The management of a firm wants to introduce a new product. The product will sell
ID: 2664026 • Letter: T
Question
The management of a firm wants to introduce a new product. The product will sell for $4 a unit and can be produced by either of two scales of operation. In the first, total costs areTC = $3000 + $2.8Q
In the second scale of operations, total costs are
TC = $5,000 + $2.4Q
a. What is the break-even level of output for each scale of operation?
b. What will be the firm’s profits for each scale of operation if sales reach 5,000 units?
c. One-half of the fixed costs are noncash (depreciation). All other expenses are for cash. If sales are 2000 units, will cash receipts cover cash expenses for each scale of operation?
d. The anticipated levels of sales are
Year Unit Sales
1 4,000
2 5,000
3 6,000
4 7,000
If management selects the scale of products with higher fixed costs, what can it expect in years 1 and 2? On what grounds can management justify selecting this scale of operation? If sales reach only 5,000 a year was the correct scale of operation chosen?
Explanation / Answer
a) BEP (qty) for scale1= fixed cost / contribution per unit => = 3000/(4 - 2.8) = 3000/1.2 = 2500 units (for scale1,AVC = 2.8 and FC = 3000) BEP (qty) for scale2 = 5000/(4 - 2.4) = 5000/1.6 = 3125 , units. (for scale2,AVC = 2.4 and FC = 5000) b) Profit for scale1, at Q = 5000, = contribution* qty above BEP = 1.2*(5000-2500) = 3000 ($) Profit for scale2, at Q = 5000, = 1.6*(5000-3125) = 3000 ($) c) for scale1, cash expenses = 3000/2 = 1500 ($) contribution of 2000 units = 2000*1.2 = 2400 ($) It covers the cash expenses. for scale1, cash expenses = 5000/2 = 2500 ($) contribution of 2000 units = 2000*1.6 = 3200 ($) It covers the cash expenses. d) at Q = 4000 in year1 Profit for scale2, at Q = 4000, = 1.6*(4000-3125) = 1400 ($) at Q = 5000 in year2 Profit for scale2, at Q = 5000, = 1.6*(5000-3125) = 3000 ($) Management can justify selection of higher FC, on higher contribution and lower BEP.
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