Question 3: This question is from chapter 5. The question is worth 20 points. (P

Question

Question 3: This question is from chapter 5. The question is worth 20 points. (Please show step by step work to receive full credits) A small firm intends to increase the capacity of a bottleneck operation by adding a new machine. Two alternatives, A & B, have been identified, and the associated costs and revenue have been estimated. Annual fixed costs would be S12600 for A and S 25200 for B; Variable cost per unit would be S 10.8 for A and S 7.2 for B, and revenue per unit would be $ 18.4. a. Determine each alternatives breakeven point in units? (5 points) b. At what volume of output would the two alternatives yield the same profit? (10 points) c. If the expected demand is 4000 units, which alternative would yield the higher profit? (5 points)

Explanation / Answer

a) Breakeven point (BEP) = Annual fixed cost / (revenue per unit - variable cost per unit)

BEP for alternative A = 12600/(18.4-10.8) = 1658 units

BEP for alternative B = 25200/(18.4-7.2) = 2250 units

b) Volume of output for same profit (point of indifference) = (Fixed cost of B - Fixed cost of A)/(Variable cost of A - Variable cost of B)

= (25200-12600)/(10.8-7.2)

= 3500 units

c) Expected demand of 4000 is greater than the point of indifference (3500) . Therefore, alternative B would yield the higher profit (because its variable cost is lesser).

We can also determine this by calculating the profit for each alternative for this level of demand

Profit for alternative A = (18.4-10.8)*4000 - 12600 = $ 17,800

Profit for alternative B = (18.4-7.2)*4000 - 25200 = $ 19,600

Alternative B yields the higher profit.

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