help with steps please Two processes are under consideration for a certain produ
ID: 2722003 • Letter: H
Question
help with steps please Two processes are under consideration for a certain production. Process A requires acquisition of a new machine that is estimated to have an initial cost of $65,000 and a salvage value of $52,000 at the end of its useful life of 6 years. In addition, the process requires a fixed cost of $47,000 per year and a variable cost of $250 per day. Alternatively, Process B requires the use of human labor. The process will need 6 workers, each earning $200 per day and will have a fixed cost of $36,000 per year and additional variable costs of $200 per day. Determine the minimum number of days per year required for the two processes to break even at an interest rate of 2% per year.Explanation / Answer
We will have to formula the Annual Worth Equations for both the processes. We will further assume that break even point is X.
Annual Worth (A) = -65,000(A/P,2%,6 Years) - 47,000 + 52,000(A/F,2%,6 Years) - 250*X
and Annual Worth (B) = - 6*200*X - 36,000 - 200*X
Using the TMV (time value of money tables tables) we will have to find the A/P and A/F values at 2% for 6 years.
Annual Worth (A) = -65,000*(.1785) - 47,000 + 52,000*.1585 - 250X = -50,360.50 - 250X
Annual Worth (B) = -1,400X - 36,000
To find the break even point in number of days, we need to equate the 2 annual worth equations and solve for X as follows:
-50,360.50 - 250X = -1,400X - 36,000
Solving for X we get,
X (Break Even) = (50,360.50 - 36,000)/(1,400 - 250) = 12.487 or 12.49 days (answer)
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