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Use X = 66Q4. For this question, X is the first two digits (from the right) of your student ID. Two machines are under consideration fo

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Answer #1

Machine A:

Initial cost = 50,000

salvage value = 6,500

useful life = 5 years

Fixed cost = 16,000

Variable cost = 55 per unit

Machine B:

Initial cost = 55,000

Salvage value = 7,000

useful life = 7 years,

Fixed cost = 14,500

Variable cost = X + 56 = 66 + 56 = 122 per unit

Interest rate = 3%

So, for break even point, the equivalent uniform annual worth of expenditure has to be equal to the uniform annual worth of revenue. Let QA be the number of units that need to be sold and produced each year for machine A and QB be the same for machine B. We also need to assume that the selling price of each of the unit of output = 200. So, that the annual revenue brought in by machine A and machine B are 200QA and 200QB respectively.

Machine A:

AW of cost = 50,000(A/P, 3%,5) + 16,000 + 55QA

= 50,000 * 0.2184 + 16,000 + 55QA

AW of cost= 26,920 + 55QA

AW of revenue = 6,500(A/F, 3%,5)

= 6500 * 0.1884 = 1224.6 + 200QA

So, AW of cost = AW of revenue,

26,920 + 55QA = 1224.6 + 200QA

26,920 - 1224.6 = 200QA - 55 QA

25,695.4 = 145QA

QA = 177

This is the quantity that needs to be produced and sold each year for machine A to breakeven.

Machine B:

AW of cost = 55,000(A/P,3%,7) + 14,500 + 122QB

= 55,000* 0.1605 + 14,500 + 122QB

= 23,327.5 + 122 QB

AW of revenue = 7,000(A/F,3%,7) + 200QB

= 7000 *0.1305 + 200QB

= 913.5 + 200QB

So, AW of cost = AW of revenue

23,327.5 + 122 QB = 913.5 + 200QB

23,327.5-913.5 = 200QB - 122QB

22,414 = 78QB

QB = 287

This is the quantity that needs to be produced and sold for machine B to break even.

So, we see for the same selling price = 200, the machine B needs to produce a much higher output = 287 >177 as compared to the amount of output that machine A needs to produce to break even. This is mainly because the variable cost of machine B is much higher than machine A, so a greater quantty is needed to recover that.

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