Question

Two possible power line routes are under consideration. Find the equivalent uniform annual cost for each if the interest rate is 7%. Which route should be chosen?

	Route A	Route B
Length (km)	15	5
First Cost ($/km)	$5,000	$25,000
Annual Maintenance ($/km)	$200	$400
Useful Life (years)	15	15
Salvage Value ($/km)	$3,000	$5,000
Yearly Power Loss ($/km)	$500	$500
Annual Property Taxes	$100	$500

Answer 1

Working notes:

(1) Annual maintenance = Length of power line x Maintenance per KM

Route A: 15 x $200 = $3,000

Route B: 5 x $400 = $2,000

(2) Annual power loss = Length of power line x Power loss per KM

Route A: 15 x $500 = $7,500

Route B: 5 x $500 = $2,500

(3) Annual Total cost = Annual maintenance + Annual power loss + Annual property tax

Route A ($): 3,000 + 7,500 + 100 = 10,600

Route B ($): 2,000 + 2,500 + 100 = 4,600

(4) Salvage value is deducted for EAC computation, since it is a cash inflow.

(5) EAC are computed as follows.

EAC, Route A ($) = 5,000 x A/P(7%, 15) + 10,600 - 3,000 x P/F(7%, 15) x A/P(7%, 15)

= 5,000 x 0.1098** + 10,600 - 3,000 x 0.3624** x 0.1098** = 549 + 10,600 - 394

= 10,755

EAC, Route B ($) = 25,000 x A/P(7%, 15) + 4,600 - 5,000 x P/F(7%, 15) x A/P(7%, 15)

= 25,000 x 0.1098** + 4,600 - 3,000 x 0.3624** x 0.1098** = 2,745 + 4,600 - 119

= 7,226

Since Route B has lower EAC, this should be chosen.

**From A/P and P/F Factor tables