1. A piece of equipment costs to purchase new. It must be replaced every years,

Question

1. A piece of equipment costs to purchase new. It must be replaced every years, at a cost of .   The capitalized equipment cost, CC, is defined as , where is the money that must be invested now, at an annual effective compound interest rate , so that, years from now, the investment is worth . Derive an equation for the capitalized cost when the interest rate is compounded annually.

2. Your company needs to purchase a new heat exchanger. There are two options: an inexpensive heat exchanger with a short lifetime and no scrap value, and a more expensive heat exchanger with a longer lifetime that can be sold for scrap.   Your company expects to earn a15% effective interest rate on all of its investments.

Complete the table below. Which heat exchanger should your company purchase?

Heat Exchanger

Purchase Price Cv

Scrap Value

Replacement cost- Cr

Capitalized Cost

Heat Exchanger

Purchase Price Cv

Scrap Value

Replacement cost- Cr

Capitalized Cost

Explanation / Answer

1. The basic equation involved in capitalized cost calculations is:

P = A / i

The validity of this equation can be easily demonstrated thru an example. Suppose one wanted to know how much money could be withdrawn forever from an account which contains $1000 earning interest at a rate of 10% per year. Obviously, it is the interest ($100 per year in this case) that can be withdrawn forever. In equation form,

Interest = Principal * Interest rate

A = Pi, or P = A / i

The procedure to find the capitalized of cash flows which contain an infinite series is

Find the PW of all finite-interval cash flows using the regular engineering economy formulas (P/F, P/A, P/G, etc)

Convert all (non-annual) recurring amounts into annual worths over one life cycle and add all A values together

Divide the A values obtained in step (2) by i to get the PW of the annual amounts.

Add all PW’s together to get the capitalized cost.

2.         NPV of Heat Exchanger A = $20,000 x .4323 = $8,646.

           Capitalized Cost :- $8,646.

NPV of Scrap Value = 4,000 x .2471 =988.40               

NPV of Heat Exchanger B = ($35,000 - 988.40) x .2471 = $8,404.27

Capitalized Cost     =    $8,404.27

Conclusion :- Heat exchanger B should may company purchase.

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