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# Break-Even Analysis, Payback Period for new product

2. 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=\$3000 +\$2.8Q.

In the second scale of operation, total costs are

TC=\$5000 +\$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 (deprecation). 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 Unit Sales
1 4,000
2 5,000
3 6,000
4 7,000

If management selects the scale of production with higher fixed cost, what can it expect in year 1 or 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?

3. A firm has the following total revenue and total cost schedules:

TR= \$2Q.
TC= \$4,000 + \$1.5Q.
a. What is the break-even level of output? What is the level of profits at sales of 9,000 units?
b. As the result of a major technological breakthrough, the total cost schedule is changed to:

TC= \$6,000 + \$0.5Q.

What is the break-even level of output? What is the level of profits at sales of 9,000 units?

4. The manufacture of a product that has a variable cost of \$2.50 per unit and total fixed cost of \$125,000 wants to determine the level of output necessary to avoid losses.

a. What level of sales is necessary to break even if the product is sold for \$4.25? What will be the manufacturer's profit or loss on the sales of 100,000 units?
b. If fixed costs rise to \$175,000, what is the new level of sales necessary to break even?
c. If variable cost decline to \$2.25 per unit, what is the new level of sales necessary to break even?
d. If fixed costs were to increase to \$175,000 while variable costs declined to \$2.25 per unit, what is the new break-even level of sales?
e. If a major proportion of fixed costs were noncash (depreciation), would failure to achieve the break-even level of sales imply that the firm cannot pay its current obligations as they come due? Suppose \$100,000 of the above fixed costs of \$125,000 were depreciation expense. What level of sales would be the cash break-even level of sales?

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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=\$3000 +\$2.8Q.

In the second scale of operation, total costs are

TC=\$5000 +\$2.4Q

a. What is the break-even level of output for each scale of operation?
In the first, total costs are TC=\$3000 +\$2.8Q.
Breakeven happens at the output when Total revenue is equal to the Total costs
Total Revenue=4Q, Hence 4Q=3000+2.8Q
1.2Q=3000
Q=3000/1.2
=2500 units
In the second scale of operation, total costs are
TC=\$5000 +\$2.4Q
Total Revenue=4Q, Hence 4Q=5000+2.4Q
1.6Q=5000
Q=5000/1.6
=3125 units

b. What will be the firm's profits for each scale of operation if sales reach 5,000 units?
Profit= Revenue-Total cost
In the first, total costs are TC=\$3000 +\$2.8Q.
Profit= 4Q-3000-2.8Q
Profit= 1.2*5000-3000
Profit=\$3000

In the second, total costs are TC=\$5000 +\$2.4Q

Profit= 4Q-5000-2.4Q
Profit= 1.6*5000-5000
Profit=\$3000

c. One- half of the fixed costs are noncash (deprecation). All other expenses are for cash. If sales are 2,000 units, will cash receipts cover cash expenses for each scale of operation?

In the first, total costs are
TC=\$3000 +\$2.8Q.
Total costs at 2000 units are 3000+2.8*2000
=8600
Cash costs= Total cost-Depreciation
=8600-1500
=\$7100
Cash receipts= 4*2000=\$8000
Cash receipts are sufficient to cover cash expenses for first scale.

In the second scale of operation, total costs are
TC=\$5000 +\$2.4Q
Total costs at ...

#### Solution Summary

Response discusses Break-Even Analysis, Payback Period for new product in two scales of operation

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