The time frame to evaluate the costs over will require all of the data to decide which conductors size is to be used. Therefore, we need to include all of the years in which the costs differ but not those when the costs will be identical.

Please show working out, so I understand the concept. Thank you.

A new electricity transmission line is planned to supply an outlying area and two different conductor sizes are being considered. The capital cost of the line is estimated at $15,600,000 for conductor A and $18,700,000 for conductor B. The energy losses in the line in the first year are estimated at $146,000 for conductor A and $75,000 for conductor B. If conductor A is used the load capacity of the line will be reached in 13 years. The line will then need to be upgraded by replacing conductor A with conductor B at a present day cost of $5,700,000. The estimated inflation rate for the costs involved is 2% p.a. The company borrows funds at an interest rate of 5% p.a. (The cost of energy will decrease because of increased renewable energy in the system, but the actual losses will increase because of the increased electrical load. For the purpose of this question, assume that these two effects can be ignored because they cancel each other out.) Which conductor should be used