Energy Affordability — Internal Rate of Return

IRR Equation, Calculation, and Usefulness

Bitesize Edition

• The next affordability metric I’m going to explore is the internal rate of return. The metric is calculated by setting the net present value of a project equal to zero and rearranging the equation to calculate the discount rate.
• This discount rate then refers to the internal rate of return on the project, which at an NPV of zero, will generate no discounted cash flows in the life cycle of the project.
• When considering IRR and the cost of capital, we can determine which projects will better handle tougher financing conditions. This is especially useful in the last few years when we’ve seen interest rate hiking cycles around the world. When coupled with NPV, we can utilise a worst-case scenario analysis, and projects that look favourable to both IRR and NPV could be projects that are pursued.
• So, let’s explore what IRR is, how it can be used, and any potential drawbacks of the metric.

Introduction

As I continue to examine affordability metrics to analyse our energy projects, I today venture into the internal rate of return. How does IRR compare to net present value? And what is IRR? Find out below.The internal rate of return is the discount rate that would need to be applied to a project for the net present value to be equal to zero in a discounted cash flow statement.Like most of these definitions of affordability metrics, there are multiple aspects to break down.Firstly, the discount rate is the percentage rate used to calculate the present value of future cash flows. Due to inflation, £1 today is worth more than £1 next year. When forecasting cash inflows or outflows in the future, we hence have to account for the time value of money.Net present value is what I’ve discussed over the last two weeks, and the articles can be found below:

I’d recommend reading these pieces first, at least the introduction to what NPV is, and then return here. A NPV of zero indicates that the cash flows generated over a project when discounted using the discount rate are equal to the initial investment in the project. In other words, the investment neither gains nor loses value and earns a rate of return equal to the discount rate in this scenario.The final part of the definition refers to a discounted cash flow statement. This is the method used to estimate an investment’s value based on these future cash flows.I’ve always been mathematically minded, and reading definitions has usually never allowed concepts to sink into my brain. With that in mind, let’s dive into an example calculation.

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Example Calculation

To calculate the discount rate when NPV equals zero, we simply set the equation for net present value to zero.

We could then do some rearranging of our equation, setting it equal to the discount rate, or internal rate of return, r. Looking at this equation, with an r on the bottom of every fraction, it looks difficult to make r the subject of the equation. It requires mathematical methods such as differentiation and iterative methods such as the Newton-Raphson method. The Newton-Raphson method even involves guessing what the discount rate could be, and so is dependent on the initial prediction. Hence it can be inaccurate.When it comes to calculating IRR, if we want to calculate an actual IRR, we need the cash flows for the project. Let’s take the same example used in the first NPV piece I linked above:

Year 0:

• Turbine Cost = $2,000,000
• Transportation = $200,000
• Construction = $800,000

Years 1–5

• Research Project = $5,000

Years 1–30 (Ongoing Costs)

• Maintenance Cost = $50,000
• Insurance Costs = $3,000
• Operation Costs = $50,000

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Now to assess the inflows:

Years 1–10

• Production Tax Credit = $75,000

Years 1–30

• Electricity Generation = $300,000
• Renewable Energy Credit = $90,000

Now we have cash flows, we can input these figures into the NPV equation, setting equal to zero.

For this part, we can use Excel.If we write out the number of years of our energy project and input the cash flows every year, not forgetting the initial investment that is a negative cash flow, we can then highlight these cash flows and use the IRR function. This will generate the discount rate that will ensure NPV is equal to zero, also known as the internal rate of return. From our example above, we achieve an IRR of 9%. For confirmation, input r=0.09 into the equation above and see what NPV is returned.This returns an NPV of £75,017.14.If we include another decimal place within the discount rate, we see that at 9.4%, we have an NPV of £556.03. At 9.5%, we have an NPV of -£17,474.91. Hence, the IRR falls between 9.4% and 9.5%. This naturally rounds down to 9%.

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NPV and IRR

As discussed in my writings on net present value, if we take a worst-case scenario approach, with high costs, lower electricity selling costs, or less electricity produced, and these projects still possess a positive NPV, this could be a project that could weather tougher conditions and be a profitable project.What IRR allows us to do is see where the threshold is for an energy project and the discounting of future cash flows. If we have a high IRR, this is a sign of a project that is generating a higher rate of return on the investment. A high IRR also implies the project being discussed could weather a variety of financial conditions, including periods of higher interest rates and hence higher costs.One area of the energy industry that IRR is useful within, is when making the decision to extend the life of a project, or whether to construct a completely new project. Both decisions could have a positive NPV, but the higher IRR will generate greater returns.One negative aspect of IRR is the assumption that every year is the same. In some years, costs could be higher. This can lead to an overestimation of a project’s rate of return, and hence paint a project as more profitable than it likely will be.Also, a smaller project that has a high IRR could be preferred to a large-scale project with a lower IRR, but the large project could generate more absolute dollar value, or contribute to greater productivity in a nation’s energy industry.Finally, the time horizon is a difficult aspect to account for. As I discussed last week with the Vogtle nuclear plant in Georgia, Unit 3 and Unit 4 of the plant were 7 years late and $17B over budget. Prior to the project’s start, it could have appeared as a more favourable project, only for other aspects such as supply chain disruptions, poor planning, and a low-skilled labour force to slow progress. In a sentence, it’s easy to make assumptions that can change over time.

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Concluding Remarks

In assessing the usefulness of IRR, as I’ve argued for NPV, it can be utilized as a metric to analyse the worst-case scenario. If a project has a high IRR, in isolation, you’d assume this project will generate a greater return. But the capital costs have to also be considered. Also, the ranking of a list of projects by IRR could differ from the ranking generated by NPV. But together, the two metrics can truly stress test our energy projects.

Thanks for reading! I’d greatly appreciate it if you were to like or share this post with others! If you want more then subscribe on Substack for these posts directly to your email inbox. I research history, geopolitics, and financial markets to understand the world and the people around us. If any of my work helps you be more prepared and ease your mind, that’s great. If you like what you read please share with others.