Discussion:
Calculation Price per unit of Electricity
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J***@eskom.co.za
2007-04-05 09:53:31 UTC
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Supose a complany develops a new power plant. The construction cost is 100
million $ payable on the 1 January 2008. The current maintenance cost s are
8 million $ per annum plus 2 million $ per 1 million units of electricity
consumed. Assume the quantity of Electrical produced is the same as the
quantity consumed. The consumption is 1 million units per annum beiinning in
2008.

Company X borrows the full amount for the construction cost as well as the
the other expenses exceeding the income at a rare of intrest of 5 %per
annum. The debt is paid with the income exceeding the expenditure. Assume
all annual costs and income are paid at the end of the year. Ignore any
taxes.

Calculate the price per unit of Electricity to enable company X to break
even over a term of 50 years starting on the 1 of January 2008, assuming the
power plant is worthless after 50 years.
Bruno Campanini
2007-04-07 17:32:16 UTC
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Post by J***@eskom.co.za
Supose a complany develops a new power plant. The construction cost is 100
million $ payable on the 1 January 2008. The current maintenance cost s are
8 million $ per annum plus 2 million $ per 1 million units of electricity
consumed. Assume the quantity of Electrical produced is the same as the
quantity consumed. The consumption is 1 million units per annum beiinning in
2008.
Company X borrows the full amount for the construction cost as well as the
the other expenses exceeding the income at a rare of intrest of 5 %per
annum. The debt is paid with the income exceeding the expenditure. Assume
all annual costs and income are paid at the end of the year. Ignore any
taxes.
Calculate the price per unit of Electricity to enable company X to break
even over a term of 50 years starting on the 1 of January 2008, assuming the
power plant is worthless after 50 years.
Figures are in million $.
You need 5.48 i.e. (100 * 0.05) / (1 - 1 / (1 + 0.05)^50)
per annum for paying back 100.
Then you need 10 every year (8 + 2) for maintenance.
5.48 + 10 = 15.48 are due at the end of each year, starting
Dec. 31, 2008.
Then you must sell your 1 million units of electricity at 15.48

It is not clear to me what "Company X borrows the full
amount for the construction cost as well as the
the other expenses exceeding the income..." really means.
First income (15.48) occurs with first payments (5.48 + 8 + 2)
i.e. Dec. 31, 2008 and the two amounts are the same...

Bruno
J***@eskom.co.za
2007-04-10 13:20:08 UTC
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Please can you send me the equation that you used.

Thanks
Post by Bruno Campanini
Post by J***@eskom.co.za
Supose a complany develops a new power plant. The construction cost is 100
million $ payable on the 1 January 2008. The current maintenance cost s are
8 million $ per annum plus 2 million $ per 1 million units of electricity
consumed. Assume the quantity of Electrical produced is the same as the
quantity consumed. The consumption is 1 million units per annum
beiinning
Post by Bruno Campanini
Post by J***@eskom.co.za
in
2008.
Company X borrows the full amount for the construction cost as well as the
the other expenses exceeding the income at a rare of intrest of 5 %per
annum. The debt is paid with the income exceeding the expenditure. Assume
all annual costs and income are paid at the end of the year. Ignore any
taxes.
Calculate the price per unit of Electricity to enable company X to break
even over a term of 50 years starting on the 1 of January 2008, assuming the
power plant is worthless after 50 years.
Figures are in million $.
You need 5.48 i.e. (100 * 0.05) / (1 - 1 / (1 + 0.05)^50)
per annum for paying back 100.
Then you need 10 every year (8 + 2) for maintenance.
5.48 + 10 = 15.48 are due at the end of each year, starting
Dec. 31, 2008.
Then you must sell your 1 million units of electricity at 15.48
It is not clear to me what "Company X borrows the full
amount for the construction cost as well as the
the other expenses exceeding the income..." really means.
First income (15.48) occurs with first payments (5.48 + 8 + 2)
i.e. Dec. 31, 2008 and the two amounts are the same...
Bruno
Bruno Campanini
2007-04-10 14:27:25 UTC
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Post by J***@eskom.co.za
Please can you send me the equation that you used.
Thanks
C = the amount you borrow
i = rate of interest
n = number of payments

Constant Amount for Payments due the end of each n periods is:

C * i
-------------------
1
1 - ------------
(1 + i) ^ n


Where i is the rate of interest related to one unit
of C and to one unit of n.
I.e. 5% per annum is i = 0.05 and n is number of years.

If you have interest 5% per annum and n is the number
of months you must convert a per-annum rate in a
per-month rate which is not 0.05/12 = 0.004167 but

(1 + 0.05)^(1/12) - 1 = 0.00407 = 0.407% per-month

Bruno
J***@eskom.co.za
2007-04-11 14:18:29 UTC
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Raw Message
Company X borrows the full
amount of 100$ for the construction cost as well as the
the other expenses of (8 + 2) exceeding the income..." really means.
Post by Bruno Campanini
Post by J***@eskom.co.za
Please can you send me the equation that you used.
Thanks
C = the amount you borrow
i = rate of interest
n = number of payments
C * i
-------------------
1
1 - ------------
(1 + i) ^ n
Where i is the rate of interest related to one unit
of C and to one unit of n.
I.e. 5% per annum is i = 0.05 and n is number of years.
If you have interest 5% per annum and n is the number
of months you must convert a per-annum rate in a
per-month rate which is not 0.05/12 = 0.004167 but
(1 + 0.05)^(1/12) - 1 = 0.00407 = 0.407% per-month
Bruno
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