View Full Version : Economics and capital

Glom

2005-Dec-30, 09:11 PM

I'm no good on economics. I took a stab at economics debunking here (http://www.geocities.com/freedomforfission/cyc/britain.html) in the bit about the cost underestimate.

I then thought about it more and realised my analysis is rather simplified. It assumes the capital costs are simply paid back uniformly over the lifetime of the reactor. However, this doesn't take it account interest repayments. I have no idea how to factor them in. Can anyone else?

montebianco

2005-Dec-30, 09:25 PM

I'm no good on economics. I took a stab at economics debunking here (http://www.geocities.com/freedomforfission/cyc/britain.html) in the bit about the cost underestimate.

I then thought about it more and realised my analysis is rather simplified. It assumes the capital costs are simply paid back uniformly over the lifetime of the reactor. However, this doesn't take it account interest repayments. I have no idea how to factor them in. Can anyone else?

A series of equal payments C made for N periods has current value V:

V == (C/r)*[1-1/((1+r)^N))]

This assumes the first payment is made one period from now, not now. r is the interest rate; if one period is one year, use an annualized interest rate; if one period is a month, then divide by twelve, etc.

It sounds like what you want to do is take an initial cost (which is V in the above equation) and find what level a series of payments have to be to cover the initial cost plus financing cost (C in the above equation). Then it can be inverted:

C == rV/[1-1/((1+r)^N))]

There is always the issue of what an appropriate interest rate is. Ideally, it ought to reflect expectations of the short-term interest rate over the life of the project, and the risk of the project. (There is one other strictly mathematical effect that I won't go into.) There are methods for estimating the appropriate interest rate, although I won't go into them here, and they are not universally accepted as good practice. In practice, people often just make them up - if you are for the project, choose a low interest rate, if you are against it, choose a high one.

If you use Microsoft Excel, it has a function to implement the above formulae; I think it is pmt, but I might be remembering it incorrectly...

Hope that helps,

Nick

montebianco

2005-Dec-30, 09:39 PM

I should add, the interest rate should be in the right units, if the payments are annual and the interest rate is 12%, then r=0.12, not 12.

Reiterating the earlier comment about monthy rates, if the payments are monthly and the annual interest rate is 12%, then r=0.12/12=0.01.

Nick

SeanF

2005-Dec-30, 09:42 PM

Reiterating the earlier comment about monthy rates, if the payments are monthly and the annual interest rate is 12%, then r=0.12/12=0.01.

But that's simple interest. What if it's compound interest?

;)

LurchGS

2005-Dec-30, 09:47 PM

I'm no good on economics. I took a stab at economics debunking here (http://www.geocities.com/freedomforfission/cyc/britain.html) in the bit about the cost underestimate.

I then thought about it more and realised my analysis is rather simplified. It assumes the capital costs are simply paid back uniformly over the lifetime of the reactor. However, this doesn't take it account interest repayments. I have no idea how to factor them in. Can anyone else?

Basically, when dealing with paying back a loan, you need to know the particulars. Some loans are pay interest first, then pay principal. Some are 50/50, etc.

For purposes of your discussion, though, I think you need only know the interest and the payback schedule. From that you could determine the total cost of the loan.

At a guess, I'd say, though, that you are correct in your assumption - cap cost repayment will likely be constant. You just need to add to that the cost of the interest.

That having been said, most large bill construction quotes I've seen include interest as part of the cost (as it should be)

montebianco

2005-Dec-30, 09:51 PM

But that's simple interest. What if it's compound interest?

;)

Well, not really, it's a monthly compounded rate quoted on an annualized basis ;) ;) ;)

montebianco

2005-Dec-30, 09:58 PM

Basically, when dealing with paying back a loan, you need to know the particulars. Some loans are pay interest first, then pay principal. Some are 50/50, etc.

For purposes of your discussion, though, I think you need only know the interest and the payback schedule. From that you could determine the total cost of the loan.

At a guess, I'd say, though, that you are correct in your assumption - cap cost repayment will likely be constant. You just need to add to that the cost of the interest.

That having been said, most large bill construction quotes I've seen include interest as part of the cost (as it should be)

I believe what Glom is trying to do (and I am sure Glom will say so if I misspeak) is to allocate the cost (capital plus financing) of the plant over the units of electricity produced. If the units produced are constant over the life of the plant, then I think the best way to do this is to assume a constant payment schedule, regardless of the actual financing arrangement. (We don't even know that there will be financing - maybe some of the cost will be covered by the operator's current capital. But we should still count opportunity cost.) The formula I presented assumes constant payments over the life of the loan, be it a real or virtual loan.

If there is inflation, it might be better to assume a series of payments which grow at the inflation rate, so that each unit of electricity gets allocated an equal cost in real dollars. There's a modification to the formulae I posted which can do that; Glom, if that's what you want, let me know, and I'll post it.

Nick

Hugh Jass

2005-Dec-30, 11:49 PM

An easy way, if you have Excel, under the functions catagory, there are finacial formulas. I'd say play around with them some, then come back and re-read what Nick has posted, should help.

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