Question

Two possible routes for a power line are under study. In both cases the power line will last 18 years, have no salvage value, have annual property taxes of 3% of first cost, and have a yearly power loss of $500/km.

	Around the Lake	Under the Lake
Length	15 km	5 km
First cost	$9000/km	$25,000/km
Maintenance	$200/km/yr	$300/km/yr

If 5% interest is used, should the power line be routed around the lake or under the lake?

Answer 1

i = 5%, t = 18 yrs

Around the lake option

First cost = 9000 * 15 = 135000

Annual Taxes = 3% * first cost = 0.03*135000 = 4050

Annual Power loss = 500 * 15 = 7500

Annual maintenance = 200 * 15 = 3000

EUAC = 135000*(A/P,5%,18) + 4050 + 7500 + 3000 = 135000*0.085546 + 14550 = 26098.71

Under the lake option

First cost = 25000 * 5 = 125000

Annual Taxes = 3% * first cost = 0.03*125000 = 3750

Annual Power loss = 500 * 5 = 2500

Annual maintenance = 300 * 5 = 1500

EUAC = 125000*(A/P,5%,18) + 3750 + 2500 + 1500 = 125000*0.085546 + 7750 = 18443.25

As EUAC of under the lake option is lower, it should be selected