Question

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?

Be sure to include the risk factor when calculating your answer.

Answer 1

	Electric Transmission company
	The decision here is regarding selection of Conductor A or B. Hence the alternatives are mutually exclusive .
	It means the selection of one will automatically lead to rejection of the other .
	Decision to be made : Selection of Conductor A or B
	Particulars	Conductor A	Conductor B
	Cost of Capital	$            15,600,000	$        18,700,000
	Rate of Interest on borrowings (p.a)	5%	5%
	Life of the conductor	13 years	No specified period
	Cost at the end of the 13th year for replacement	$               5,700,000	$                          -
	Estimated inflation rate of costs p.a	2%	2%
	Losses at the beginning	$                  146,000	$                75,000
	PVF @ 5% at the end of 1st year	0.53032
	PVF@ 5% at the end of 1st year	0.95238	0.95238
	Present value of cash outflow
	Capital outflow at the beginning	15,600,000	18,700,000
	Present value of cash outflow of Replacement cost at the end of 13th year (7373558 x 0.53032)	3,910,355
	PV of losses	139,048	71,429
	Present value of total cash outflows	19,649,403	18,771,429
	Decision :
	Conductor B should be purchased as the PV of cash outflows is less in its case.
	Notes :
1	Risk factors :
	The inflation rate is estimated at 2 % pa. Any upward change in this rate will have impact on the decision of the company.
	With increasing rate of inflation , the borrowing costs or interest rates will be high as well. Hence the rate of interest will also change .
2	The repayment schedule of the borrowings or amount of borrowings is not given , hence interest cost has been ignored.
3	The rate of interest has been considered for discounting the cash flows and computing the present value.
4	Since the inflows are not given , the cash outflows have been considered for decision making.
5	Present Value = 1/(1+r)^t
	For PV of DF @ 5% at the end of 1st year = 1/(1+0.05)^1	0.9524
	For PV of DF @ 5% at the end of 13th year = 1/(1+0.05)^13	0.5303
6	The rate of inflation is expected to be 2% pa . So the costs of replacement at the end of 13th year will be as follows :
	Today's value of replacement at the end of 13th year	$          5,700,000
	Rate of Inflation p.a		2%
	By compounding , we get P x ((1+(r/100))^n
	where , P is the value of money investd ie. 57,00,000
	r = rate of inflation ie. 2%
	n = number of years = 13
	5700000 x ((1+(2/100))^13		$          7,373,558
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