A new engineer is evaluating whether to use a higher- voltage transmission line.

Question

A new engineer is evaluating whether to use a higher- voltage transmission line. It with cost %250,000 more initially, but it will reduce transmission losses. The optimistic, most likely, and pessimistic projections for annual savings are $25,000, $20,000, and $13,000. The interest rate is 6%, and the transmission line should have a life of 30 years. Calculate the present worth for each estimated value. Use the range of estimates to compute the mean annual savings. Determine the present worth of the mean annual saving in part (b).

Explanation / Answer

(a) Present Worth (PW)

(i) Optimistic scenario:

PW ($) = - 250,000 + 25,000 x PVIFA (6%, 30 years)

= - 250,000 + 25,000 x 13.7648 [From PVIFA table]

= - 250,000 + 344,120

= 94,120

(ii) Most likely scenario

PW ($) = - 250,000 + 20,000 x PVIFA (6%, 30 years)

= - 250,000 + 20,000 x 13.7648 [From PVIFA table]

= - 250,000 + 275,296

= 25,296

(iii) Pessimistic scenario

PW ($) = - 250,000 + 13,000 x PVIFA (6%, 30 years)

= - 250,000 + 13,000 x 13.7648 [From PVIFA table]

= - 250,000 + 178,942.4

= - 71,057.6

(b)

Mean annual savings = $(25,000 + 20,000 + 13,000) / 3 = $58,000 / 3 = $19,333.33

(c)

PW ($) = - 250,000 + 19,333.33 x PVIFA (6%, 30 years)

- 250,000 + 19,333.33 x 13.7648 [From PVIFA table]

= - 250,000 + 266,119.42

= 16,119.42

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