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Leviafan [203]
2 years ago
10

An existing electrical power line needs to have its capacity increased, and this can be done in either of two ways. The first me

thod is to add a second conductor to each phase wire using the same poles, insulators and fittings, at a construction cost of $15,000. The second method for increasing capacity is to build a second line parallel to the existing line, using new poles, insulators and fittings, at a construction cost of $23,000. At some time in the future, the line will require another increase in capacity, with the first alternative now requiring a second line at a cost of $32,500, and the second alternative requiring added conductors at a cost of $23,000. If interest rate is 6%, how many years between the initial expenditure and the future expenditure will make the two methods economically equal
Business
1 answer:
nekit [7.7K]2 years ago
3 0

Answer:

3 years

Explanation:

<u>First method</u>

The PV of the investment can be written as:

PV1 = $15,000 + $32,500/(1+0.06)^n

<u>Second method</u>

The PV of the investment can be written as:

PV2 = $23,000 + $23,000/(1+0.06)^n

After n years both projects will be economically equal. Hence their present value must be equal PV1 = PV2

$15,000 + $32,500/(1.06)^n = $23,000 + $23,000/(1.06)^n

$23,000 - $15,000 = $32,500/(1.06)^n - $23,000/(1.06)^n

$8,000 = $9,500/(1.06)^n

(1.06)^n = $9,500/$8,000

(1.06)^n = 1.1875

Taking log on both sides we get:

nlog1.06 = log 1.1875

n = log 1.1875/log 1.06

n = 0.07463361829/0.02530586526

n = 2.94926166417121

n = 3

So, the answer is 3 years

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