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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