A quick question about Cost_INV

[[email protected]]

Hi,

Here again. In my sensitivity analysis, I've constrained the capacity expansion of a specific technology (e.g.,FX-limiting gas peaker additions to 1MW in a given province/region in 2030). The model's cost results show investment costs (Cost_Inv) occurring in multiple periods over the technology's lifetime (e.g., 2030, 2035, and 2040, assuming a 16-year lifespan; that is reasonable given that this attribute is annual investment costs). But the sum of these Cost_Inv values doesn't match the capital expenditure (CAPEX) I initially specified, even after accounting for learning-related cost reductions or after including discount rate. 

Then how should I calculate the total discounted cost of this capital expenditure based on the resulting Cost_Inv values across these periods? 

1. The below is the NCAP_COST I set with the 5 interpolation rule:
2020 2030 2050
1244.70 497.88 311.17

2. Discount 0.05; G_Dyear 2011

3. The cost_inv results:
Attribute 2030 2035 2040
Cost_Inv 8.61 8.61 8.61

4. Lifetime: 16

Best,
Xiao

[Antti-L]

Reproducing the objective function of TIMES (the total discounted costs) from the reported annualized costs (such as Cost_inv) is easy and very accurate (when using the ANNCOST LEV option), and has been discussed many times on this forum.  See for example:
   • https://forum.kanors-emr.org/showthread.php?tid=614
   • https://forum.kanors-emr.org/showthread.php?tid=1130
   • https://forum.kanors-emr.org/showthread.php?tid=578

[Antti-L]

> the NCAP_COST I set with the 5 interpolation rule

You should not use any such interpolation rule 5 for NCAP_COST, unless you actually want that the investment costs are zero up to the first data point (usually that would not make any sense). Remember how the investment costs are divided into streams.

[Antti-L]

I tested quickly with a tiny model to reproduce your Cost_Inv:

                    2020    2030    2050
NCAP_COST =        1244.70 497.88  311.17
NCAP_TLIFE =          16      16      16
G_DRATE   =          0.05    0.05    0.05

                    2030    2035    2040
Cost_Inv =          8.61    8.61    8.61

I was indeed able to reproduce the Cost_Inv values, 8.61 for 2030, 2035 and 2040.
The capacity was reported as 0.1514, and the LUMPINV was reported as 97.979. The corresponding specific investment cost was thus 97.979 / 0.1514 = 647.244. And exactly the same value was obtained from the NCAP_COST values, 647.244 (average of interpolated NCAP_COST values for 2026–2030), just as it should be.

So, I got a perfect match between LUMPINV and NCAP_COST. In addition, the Cost_Inv values were equal to the annualized investment cost for that average investment cost (647.244). So, it was a perfect match also between Cost_inv and NCAP_COST.

[[email protected]]

I tested quickly with a tiny model to reproduce your Cost_Inv:

                    2020    2030    2050
NCAP_COST =        1244.70 497.88  311.17
NCAP_TLIFE =          16      16      16
G_DRATE   =          0.05    0.05    0.05

                    2030    2035    2040
Cost_Inv =          8.61    8.61    8.61

I was indeed able to reproduce the Cost_Inv values, 8.61 for 2030, 2035 and 2040.
The capacity was reported as 0.1514, and the LUMPINV was reported as 97.979. The corresponding specific investment cost was thus 97.979 / 0.1514 = 647.244. And exactly the same value was obtained from the NCAP_COST values, 647.244 (average of interpolated NCAP_COST values for 2026–2030), just as it should be.

So, I got a perfect match between LUMPINV and NCAP_COST. In addition, the Cost_Inv values were equal to the annualized investment cost for that average investment cost (647.244). So, it was a perfect match also between Cost_inv and NCAP_COST.

Hi Antti,

These answers have been very helpful. I’ll also review the attribute that uses interpolation rule 5 to ensure the model doesn’t apply zero costs before my base year. 

Just one quick question: I actually set my capacity as 0.1 rather than 0.1514, where VAR_NCAP also show 0.1. But why did yours report 0.1514? 

Best,
Xiao

[Antti-L]

With those data you provided, that amount of new capacity (0.1514) in 2030 happens to be the solution producing those Cost_Inv values, probably also the only one (and I cannot imagine any other solution).

You say that "VAR_NCAP also show 0.1 [starting from 2024]", which is basically impossible using just the data you gave earlier, sorry.    But the important point here is that I verified that the Cost_Inv values do match perfectly with NCAP_COST.

[Lukas]

Hello,
I am struggling with replicating the Cost_Inv. Even in the simple DemosS_001 model, I do not get the same value for the annualized investment in the DTPSCOA process for 2005. I have attached my calculations.
Could you advise me on what I might be missing in the documentation, please?
Thank you.

[Antti-L]

You are missing the input setting: $SET MID_YEAR YES
For valuing streams of annual payments, mid-year discounting is usually considered more consistent than either end-of-year or beginning-of-year discounting, and is thus the preferred option. I guess that's why it is used in the DemoS as well. It is described in the documentation, so perhaps you missed it there as well?  I fixed your calculations, see attached.

[Lukas]

You are missing the input setting: $SET MID_YEAR YES
For valuing streams of annual payments, mid-year discounting is usually considered more consistent than either end-of-year or beginning-of-year discounting, and is thus the preferred option. I guess that's why it is used in the DemoS as well. It is described in the documentation, so perhaps you missed it there as well?  I fixed your calculations, see attached.

Oh, I see. Thank you very much!