Question

Please show all work and calculations for a thumbs up!

Suppose a company has a forklift but is considering purchasing a new electric lift truck that would cost $230000 and has operating cost of $25000 in the first year. For the remaining years, operating costs increase each year by 5% over the previous year’s operating costs. It loses 15% of its value every year from the previous year’s salvage value. The lift truck has a maximum life of 4 years. The firm’s required rate of return is 5%. Find the economic service life of this new machine.

Answer 1

The economic service life is the year in which the equivalent annual worth of the costs is at lowest value.

The cash flows associated with the project is shown in the following table.

The economic service life is 4 years, because the total annual worth of the costs is lowest is year 4 compared to other year.

--------------------------------------------------------------------------------------

Calculation:-

Capital recovery = - initial investment ( A/P, i%, n years ) + Market value ( A/F, i%, n years )

( A/P, i%, n years ) = capital recovery factor

( A/F, i%, n years ) = sinking fund factor

Capital recovery in year 1 = - $ 230,000 1.0500 + $195,500.00   1.0000 = - $ 46000

Capital recovery in year 2 = - $ 230,000 0.5378 + $ 166,175 0..4878 = - $ 42633.84

capital recovery in year 3 = - $ 230,000 0.3672 + $ 141,248.75 0.3172 = - $ 39,651.9

capital recovery in year 4 = - $ 230,000 0.2820 + $ 120061.44 0.2320 = - $ 37005.75

Annual worth = Present worth capital recovery factor

Annual worth of operating cost year 1 = - $ 25,000 .9524 1.0500 = - $ 25000.5

Annual worth of operating cost year 2 = [ present worth of costs year 1 + present worth of costs year 2 ] capital recovery factor year 2

Annual worth of operating cost year 2 = [ - $ 25,000 .9524 - $ 26250 0.9070 ] .5378

Annual worth of operating cost year 2 = - $ 25609.36

Annual worth of operating cost year 3 =   [ present worth of costs year 1 + present worth of costs year 2 +  present worth of costs year 3 ] capital recovery factor year 3

Annual worth of operating cost year 3 = [ - $ 25,000 0.9524 - $ 26250 0.9070 - $ 27562.50 0.8638 ] 0.3672

Annual worth of operating cost year 3 = - $ 26,228.08

Annual worth of operating cost year 4 =   [ present worth of costs year 1 + present worth of costs year 2 +  present worth of costs year 3 +  present worth of costs year 4 ] capital recovery factor year 4

Annual worth of operating cost year 4 = [ - $ 25,000 0.9524 - $ 26250 0.9070 - $ 27562.50 0.8638 - $ 28940.63 0.8227 ] 0.2820

Annual worth of operating cost year 4 = - $ 26856.74