A small firm intends to increase the capacity of a bottleneck operation by addin

Question

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 $39,000 for A and $30,000 for B; variable costs per unit would be $10 for A and $11 for B; and revenue per unit would be $15.

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 $39,000 for A and $30,000 for B; variable costs per unit would be $10 for A and $11 for B; and revenue per unit would be $15.

Explanation / Answer

a. break even points can be calculated as below

Cost of production would be same for both alternatives A and B

lets consider X units is the break even quantity

Consider the cost of A = 39000 ( Fixed cost ) + 10 * X

cost of B = 30000 + 11 *B

39000 ( Fixed cost ) + 10 * X = 30000 + 11 * X

X = 9000 Units .

So the break even quantity is 9000 units

b. At break even point both the alternatives yeild same profit as cost is same

consider the cost of A = 39000 + 10 * 9000 = 39000 + 90000 = $ 129000

Total revenue at break even = $ 15 ( price per unit ) * 9000 ( number of units ) =$ 135000

Profit = 135000 - 129000 = $ 6000

c. if the number of units are 16000 units

cost of alternative A = 39000 + 10 * 16000 = 199000

cost of alternative B = 30000 + 11 * 16000 = 206000

So the profit of A = 15 * 16000 - 199000 = 240000 - 199000 = 41000

profit of B = 15 * 16000 - 206000 = 340000

So profit of alternative A is more than alternative B .

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