Most economical conductor, five options (Rs 9)

The most economical conductor is the one with the minimum total annual cost per km: the annual charge on capital (towers plus conductor) plus the annual cost of energy lost (Kelvin's law idea).

Capital recovery factor

$$CRF = \frac{i(1+i)^n}{(1+i)^n-1} = \frac{0.1(1.1)^{20}}{(1.1)^{20}-1} = \frac{0.1\times6.7275}{5.7275} = 0.11746$$

The annual capital charge is (tower cost + conductor cost) × 0.11746. The annual loss cost is the energy lost per year × the energy rate.

The annual loss cost is (energy lost in 1000 kWh) × Rs 9.0, in 1000 Rs.

Annual cost comparison

Sample (Zebra): $2559\times0.11746 = 300.58$ and $24\times9.0 = 216.00$, total 516.58 thousand Rs/km per year.

Deer has the same loss as Zebra but costs more, so it is ruled out. Elk has the lowest loss, but its extra capital charge (about Rs 30 thousand per year) exceeds its loss saving (Rs 27 thousand per year). Zebra gives the best balance.

Answer: choose Zebra, with a minimum total annual cost of Rs 516.58 thousand per km.