Investment Cost Loan Time

[Nataly Panczyk]

Hello,

I'm currently running a pretty simple model on Temoa to show an energy flow for a steel mill and am having a bit of trouble interpreting the costs outputs I'm getting. I am only running one year of the model, because my analysis doesn't really depend on an extended time period at this point. As Temoa doesn't output the costs by year, I would like to model two scenarios:

1) when the total investment costs are paid in full during the first year of operation (i.e. the total costs include all of the capital costs, plus one year of variable costs based on demand and one year of fixed costs). 

2) when the total investment costs are paid over a time period equal to the lifetime of the technology. Then, for the year I'm modeling, I would expect the total costs to include the first payment for the loans on each technology, plus one year of fixed costs and one year of variable costs based on demand. 

I figured this could be adjusted using the LifetimeLoanTech table and for scenario 1, setting each technology to a time period of 1 year, and for scenario 2, setting each technology to a time period equal to its previously defined lifetime. However, when I change the values in the LifetimeLoanTech table, nothing changes in my outputs. When I alter the LifetimeProcess table, though, my outputs change. I'm a little unclear about how LifetimeTech, LifetimeLoanTech, and LifetimeProcess each impact the costs of this system and the system as a whole, and also how I might be able to adjust my input file so Temoa gives me the output I'm expecting. 

I've attached my input SQL file. Please let me know if there's anything else I can provide, and thank you in advance for your help!

Best,

Nataly

[Joe]

Hi Nataly,

My apologies for the delayed response. The objective function cost calculation is a bit more complicated than a simple present cost calculation. The explanation of the objective function is here in the documentation. In essence, we're trying to avoid end effects (i.e., skewed results near the end of the model time horizon) while properly capturing technology specific discount rates and loan periods. Take a look at the objective function description and see if your results make sense in light of this formulation. I would have thought that changing either the LifetimeTech or LifetimeProcess values would have changed the objective function value.

If you just want to solve the one time period problem using a simple present cost calculation, try simplifying the objective function formulation in temoa_rules.py beginning on Line 231.

Hope this helps.

Best,

Joe

[Samuel Dotson]

Hi all, 

I'm bumping this question again because I'm running into a similar issue (I think), which is changing the loan period for a technology doesn't change the results at all. Based on the documentation, I would expect this to change the results, even marginally, but the outputs are exactly the same. Maybe I still don't understand how the objective function is calculated. 

My understanding is the following: 

If I have two technologies with similar costs, ceteris paribus, when deployed, but technology A has a loan period of 10 years and technology B has a loan period of 25 years. The total cost (which Temoa minimizes) should be higher for Tech B than Tech A. However, changing the loan period of Tech B to < 10 years does NOT change the results at all, which I think is unexpected.

Any guidance on this issue is appreciated.

Best, 

Sam Dotson

[Cameron Wade]

Hi everyone,

I've also come across this issue. I've taken a closer look at the objective function and on first pass it appears as though it may not be a function of the loan lifetime after all.

Have a look at the photo below, which simplifies the C_loans term from the objective function:

We see that the only terms that are affected by the lifetime loan ("LLN") appear in terms A and B. Under the assumption that the technology discount rate (DR) is equal to the global discount rate (GDR), we see the LLN terms cancel. This means that the objective function is not influenced by the LLN term.

I've run two scenarios on temoa_utopia.sqlite to confirm. I've changed the LifetimeLoan of a particular technology and the objective functions in their respective .lp files are identical.

I should note that I've done this rather quickly and haven't taken the time to generalize for GDR != DR, but I thought I'd at least share my initial thoughts.

Cam

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Cameron Wade

Principal, Sutubra Research

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[Joe]

Hi Cam and Sam,

Thanks for raising this issue. The effect of the loan period in the Temoa objective function depends on a couple factors. The first is the use of hurdle rates (i.e., technology-specific discount rates). If a technology is deployed and retired within the model time horizon and the hurdle rate  = global discount rate, then changing the loan priod would be no effect on the objective function value. As noted in Cam's notes, the LLN term cancels and has no effect. If you add a hurdle rate that differs from the global rate, however, you should see a difference in the objective function value.

Second, is the choice of the loan period itself. We amortize the capital costs and truncate the payments that extend beyond the end of the model time horizon. (A more detailed description of the objective function is here in the documentation.) Thus if you change the loan period for technology vintages that extend beyond the end of the model time horizon, using different loan periods should also have some effect.

If the objective function does not seem to changing when you think it should (accounting for the considerations above), let us know and we can investigate further.

Thanks,

Joe

[Samuel Dotson]

Hi Joe, 

Thanks for the quick response. I’m still confused because your first point tells me that the for the loan period to have any effect, the technology-specific discount rate needs to be specified. Your second point tells me that changing the loan period SHOULD affect the objective function. 

