The management of a firm wants to introduce a new product. The product will sell
ID: 2665243 • 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 are TC= $3,000 + $2.8Q.In the second operation, 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 2,000 units, will cash receipts cover cash expenses for each scale of operation?
d.) The anticipated levels of sales are Year 1= 4,000 unit sales, Year 2= 5,000 units sales, Year 3= 6,000, Year 4= 7,000.
If management selects the scale of production with higher fixed cost, 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 operations chosen?
Explanation / Answer
2. a. The break even levels of output: $3,000/($4 2.80) = 2,500 and $5,000/($4 2.40) = 3,125 b. Earnings = total revenues total costs Total revenue = $4(5,000) = $20,000 Earnings under the two alternatives: 1. $20,000 $3,000 $2.80(5,000) = $3,000 2. $20,000 $5,000 $2.40(5,000) = $3,000 Sales of 5,000 units equates earnings. If output is less than 5,000 units, then the cost function with the lower fixed costs and higher variable costs produces the higher profits (or smaller losses). If output exceeds 5,000 units, then the scale of operation with higher fixed costs and lower per unit costs will generate the higher earnings. c. At sales of 2,000 and scale of operation with TC = $3,000 + $2.80Q, then earnings are $4(2,000) $3,000 $2.80(2,000) = ($600). However, $1,500 of the expenses is non cash depreciation, so the cash flow generated by operations is earnings ($600) depreciation 1,500 $900 (Be certain to point out that a firm may operate at an accounting loss but still generate positive cash flow.) If the second scale of operations is used and TC = $5,000 + $2.4Q, the earnings would be earnings = $4(2,000) $5,000 $2.4(2,000) = ($1,800). Cash flow would be earnings ($1,800) depreciation 2,500 $ 700 Either scale of operation generates positive cash flow. d. If the firm selects the scale with more fixed costs (i.e., higher operating leverage), its earnings will be lower in year 1. This could be justified on the grounds that the lower earnings are only temporary. If the level of sales only reaches 5,000 units, earnings are the same for either scale of operation. The student should not conclude that the scale of operation is unimportant in this case. The scale with the higher fixed costs is riskier. The use of that scale increases risk. Since earnings are the same under both alternatives, the scale with the less risk (i.e., lower operating leverage) is to be preferred.
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