der to increase their productivity. They know that a A company wants to purchase

Question

der to increase their productivity. They know that a A company wants to purchase a new front end loa new loader will cost $565.780, out the and they estimate that the operations cost will escalate by Si0/year after the first year. They also estimate that the new loader will result in a S280/year benefit cost of the existngequipment. They know that the benefit will decrease as the equi $18/year after the first year for five years and then hold steady at $90/year for the emainder of the life of the equipment. They estimate that they can sell the loader for $52,000 at the end of it useful life which will be 12 years. The long term interest rate is 9%. door." I will cost the company S600/year to operate the loader to the company when compared to the What is the Net Annual Worth of the loader?

Explanation / Answer

Step 1:

We'll first calculate the costs:

1. Purschasing Cost = 565,780. To get an annual series, we need to multiply by ( A/P , i% , n )

Where, P = 565,780

i = 9%

n = 12 years

( A/P , 9% , 12 ) = 0.14

Hence, 0.14 * 565780 = 79012

2. Operation Cost is 600 per year, which is already an annual series.

3. After first year operation cost is going to increase by $10 per year. Hence, ( A/G , i , n ) of $10.

( A/G , 9% , 12 ) = 4.49

Hence, 4.49 * 10 = 44.9 or 45.

So, total annual worth of costs = 45 + 600 + 79012 = $79657

Step 2:

Now we'll look at the benefits or incomings.

1. Scrap value at the end of useful life is $52000. To get an annual series we'll use ( A/F , i% , n )

( A/F , 9% , 12 ) = 0.049

Hence, 0.049 * 52000 = 2582

2. Annual benefits of $280, which decrease per year by $18 for first 5 years, then hold steady at $90 for rest of the life.

Useful life = 12 years, so, remaining years after first 5 years would be 7 years.

Hence, for the later 7 years, $90 are going to come annually. Hence, ( P/A, 9%, 7 ) * 90 = 5.03 * 90 =453

Now, let's bring it to present = ( P/F, 9%, 5) * 453 = 294

Present worth of initial 5 years benefits = 280 * (P/A, 9%, 5) = 280 * 3.89 = 1089

With a deduction of 18 * (P/G, 9%, 5) = 18 * 7.11 = 128

Hence, net present worth of initial 5 years benefits = 294 + 1089 - 128 = 1255

Converting this to an annual series = 1255 * ( A/P , 9% , 12 ) = 1255 * 0.14 = 175

Hence, annual worth of benefits = 2582 + 175 = 2757

Net Annual worth of the loader = 2757 - 79657 = $ -76900

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