Most economical conductor from cost data

The most economical conductor is the one with the lowest total annual cost per km. This is the annual charge on the capital (towers plus conductor), spread over the project life at the given interest rate, plus the annual cost of energy lost.

Capital recovery factor

With $i = 14\%$ and $n = 25$ years:

$$\begin{aligned} CRF &= \frac{i(1+i)^n}{(1+i)^n - 1} \\ &= \frac{0.14(1.14)^{25}}{(1.14)^{25} - 1} = 0.14550 \end{aligned}$$

Annual cost of energy loss

Column C is in thousands of kWh per km per year, and the energy rate is Rs 9 per kWh. So the loss cost in thousand Rs is $9C$. For Goat: $32 \times 9 = 288$ thousand Rs.

Comparison (per km)

Sample calculation for Deer: $(910 + 1663) \times 0.14550 = 374.37$, and $374.37 + 20 \times 9 = 554.37$ thousand Rs.

Answer: Deer is the most economical conductor, with a total annual cost of about Rs 554.37 thousand per km. Its higher capital cost is more than recovered by its much lower energy loss.

If the energy loss is instead worked as a present worth (annual loss cost ÷ CRF, added to the capital), the ranking is the same, because both methods differ only by the factor CRF.