Please give me a step by step explanation. An entrepreneurial civil engineer who
ID: 2796172 • Letter: P
Question
Please give me a step by step explanation.
An entrepreneurial civil engineer who owns his own design/build company purchased a small crane 2 years ago at a cost of $71,000. At that time, it was expected to be used for 10 years with an annual cost of $15,000 per year and then traded in for its salvage value of $10,000. Due to increased construction activities, the company would prefer to trade for a new, larger crane now which will cost $93,000. The company estimates that the old crane can be used, if necessary, for another 4 years, at which time it will have a $25,000 estimated market value. Its current market value is estimated to be $39,000, and if it is used for another 4 years, it will have M&O; costs (exclusive of operator costs) of $17,000 per year. Determine the annual worth of the presently- owned crane if a replacement analysis is performed today and the company's MARR is 10% per year (a) $-27,0248 (b) $-26,329 (c) S-25,927 (d) S-24,917 (e) S-23,917Explanation / Answer
Answer: Option [e] -$23,917 Calculation and explanation: 1) AW of the first cost (Current market value) = 39000*0.10*1.10^4/(1.10^4-1) = $ (12,303) By this step the curent market value (opportunity cost) is converted into an annuity, $39,000 being its PV. The formula used is for finding the annuity given its PV. 2) Annual M&O costs $ (17,000) This need no conversion as it is an annualized amount. 3) AW of salvage value = 25000*0.1/(1.1^4-1) = $ 5,387 The salvage value is a cash inflow. It is converted as an annuity whose FV = 25000. 4) AW of the presently owned crane = 12303+17000-5387 = $ (23,917) The first two are annualized costs and the third one is annualized benefit. Hence, the net amount gives the AW of the crane.
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