Question
In: Accounting
A small firm intends to increase the capacity of a bottleneck operation by adding a new...
|
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 $36,000 for A and $31,000 for B; variable costs per unit would be $8 for A and $11 for B; and revenue per unit would be $16. |
| a. | Determine each alternative’s break-even point in units. (Round your answer to the nearest whole amount.) |
| QBEP,A | units |
| QBEP,B | units |
| b. | At what volume of output would the two alternatives yield the same profit? (Round your answer to the nearest whole amount.) |
| Profit | units |
| c. | If expected annual demand is 11,000 units, which alternative would yield the higher profit? |
| Higher profit | (Click to select)BA |
Solutions
Expert Solution
| a | The break even quantity for Machine A | ||||||||
| Qbep | FC /Contribution Per unit | ||||||||
| $36000/($16-$8) | |||||||||
| 4500 units | |||||||||
| The break even quantity for Machine B | |||||||||
| Qbep | FC /Contribution Per unit | ||||||||
| $31000/($16-$11) | |||||||||
| 6200 units | |||||||||
| b | The contribution per unit | ||||||||
| Contribution per unit | = | SP per unit-VC per unit | |||||||
| Therefore the qty when the profit of both the machines will be the same would be | |||||||||
| Q(R-Va)-Fca = | Q(R-Vb)-Fcb | ||||||||
| Q= | (Fca-Fcb)/(R-Va)-(R-Vb) | ||||||||
| Where | |||||||||
| Fcx | Fixed Cost for Machine X | ||||||||
| Vx | Variable cost for Machine x | ||||||||
| R | Revenue per unit | ||||||||
| Q= | $36000-$31000/($16-$8)-($16-$11) | ||||||||
| $5000/$8-$5 | |||||||||
| $5000/$3 | |||||||||
| 1667 | |||||||||
| The volume at which the profits would be the same using either machine would be 1667 units | |||||||||
| c | If the expected volume is 11000 units then the profit by each machine would be | ||||||||
| Profit | = | Qty * Contribution -F.C | |||||||
| Profit Machine A | = | 11000*$8-$36000 | |||||||
| = | $88000-$36000 | ||||||||
| = | $52,000 | ||||||||
| Profit Machine B | = | Qty * Contribution -F.C | |||||||
| = | 11000*$5-$31000 | ||||||||
| = | $55000-$31000 | ||||||||
| = | $24,000 | ||||||||
| Hence when the expected annual demand is 11000 units alternative A would yield higher profit. | |||||||||
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