 0.032, an energy efficiency installation of cost $10K would break-even over the 50 year span if the current annual energy savings were $320. (The annual savings 50 years from now would be much more.)

So the net result is that for the situation in which the interest rate is higher than the rate of increase of energy cost, the break-even point is a little higher than the difference of these rates. If the interest rate is lower, then the break-even point becomes much lower.

That's it. So what about a guess for what the price of electricity will be for the next 50 years?

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