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A small firm intends to increase the capacity of a bottleneck operation by adding a new machine. Two alternatives, A and B, have been identified, and the associated costs and revenues have been estimated. Annual fixed costs would be $37,000 for A and $31,000 for B; variable costs per unit would be $9 for A and $11 for B; and revenue per unit would be $19. a. Determine each alternative’s break-even point in units. (Round your answer to the nearest whole amount.) QBEP,A 3700 units QBEP,B 3875 units b. At what volume of output would the two alternatives yield the same profit (or loss)? (Round your answer to the nearest whole amount.) Profit units c. If expected annual demand is 15,000 units, which alternative would yield the higher profit (or the lower loss)? Higher profit

Respuesta :

Answer:

(a) 3,700; 3,875

(b)  3000 Units

(c) Alternative A would yield a higher profit as compared to Alternative B.

Explanation:

Given that,

Alternative A:

Annual fixed costs = $37,000

Variable costs per unit = $9

Revenue per unit = $19

Alternative B:

Annual fixed costs = $31,000

Variable costs per unit = $11

Revenue per unit = $19

(a)

[tex]QBEP,A=\frac{Annual\ fixed\ costs}{revenue\ per\ unit-variable\ costs\ per\ unit}[/tex]

[tex]QBEP,A=\frac{37,000}{19-9}[/tex]

                   = 3,700

[tex]QBEP,B=\frac{Annual\ fixed\ costs}{revenue\ per\ unit-variable\ costs\ per\ unit}[/tex]

[tex]QBEP,B=\frac{31,000}{19-11}[/tex]

                   = 3,875

(b)

Profit earned by Alternative A = 19X - 9X - 37000

Profit earned by Alternative B = 19X - 11X - 31000

Since both the profits should be equal:

Equation for yielding same profit at particular number of units

10X – Annual fixed costs of A = 8X – Annual fixed costs of B

10X – 37,000 = 8X – 31,000

X = 3000 Units

At this volume both the alternatives have an equal loss of $7,000.

(c) Alternative A:

Gross Profit/unit = Sale Price/Unit - Variable Price/Unit

                           = $19 - $9

                           = $10

Overall gross profit = No. of units × Gross Profit/unit

                                = 15,000 × $10

                                = $150,000

Net Profit = Overall gross profit - Fixed Overheads

                = $150,000 - 37000

                = $113,000

Alternative B:

Gross Profit/unit = Sale Price/Unit - Variable Price/Unit

                           = $19 - $11

                           = $8

Overall gross profit = No. of units × Gross Profit/unit

                                = 15,000 × $8

                                = $120,000

Net Profit = Overall gross profit - Fixed Overheads

                = $120,000 - 31,000

                = $89,000

From the analysis, it is clear that Alternative A would yield a higher profit as compared to Alternative B by $24,000.