**Linking
Rivers: Some **

Elementary Arithmetic

**By Nilakantha Rath **

Economic
And Political Weekly

28 July, 2003

**V**ery
little factual information is available, in published form, to the interested
private student about the projected linking of rivers in India. A senior
member of the Institute of Engineers, Pune Branch, has collected some
very broad figures. The total cost of the project is put at Rs 5,60,000
crore. It has three components: the Peninsular component will cost Rs
1,06,000 crore; the Himalayan component will cost Rs 1,85,000 crore;
and the Hydroelectric component will cost Rs 2,69,000 crore. The quantity
of water diverted in the Peninsular component will be 14,100 crore cubic
metres and in the Himalayan component 3,300 crore cubic metres. The
total power generated will be 3,400 crore watts – 400 crore watts
in the Peninsular component and 3,000 crore watts in the Himalayan component.

There is no information
if the estimated capital costs include the cost of acquisition of land
and the cost of resettlement of displaced persons. I assume these costs
are not included. There is a figure of the estimated extra agricultural
land that can be irrigated by using the extra ground-water as a result
of the diversion of flow water. But this does not help us estimate the
extra quantity of water that can be so lifted. Nor is there any information
about the capital cost of lifting this water. So we ignore this.

There is no information
about the estimated time that will be taken to complete the construction
of the project. On the advice of a former engineer-secretary of irrigation,
government of India, we assume 20 years as the period in which each
component of the project will be completed. There is no information
about the stages in which the project will be completed and the time-period
in which partial benefits may flow. We, therefore, assume that the benefits
will begin to flow after each component of the project is completed,
i e, 20 years from the start of construction. Nor is there any information
on the expected annual instalment of expenditure. We, therefore, assume
that every year equal amount will be spent on construction.

On the basis of
these few facts and assumptions, we attempt some elementary arithmetic
about the cost per unit of water and per watt of power in the three
components separately.

We attempt this
arithmetic under three other alternative assumptions. In the first,
we assume that no interest shall be charged on the capital during the
20-year period of construction. But interest at 7 per cent a year will
be charged for recovery of the capital cost over an estimated recovery
period of 50 years.

The second alternative
assumption is that compound interest will be charged on the capital
spent each year on construction over the 20-year period. The total capital
cost of each component will turn out to be much larger than what is
estimated on an interest-free basis. The annual cost of recovery of
this larger capital over the next 50 years will also be calculated assuming
an annual interest of 7 per cent.

The third alternative
assumption is that the annual capital cost, inclusive of interest, will
increase at an annual rate of 5 per cent every year due to inflation.
This is attempted only to suggest a realistic estimate of the total
capital expenditure at the end of the period of construction, i e, 20
years. A capital recovery factor is not calculated assuming inflation
since prices of all products will rise.

Using the above
methods it is possible to calculate the annual cost of a cubic metre
of irrigation water in each of the two components. But this does not
help the reader to compare the present water charge in the region with
the estimated costs. For that purpose, it is necessary to calculate
the capital cost of irrigating an acre or hectare of land under a particular
crop. We calculate the annual capital cost of irrigating an acre of
hybrid jowar in both the component regions. An acre of hybrid jowar
under lift irrigation requires 18 acre inches of irrigation water at
the field end. It is safe to assume that to reach this amount of irrigation
water to the field, in a flow irrigation system, half the water will
be lost in transit, due to evaporation and seepage. So the annual capital
cost of providing one acre of hybrid jowar with irrigation will be the
cost of 36 acre inches of water. (The reader can calculate the cost
for other crops. For example, an acre of sugar cane in the Peninsular
region requires 180 acre inches of water.)

Now, assuming no
interest and no inflation during the construction period, the total
capital cost for providing irrigation to an acre of hybrid jowar will
be Rs 27,815 in the Peninsular region and Rs 2,07,418 in the Himalayan
region. Assuming a 7 per cent interest rate per year, the equated annual
instalment of capital and interest for recovery of the total capital
over 50 years will be Rs 2,015 in the Peninsular component and Rs 15,030
in the Himalayan component. This is useful arithmetic. It helps to compare
the estimated annual capital cost (which does not include the cost of
administration of the water supply system) of irrigating an acre of
hybrid jowar, after instantaneous completion of the project, with the
present irrigation charges and the income net of other material expenses.

But interest over
20 years cannot simply be assumed away. Assuming interest at 7 per cent,
the compounded total capital cost of the Peninsular component at the
end of 20 years will be Rs 2,17,276 crore. The total capital cost per
acre of hybrid jowar will be Rs 57,014 and the annual capital recovery
cost alone for the crop will be Rs 4,131.

The total capital
cost of the Himalayan component, at 7 per cent annual interest compounded
over 20 years, will be Rs 3,79,208 crore. The capital cost per acre
of hybrid jowar comes to Rs 4,25,173. The annual capital recovery cost
per acre of hybrid jowar, at 7 per cent interest over 50 years, comes
to Rs 30,808. Since a large part of the water will be used in Rajasthan
and north Gujarat, the capital cost of water per year per acre turns
out to be phenomenal.

The capital cost
per watt of electricity, calculated without any interest over the construction
period, comes to Rs 89.6. The annual capital recovery cost, at 7 per
cent interest over 50 years, comes to Rs 6.5 per watt. If we assume
an interest rate of 7 per cent over the construction period, the capital
cost per watt of power comes to Rs 183.8. The annual capital recovery
cost, at 7 per cent interest over 50 years, comes to Rs 13.3 per watt.

Finally, a word
about the likely actual cost. The official estimate does not mention
the factor of interest or inflation in calculating the total cost. We
have seen above that if we assume a 7 per cent interest rate to be charged
on the capital during the construction period, the total cost of the
three components will come to Rs 11,47,873 crore, approximately double
what is now suggested.

But, the above does
not take into account the factor of inflation during the construction
period. Assuming an annual rate of inflation of 5 per cent, the total
capital cost of the three components, at the end of 20 years, will come
to: Peninsular Rs 3,81,878 crore + Himalayan Rs 6,66,485 crore + Hydroelectric
Rs 9,69,105 crore = Rs 20,17,468 crore at the end of 20 years. This
comes roughly to one lakh crore rupees a year.

There is a saying
in Oriya ‘collect sixty maunds of ghee, only then will Radha dance’.
It is a pity that instead of doing the first things that are crying
out to be done first in regard to irrigation, people are being fed with
this pie-in-the-sky type of slogan.

[This is part of
a presentation at a meeting of the Institute of Engineers in Pune on
June 20, 2003.]