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About Cost_Inv
#1
Dear all.

Please let me ask a basic question.
Could you explain Cost_Inv to me?

For example, when we input Capex 2000$ and 20 LIFETIME of one vehicle, Cost_Inv per year is 100$ (2000$ / 20yr) . isn't it?
I thought Cost_Inv / VAR_Cap = CAPEX / LIFETIME

But actually, I can say that expectations and reality do not seem to match.

Sorry for my poor English. Thank you for your advice in advance.

Ryo Ishida
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#2
Welcome to the Forum.

> Could you explain Cost_Inv to me?

I assume you are using VEDA-TIMES (other VEDA users may also use OseMoSys or TEMOA).

As described in the TIMES documentation, Cost_Inv is a reporting parameter representing "Annual undiscounted investment costs (caused by NCAP_COST) in period (t) spread over the economic lifetime (NCAP_ELIFE) of a process".  Admittedly, from that it is not quite clear what those "Annual undiscounted investment costs" exactly mean, but they refer to the annualized investment cost payments described in Part II, section 6.2.2. Consequently, the annual investment cost payments are equivalent to the lump-sum total investment costs when discounted back to the beginning of the commissioning year, using the technology-specific discount rate. Note also that by default these payments are spread over the economic lifetime, but when using the levelized annual cost option (SET ANNCOST LEV), they are spread over the technical lifetime (this option only affects reporting, not the objective function).

> I thought Cost_Inv / VAR_Cap = CAPEX / LIFETIME

Well, assuming that CAPEX=NCAP_COST, it would be so in the special case where the discount rate would be zero, but not in general, because with such annual payments the total investment cost would not be covered. Note also that if using NCAP_ILED, the payments would also include the effect of the interest during construction (IDC).
[+] 1 user Likes Antti-L's post
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#3
Antti-san

Thank you very much for your reply.
Please let me additional questions for your reply.

>Cost_Inv is a reporting parameter representing "Annual undiscounted investment costs (caused by NCAP_COST) in period (t) spread over the economic lifetime (NCAP_ELIFE) of a process". Admittedly, from that it is not quite clear what those "Annual undiscounted investment costs" exactly mean, but they refer to the annualized investment cost payments described in Part II, section 6.2.2.
→I cannot understand "Annual undiscounted investment costs (caused by NCAP_COST) in period (t) spread over the economic lifetime (NCAP_ELIFE) of a process". If so, Cost_Inv / VAR_Cap = CAPEX / LIFETIME should be true? because with investment costs should not be discounted.

>because with such annual payments the total investment cost would not be covered.
→Could you be kind enough to explain the detail with something like formula...?

Thank you in advance.
Best regards
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#4
> Cost_Inv / VAR_Cap = CAPEX / LIFETIME should be true? because with investment costs should not be discounted.

Not true. Investment costs must be discounted just like any other costs. And your relation Cost_Inv / VAR_Cap = CAPEX / LIFETIME would be economically inconsistent with any positive discount rates.

> Could you be kind enough to explain the detail with something like formula...?

It is all explained in detail in the documentation, Part II, section 6.2 Objective function.  Specifically, section 6.2.1 introduces the Capital Recovery Factor (CRF), which is used to derive the annual investment payments (INVCOST(y)), and section 6.2.2 Investment costs: INVCOST(y), which gives the detailed formulas for deriving these annual payments (annual costs) from the full investment costs. They can be in simplified terms expressed for vintage v as shown below:

   INVCOST(v,y)  = CRF(v) × NCAP_COST(v) × VAR_NCAP(v),  for {y | v ≤ y ≤ v+NCAP_ELIFE(v)−1}

As you can see, from the expression above we get: INVCOST(v,y) / VAR_NCAP(v) = CRF(v) × NCAP_COST(v). That is quite different from CAPEX / LIFETIME, because the latter is indeed generally inconsistent and incorrect. And the reported Cost_Inv(v,y) values correspond to these INVCOST(v,y) values.

So, please just read the documentation: You can find it all explained there, with detailed formulas.
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#5
Thank you for your reply!
I'll give it some thought...
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