(30 points) Two possible routes for a power transmission line are under consider

Question

(30 points) Two possible routes for a power transmission line are under consideration. Relevant data are as follows: 5. Route 1 15 miles $5,000/mile $200/mile Route 2 5 miles $25,000/mile $300/mile 15 $5,000/mile Length of the Route Initial Cost Annual Maintenance Useful Life Scrap Value of the line at the end of $3,000/mile ars 15 years Annual Cost of Power Loss $500/mile $500/mile Assuming that all cash flows are end of period, calculate the equivalent annual costs to determine which route should be taken using a nominal annual interest rate of 8% (State your assumptions)?

Explanation / Answer

5.

For Route1:

Initial cost = 5000*15 = $75000

Annual maintenance cost = 200*15 = $3000

Scrap value = 3000*15 = $45000

Annual cost of power loss = 500*15 = $7500

Time = 15 years

R = 8%

Present value of the total cost = 75000 + (3000+7500)*(1-1/1.08^15)/.08 - 45000/1.08^15

Present value of the total cost = $150688.65

Let, uniform annual cost = EUAC1

Then,

EUAC1 = 150688.65/((1-1/1.08^15)/.08)

EUAC1 = $17604.89

For Route 2:

Initial cost = 25000*5 = $125000

Annual maintenance cost = 300*5 = $1500

Scrap value = 5000*5 = $25000

Annual cost of power loss = 500*5 = $2500

Time = 15 years

R = 8%

Present value of the total cost = 125000 + (1500+2500)*(1-1/1.08^15)/.08 - 25000/1.08^15

Present value of the total cost = $151356.87

Let, uniform annual cost = EUAC2

Then,

EUAC2 = 151356.87/((1-1/1.08^15)/.08)

EUAC2 = $17682.95

Since, the uniform annual cost of route 1 is lesser than the uniform annual cost of route 2, then route 1 should be selected, because of its more cost effective nature.

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