Answers in the wind

Project valuation means making calculated assumptions that aren’t always accurate. Brett Humphreys discusses the assumptions that may be embedded within a valuation and how these assumptions can affect the final value

Project valuations are always tricky problems. Invariably time is short and the value needs to be determined quickly. The modeller must therefore make assumptions and take shortcuts to reach a final valuation by the deadline. Experienced modellers usually recognise the assumptions embedded within their models and the explicit trade-off between more accurate valuations and either increased calculation time or difficulty of implementation. However, occasionally the modeller does not recognise the assumptions and the impact they might have.

To see the impact assumptions can have, consider a potential wind-farm project consisting of 2 megawatt (MW) turbines. Let us assume the turbines have the following characteristics:

The turbines can start generating power at wind speeds of 5mph or 2 metres a second (the cut-in speed)
The turbines reach maximum generation at wind speeds of 15mph or 7 m/s (the nominal speed)
The turbines must be shut off at wind speeds exceeding 30mph or 13 m/s (the cut-out speed)
If we know the cost of constructing the wind farm, then the question facing the modeller simplifies to: what is the potential revenue that will be realised from the wind farm?

The first pass
If the answer is needed extremely quickly for this valuation, a logical first step is to calculate the average wind speed at the planned construction location. Using this speed and the turbine power curve1, we can determine the expected generation each year. To get the revenues associated with the turbine we would multiply the expected generation by the current power forward curve to get an estimate of revenues.

Any potential development should have at least one year of historical wind speed data that could be used to estimate potential generation from the turbines. Assume that we do have one year of historical wind speed data at the proposed site and that this data indicates an average wind speed of 11.6mph. Based on the turbine power curve, this wind speed would create 1.32 megawatts of power per hour – or 11,500 MWh each year. At an average forward price of $60/MWh, this would imply annual revenues of $693,000.

While this is an ‘answer’, it includes a number of embedded assumptions, all of which may be wrong and lead to an incorrect conclusion.

Assumption: average annual wind speed
The first assumption embedded within this analysis is that one year of historical wind data can be generalised to represent all future years. While additional data at the specific development site may not be available, additional wind data is often available from government sources2.

Using some statistical techniques it should be possible to relate the wind speed from known areas to the wind speed at the planned construction site.

For example, using the US National Oceanic and Atmospheric Administration (NOAA) data we can obtain hourly wind speed data from 1995 through 1999. Let us assume that using this data we identify the location that has attributes most similar to the planned construction site and note that based on the last year of data the wind speeds at the planned construction site are on average 1.2 mph higher than the associated location3. Using this relationship we can create synthetic historical wind speeds. This synthetic data indicates that the average wind speed at the planned location over the full five-year period is 11.3 mph, with a standard deviation of 0.5 mph. Based on this information, the expected annual generation would be 11,000 MWh with a 95% confidence range of 9,300 MWh to 12,700 MWh.

This revised windspeed data would imply an expected annual revenue of $659,000. While this is only 5% less than the first estimate, the standard deviation implies a potential range of revenues in any year ranging from $556,000 to $761,000. This uncertainty may have a significant impact on the project’s economics.

Assumption: average wind-speed generation
The second assumption is that it is appropriate to use the average wind speed within the turbine power curve to determine the expected generation within the year. This assumption would be appropriate if the turbine power curve was linear. However, the relationship of power to wind speed is asymmetric due to the cut-in, nominal and cut-out speeds. If we instead use the actual hourly wind speeds to estimate generation we would estimate annual production of 9,800 MWh per year based on historical data for the past five years. From the data we can also determine the actual 95% range to be from 8,800 MWh to 10,700 MWh. This is 10% less than the first assumption. The reason for this decrease is the asymmetric exposure to wind changes. Consider that at the average wind speed, 1.32MW of power are generated. If the wind speed increases by 10mph, the generation would increase by 0.68MW to 2MW (the maximum). However, if wind speed drops by 10 mph the generation decreases by 1.32MW to 0MW. This asymmetry creates the negative bias in average production when the full distribution is considered.
Using this revised assumption, the expected revenues of the project are now $587,000.

Assumption: No relationship between wind speed and time
The next assumption is that power is generated as a constant stream over the course of the year. If this is true, then multiplying the generation by the annual price is an appropriate assumption. But in reality this is not the case. Historical wind data shows both daily and annual patterns. Figures 1 and 2 show the expected wind pattern in a typical day and in a typical year.

As can be seen from the figures, daily winds tend to have a peak in the early morning and the late evening. The annual peaks appear to occur in the winter and spring. Given that power prices also have a seasonal structure, we need to take into account the on-peak and off-peak price differentials, as well as the seasonal shape of power when determining potential revenues.

The combined effect of the annual shape of power prices and the increased production in off-peak hours is to decrease the average realised power price to $58.33. Based on this lower realised price, the expected revenues from generation are now only $571,000 – nearly 20% less than the first-pass calculation.Project valuations are always tricky problems. Invariably time is short and the value needs to be determined quickly. The modeller must therefore make assumptions and take shortcuts to reach a final valuation by the deadline. Experienced modellers usually recognise the assumptions embedded within their models and the explicit trade-off between more accurate valuations and either increased calculation time or difficulty of implementation. However, occasionally the modeller does not recognise the assumptions and the impact they might have.

To see the impact assumptions can have, consider a potential wind-farm project consisting of 2 megawatt (MW) turbines. Let us assume the turbines have the following characteristics:

The turbines can start generating power at wind speeds of 5mph or 2 metres a second (the cut-in speed)
The turbines reach maximum generation at wind speeds of 15mph or 7 m/s (the nominal speed)
The turbines must be shut off at wind speeds exceeding 30mph or 13 m/s (the cut-out speed)
If we know the cost of constructing the wind farm, then the question facing the modeller simplifies to: what is the potential revenue that will be realised from the wind farm?

Assumption: hedgeable revenues
The final assumption that may be embedded in the valuation is the belief that the forward power price is appropriate for valuing the wind generation. In truth, as the wind speed data shows, while the average generation over a long period can be reasonably predicted, actual generation in any single hour is actually fairly uncertain. Unlike a standard power plant, operation depends on an external factor – the presence of sufficient wind. We therefore cannot guarantee that the plant will be able to generate.

While selling the expected production forward is possible, it may not be a good strategy. If power prices and wind speeds are uncorrelated, then this strategy is a partial hedge of the exposure, but the owner is still faced with volumetric risks. However, if there is any potential relationship between wind speed and power price, such a hedge may be costly.
For example, assume that when wind speeds are high, power prices tend to be lower – and when wind speeds are lower, power prices tend to be higher. Such a situation would lead to selling extra power at a price that is on average lower than the price that excess power would need to be purchased.

While the exact impact of this assumption was not assessed in this case, it could justify using a higher discount rate when evaluating the project or even taking a risk charge against the project.

Conclusions
As this example shows, simplifications often contain embedded assumptions that may dramatically change the value of a project. While we frequently hope that the errors arising from assumptions will tend to cancel out, in some situations the errors instead reinforce.

While this example showed how a project may be significantly overvalued, a different set of assumptions might lead to significant undervaluation. It is the job of the modeller to understand the models: know their limitations and test their assumptions to determine the impact. Only by taking such actions can we be confident that our simplifying assumptions are not simply misleading.
Brett Humphreys is a managing director at Risk Capital in New York. Email: [e-mail]