So, because Temoa utopia has no tech-specific discount rates, we expect the objective function value to be unchanged when the loan period changes — is that correct?

Finally, if that is the case, why is that behavior desired? If I buy a house and amortize over 30 years, the total cost is greater than if I amortize over 15 years. This intuition is causing confusion, I think.

Thanks for your help!

Best, 

Sam

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Samuel G. Dotson

Master of Science in Nuclear Engineering 2021

Bachelor of Science in Engineering Physics

University of Illinois at Urbana-Champaign

Pronouns: he/him/his

sg...@illinois.edu

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Samuel G. Dotson

Master of Science in Nuclear Engineering 2021

Bachelor of Science in Engineering Physics

University of Illinois at Urbana-Champaign

Pronouns: he/him/his

sg...@illinois.edu

[Cameron Wade]

Hi Sam,

I've put a bit more thought into the formulation and think I may understand Joe's point and what's going on. Here's another way to view the loan payments:

• The technology specific discount rate and technology specific loan lifetime determine how the loan payments are amortized. The LA parameter determines the fraction of the capital cost (CI) that is paid in each period of the loan's lifetime. Therefore, if you sum the product of CI and LA over the loan lifetime, you would get the undiscounted capital cost. For instance, with a discount rate of 0.06 and a loan period of 30 years, LA = 0.07265 and LLN*LA = 2.18. Therefore, you would pay 2.18*CI in total.
  
  
• Temoa seeks to minimize the total discounted cost, or the net present value of all costs. That means that all future costs are discounted by the global discount rate (GDR). So we still need to discount the loan payments calculated above.
  
  
• That's why if DR = GDR things cancel -- essentially, the premium you're paying to service the interest payments on the loan are discounted away by the GDR. However, if DR > GDR, then the discounting only accounts for a fraction of the interest payments.
  
  
• I found the formulation provided in the journal paper to be a little bit easier to understand. I've included the relevant bit below:
  

Hopefully this framing helps to clear things up. Joe or Aranya, if I've misunderstood the loan costs please correct me!

Best,

Cam

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[Joe]

Thanks to Cam for the detailed explanation on the loan costs in the objective function. The only thing I would mention is that the loan cost component of the objective function has been updated (since paper publication) to better account for end effects -- see here. However, all the dynamics that Cam described are correct.

Sam -- I also wanted to address your questions. Regarding my first point, for the loan period to have an effect, a technology-specific discount rate must be supplied. As noted in my earlier email, this point only applies to technologies that are deployed AND retired within the model time horizon. As Cam noted, if you assume that DR = GDR, then you will get back the same lump sum capital cost with which you started, which is the desired behavior. It's effectively assuming that the time value of money associated with the investment is equal to the global discount rate. To your example, I may mortgage my house over 15 or 30 years, but if I value future money at the same rate as the bank, then the present value of my house is equal to it's purchase price regardless of the loan term.

Note that even in the absence of technology-specific discount rates (as in the case of utopia), we still want to amortize the capital costs. Why? Because if we don't, the model will avoid capital-intensive investments near the end of the time horizon, resulting in weird "end-effects". So for capacity that is retired after the end of the time horizon, we need to truncate the loan payments to those that occur within the time horizon. Which brings me to my second point in the previous email: the loan period alone DOES matter for technologies whose life is truncated by the end of the time horizon. To the mortgage example again, if I am making payments on a 15-year mortgage and the end of the time horizon comes, my capital outlay will look different then if I had the 30-year mortgage. The Temoa objective function takes additional measures to try and reduce this effect, which are noted in the online documentation referenced above.

I hope this helps!

Best,

Joe

[Samuel Dotson]

Hi Joe, 

Thank you for taking the time to answer my questions (and confirming Cam's explanation). Your explanations are tremendously helpful!

if I value future money at the same rate as the bank, then the present value of my house is equal to it's purchase price regardless of the loan term.

That explanation was particularly clear.  

Best, 

Sam 

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[Cameron Wade]

Hi everyone,

Thanks for bringing this to everyone's attention Nataly and Sam. I've taken a closer look at the objective function and on first pass it appears as though it may not be a function of the loan lifetime after all.

Have a look at the photo below, which simplifies the C_loans term from the objective function:

We see that the lifetime loan (LLN) parameters appears in terms A and B. However, under the assumption that the technology discount rate (DR) is equal to the global discount rate (GDR), we see the LLN terms cancel. This means that the objective function is not influenced by the LLN term.

I've run two scenarios on temoa_utopia.sqlite to confirm. I've changed the LifetimeLoan of a particular technology and the objective functions in their respective .lp files are identical.

I should note that I've done this rather quickly and haven't taken the time to generalize for GDR != DR, but I thought I'd at least share my initial thoughts.

Cam