Problem Week 09 - scale of operations

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1. Management believes it can sell a new product for \$250. The fixed costs of production are
estimated to be \$50,000 and the variable costs are \$215 a unit for the first scale of operations. The
fixed costs of production are estimated to be at \$150,000 and variable costs are \$170 a unit for the
second scale of operations.
a. Prepare a table similar to the one below and complete with the given levels of output and
the relationships between quantity and fixed cost, quantity and variable costs, and
quantity and total costs.

First Scale of operations
Total       Variable                                  Profits
Quantity                             Fixed Costs Total Costs
Revenue       Costs                                    (Loss)
0
500
1,000
1,500
2,000
2,500
3,000

Second scale of operations
Total       Variable                                  Profits
Quantity                             Fixed Costs Total Costs
Revenue       Costs                                    (Loss)
0
500
1,000
1,500
2,000
2,500
3,000

b. What is the exact break-even number of units sold for each scale of operations?
c. Assume that ½ of the fixed costs in each scale of operations is non-cash depreciation.
What is the cash flow generated by each scale of operations if 1,000 of units are sold?
d. You have been asked to advise the management of this company on which scale of
production to use. Let us assume that the management is uncertain on how many units
they can sell, but estimate it will be between 500 and 3,000 units during the first year and
progressively more after that. Please advise management what you learned from the
breakeven analysis and the tables that you devised that should help them make up their
minds. Give them pros and cons for both alternatives.
2. The management of a firm wants to introduce a new product. The product will sell for \$15.00 a
unit and can be produced by either of two scales of operation. Following are the total costs:

First scale of operation
TC = \$20,000 + \$10.00Q

Second scale of operation
TC = \$40,000 + \$5.00Q

Following are the anticipated levels of sales:

Year   Unit Sales
1          3,000
2          3,500
3          4,000
4          5,000

What can management expect for profits or losses in years 1 and 2 if it selects the scale of operations with
lower fixed costs? On what grounds can management justify selecting this scale of operation? If sales
reach 5,000 a year, which is the correct scale of operation?

3. You have been asked to rank the payback periods of three investments for a business. They each
cost \$35,000.

Year         A      B           C
1      \$10,000 \$25,000 \$12,500
2      \$10,000 \$10,000        \$8,500
3      \$10,000    \$4,000      \$6,000
4      \$10,000      \$500      \$8,000
5      \$10,000           0    \$5,000

Rank the investments based on payback period. Would you rank them as investments in that order? Why
or why not? See the table below for the cash flows of each.

4. Given the following information answer the following questions:

TR = \$3Q

TC = \$1,500 + \$2Q

a.   What is the breakeven level of output?
b.   If the firm sells 1,300 units, what are the firm's earnings or losses?
c.   If sales rise to 2,000 units, what are the firm’s earnings or losses?
d.   What happens to the breakeven level of output units if the total cost equation were: TC = \$2,000
+ \$1.80Q

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