Why long lifetimes are not necessarily a "good investment"

TL;DR

For projects with long lifespans, a high discount rate significantly reduces the impact of future costs and revenues on the Net Present Value (NPV). This means periods beyond, say, 20 years, often add surprisingly little value to the project's NPV from a high-yield investor's perspective.

The time value of money

There are builders and advocates out there that put a lot of emphasis on energy technology that has a long lifespan. While a long resource lifespan can be beneficial from a sustainability perspective it may not move the needle for investors. Let’s take a quick dive into how resource lifetime is valued by different stakeholders.

At the core of this is the time value of money, which is quantified by the metrics like annuity, net present value (NPV)^[1], and internal rate of return (IRR)^[2]. What changes whether something is worth it or not is the value that someone applies to time. We use the cost of capital or discount rate as a measure of someone’s value of time, for example someone using a savings account at 1% effectively values their money at 1%. For someone putting their money in an index fund, they might be looking for 8% or higher returns.

Let’s look at how the time value of money affects a project’s financials. There are two places in which the time value of money pops up, in the revenue and in the costs. Let’s look at revenues first, first we assume that the energy generator produces the same amount of energy each year and sells it at the same price, for a total of $10,000/year.

How lifespan changes NPV - revenue

In Figure 1 below we plot the fraction of NPV value relative to the 50-year NPV with a discount rate of 8%. We see that our NPV plateaus very quickly, reaching 80% by 20 years and 93% by 30 years. This means the period from year 31 to 50 adds only 7% to the NPV. This is the power of compound rates. Since investors use metrics like the NPV to make decisions on investments, it’s true that a 50-year lifespan would improve the NPV, it only performs marginally better than 30 years and not much better than 20 years. This is one of the reasons why extraordinarily long equipment lifetime isn’t perceived as being a better investment.

Cumulative contribution to NPV by year (8% discount rate)

Figure 1: The cumulative fraction of the 50-year lifetime NPV calculation for each incremental year considered at an 8% discount rate. If considering only a 20-year lifespan, one would recover about 82% of the NPV of the 50-year time horizon.

Given that the discount rate is central here, let’s take the perspective from a more conservative perspective, perhaps a municipality that has a lower discount rate of 4%. As demonstrated in Figure 2, in this case the longer lifespan has a much larger impact. At 20 years we’ve only recovered slightly more than 60% of the 50-year NPV and now at 30 years we are sitting at 80%. This is one of the reasons that financially more conservative investors like municipalities are more likely to invest and value long-term investments.

Cumulative contribution to NPV by year (4% discount rate)

Figure 1: The cumulative fraction of the 50-year lifetime NPV calculation for each incremental year considered at a 4% discount rate. If considering only a 20-year lifespan, one would recover about 64% of the NPV of the 50-year time horizon.

For those looking to sell new technologies, especially ones where lifespan is a key advantage, consider who your potential buyers and investors are and how important that lifespan might be to them.

It’s important to distinguish this lifespan from the concept of degradation. Degradation is the slow loss of capacity and structural breakdown of the materials and plant over time. This can result in reduced capacity over time and eventually failure (end of life). In these examples we take a more binary approach, there are no degradation effects and we simply have a plant end of life. Degradation can have massive consequences for NPV as well, but that is for another post. This example also doesn’t consider additional investment aspects like amortization for tax purposes or other mechanics that value earlier time periods more and is beyond the scope of this post.

How lifespan changes NPV - costs

Let’s now look at how this time value of money impacts costs. One of the reasons that metrics like LCOE and LCOS consider the time value of money is because this allows us to better compare different technologies that have different time-dependent parameters such as cost, generation, and degradation. For example, let’s look at a 1MW solar project and a 1MW fossil fuel project with equal annual energy production, 1000MWh/year. In the solar case we have high upfront costs and no fuel costs, in the fossil fuel case we have lower upfront costs but non-zero fuel costs. The results are tabulated in Table 1.

In the case of solar, let’s assume the plant costs $950/kW. The fossil fuel plant costs $500/kW upfront and $45/MWh in fuel costs. Assuming neither has considerable degradation over the 25-year lifetime, we find that their NPV of their costs are the same (8% discount rate and 25 year lifespan). On the one hand, they have completely different cost structures, one is twice the upfront cost the other has fuel costs, but on the other from a discounted cashflow perspective they’re effectively identical. Furthermore, while the solar plant has a total nominal cost of $950,000, the fossil fuel plant has a total nominal cost of $1,625,000, which is about 70% higher.

How can the NPV be the same, even though the fossil fuel plant has higher nominal costs? What the NPV means is that in the first year, the fossil fuel plant saves $450,000 relative to the solar plant. Hypothetically, if the fossil plant goes ahead and puts this money into an 8% yielding account (8% cost of capital or discount rate), it will earn interest on this $450,000 over the course of 25 years. However, each year it must also draw from this account to pay for fuel. What we would see at the end of the 25 years, is that the fossil fuel plant was able to cover all fuel costs from this “savings” account and the account would be empty at 25 years. While this isn’t how a fossil fuel plant would invest in reality (they would build more projects in lieu of a “savings” account), it illustrates how the NPV works and why it equalizes the different nominal cash flows.

Another way of looking at it is what would happen if the predicted discount rate differed from the real one? In the case that the fossil fuel plant was able to earn 10% per year instead of 8%, it would be net positive after 25 years relative to the solar plant (assuming equal revenues). However, if the realized rate was 6% per year, the fossil fuel plant would need money beyond the “savings” account to cover its fuel costs. Hence, when making decisions on how to discount cashflows, investors need to consider what their true cost of capital is, or how much they can earn if they put their money elsewhere, otherwise they risk over or undervaluing their cash streams.

Frontload earnings and backload costs

The point of these examples is to show that the time value of money is real and that interest rates acting over the long time periods of generator lifetimes can severely impact the present-day value of the later revenues and/or costs. For technologies that place a strong emphasis on lifespan, this can make selling to high yield investors difficult, since they place less value on lifespan.

At a high level discount rates are important to consider for technology and project viability. For technologists, this gives a sense for how an investor may or may not value the lifetime performance metric of their inventions, since future revenues and costs are so discounted they don’t move the financial needle much. For environmentalists, this gives a sense for why investments are made into technologies that may not be the most sustainable. Time matters, especially when it comes to money, the goal should be to frontload earnings and backload costs!