02-03-2017, 04:29 PM
I have a question regarding the use of hurdle rates. I'm wondering whether the use of hurdle rates (technology specific discount rates) actually reflects the decision making by private investors.
Below, I’ve included the reasoning I used. Based on this reasoning, I seem to come to the conclusion that, when technology specific discount rates are used, the results of the optimization model (TIMES) do not necessarily correspond to the the equilibrium that would be formed if private investors would value their investments with their respective technology-specific discount rates. And even, there seems to be no way to compute the equilibrium using an optimization model whenever technology-specific discount rates are used. As this seems to touch the essence of the idea of technology-specific discount rates and I’m not aware of any discussion about this, I’m wondering if my reasoning is correct..
Reasoning:
If no technology specific discount rates are used, the costs and value (~revenues) related to an investment will equal. Assuming for simplicity a technology with no costs related to the activity, i.e., only an investment cost (e.g., wind turbines). This technology generates electricity and generates revenues in year a equal to revenue(a) which can be calculated based on the dual variables of the COMBAL constraint for electricity and the generation in each time slice.
- the contribution of a unit investment in this technology to the objective function equals NCAP_COST (assuming the objective function discounts to the year of the investment and no lead time is considered)
- the value perceived by the model equals: sum_a=1^TLIFE (revenue(a) * r^(a-1))
If the hurdle rate equals the general discount rate r (meaning no hurdle rate is used in the model), both the cost and the value related to an investment are perceived the same by the model and by a private investor.
Now, assume that a hurdle rate r_s is introduced for this technology which differs from the general discount rate r.
- The cost perceived by the model now equals: NCAP_COST*(CRF_s/CRF) (1) . Here, CRF_s/CRF can be considered as a cost mark-up for the investment cost.
- The value perceived by the model again equals: sum_a=1^TLIFE (revenue(a) * r^(a-1)) (2)
The costs and values perceived by a private investor are the following:
- The costs perceived by a private investor equals: NCAP_COST (3)
- The value perceived by a private investor equals: sum_a=1^TLIFE (revenue(a) * r_s^(a-1)) (4)
So, both the costs and the value perceived by the model differ from those perceived by a private investor. The value perceived by the model is directly related to the general discount rate and thus cannot be easily adapted. The costs perceived by the model can be adapted such that, whenever costs = value from an investor perspective, this is also true for the model (such that the model would have similar decision making to a private agent).
The perceived value of the model can be related to the perceived value of the private investor:
Value model = (sum_a=1^TLIFE (revenue(a) * r^(a-1)) / sum_a=1^TLIFE (revenue(a) * r_s^(a-1))) * value perceived by investor.
When the revenue term is assumed constant over all years the investment is operational, this gives:
Value model = (CRF_s/CRF)*value perceived by investor.
For the model to have the same decision making as the investor, the costs in the investment costs in the model should also be increased by this factor. This is exactly what is done in TIMES (see (1)).
The problem I face is that this no longer holds whenever the revenue streams are not constaint over the years. For example, assuming d_s > d and decreasing revenue streams over the lifetime of the investment, value_model/value_investor < CRF_s/CRF. Thus, the revenues are not sufficiently valued by the model (or seen differently, the investment cost mark-up used is too high).
Sorry for the long post, but I did not manage to find a more concise way to formulate the question.
Below, I’ve included the reasoning I used. Based on this reasoning, I seem to come to the conclusion that, when technology specific discount rates are used, the results of the optimization model (TIMES) do not necessarily correspond to the the equilibrium that would be formed if private investors would value their investments with their respective technology-specific discount rates. And even, there seems to be no way to compute the equilibrium using an optimization model whenever technology-specific discount rates are used. As this seems to touch the essence of the idea of technology-specific discount rates and I’m not aware of any discussion about this, I’m wondering if my reasoning is correct..
Reasoning:
If no technology specific discount rates are used, the costs and value (~revenues) related to an investment will equal. Assuming for simplicity a technology with no costs related to the activity, i.e., only an investment cost (e.g., wind turbines). This technology generates electricity and generates revenues in year a equal to revenue(a) which can be calculated based on the dual variables of the COMBAL constraint for electricity and the generation in each time slice.
- the contribution of a unit investment in this technology to the objective function equals NCAP_COST (assuming the objective function discounts to the year of the investment and no lead time is considered)
- the value perceived by the model equals: sum_a=1^TLIFE (revenue(a) * r^(a-1))
If the hurdle rate equals the general discount rate r (meaning no hurdle rate is used in the model), both the cost and the value related to an investment are perceived the same by the model and by a private investor.
Now, assume that a hurdle rate r_s is introduced for this technology which differs from the general discount rate r.
- The cost perceived by the model now equals: NCAP_COST*(CRF_s/CRF) (1) . Here, CRF_s/CRF can be considered as a cost mark-up for the investment cost.
- The value perceived by the model again equals: sum_a=1^TLIFE (revenue(a) * r^(a-1)) (2)
The costs and values perceived by a private investor are the following:
- The costs perceived by a private investor equals: NCAP_COST (3)
- The value perceived by a private investor equals: sum_a=1^TLIFE (revenue(a) * r_s^(a-1)) (4)
So, both the costs and the value perceived by the model differ from those perceived by a private investor. The value perceived by the model is directly related to the general discount rate and thus cannot be easily adapted. The costs perceived by the model can be adapted such that, whenever costs = value from an investor perspective, this is also true for the model (such that the model would have similar decision making to a private agent).
The perceived value of the model can be related to the perceived value of the private investor:
Value model = (sum_a=1^TLIFE (revenue(a) * r^(a-1)) / sum_a=1^TLIFE (revenue(a) * r_s^(a-1))) * value perceived by investor.
When the revenue term is assumed constant over all years the investment is operational, this gives:
Value model = (CRF_s/CRF)*value perceived by investor.
For the model to have the same decision making as the investor, the costs in the investment costs in the model should also be increased by this factor. This is exactly what is done in TIMES (see (1)).
The problem I face is that this no longer holds whenever the revenue streams are not constaint over the years. For example, assuming d_s > d and decreasing revenue streams over the lifetime of the investment, value_model/value_investor < CRF_s/CRF. Thus, the revenues are not sufficiently valued by the model (or seen differently, the investment cost mark-up used is too high).
Sorry for the long post, but I did not manage to find a more concise way to formulate the question.
