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Complete the following four problems. For assistance, you may want to refer to these examples: Week 09 Example Problems .Required:
- 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.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
|
Quantity |
Total Revenue |
Variable Costs |
Fixed Costs |
Total Costs |
Profits (Loss) |
||||||
|
500 |
|||||||||||
|
1,000 |
|||||||||||
|
1,500 |
|||||||||||
|
2,000 |
|||||||||||
|
2,500 |
|||||||||||
|
3,000 |
Second scale of operations
QuantityTotal RevenueVariable CostsFixed CostsTotal CostsProfits (Loss)0 500 1,000 1,500 2,000 2,500 3,000
- What is the exact break-even number of units sold for each scale of operations?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?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.
- 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 |
|
|
3,500 |
||
|
4,000 |
||
|
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?
- You have been asked to rank the payback periods of three investments for a business. They each cost $35,000.
|
$10,000 |
$25,000 |
$12,500 |
|||||
|
$8,500 |
|||||||
|
$4,000 |
$6,000 |
||||||
|
$500 |
$8,000 |
||||||
|
$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 above for the cash flows of each.
- Given the following information answer the following questions:
TR = $3Q TC = $1,500 + $2Q
- What is the break even level of output?
- If the firm sells 1,300 units, what are the firm’s earnings or losses?
- If sales rise to 2,000 units, what are the firms earnings or losses?
- What happens to the breakeven level of output units if the total cost equation were: TC = $2,000 + $1.80Q
Week
0
9 Example
P
roblems
1. Management believes it can sell a new product for $10.00. The fixed costs of production are estimated to be
$5,000
and the variable costs are $5.00 per unit.
a. Complete the table at the given levels of output and the relationships between quantity and fixed costs, quantity and variable costs, and quantity and total costs.
Q
uantity
Total Revenue
V
ariable Costs
Fixed Costs
Total Costs
Profits
(
Loss
)
500
1,000
1,500
2,000
2,500
3,000
b. Determine the breakeven point using the table and use the following equation to calculate breakeven point:
)
(
)
(
V
P
FC
Q
–
¸
=
c. What would happen to the total revenue schedule, the total cost schedule, and the breakeven level of output if management determined that fixed costs would be $8,000 instead of $5,000?
Solution:
|
Quantity |
Variable Costs |
Profits
(Loss) |
|||||||||
| $5,000 |
($5,000) |
||||||||||
|
$2,500 |
$7,500 |
($2,500) |
|||||||||
|
$10,000 |
|||||||||||
|
$15,000 |
$12,500 |
||||||||||
|
$20,000 |
|||||||||||
|
$25,000 |
$17,500 |
||||||||||
|
$30,000 |
1000
)
5
10
(
)
5000
(
=
–
¸
=
Q
Q
1600
)
5
10
(
)
8000
(
=
–
¸
=
Q
Q
2. The management of a firm wants to introduce a new product. The product will sell for $6.50 a unit and can be produced by either of two scales of operation. Following are the total costs:
First scale of operation: TC = $2,500 + $5.00Q
Second scale of operation: TC = $4,000 + $4.30Q
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. 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 4,000 a year, was the correct scale of operation chosen?
Following are the anticipated levels of sales:
Year
Unit Sales
1
3,000
2
3,500
3
4,000
4
5,000
Solution:
a. First scale: $2,500/ $6.50 – $5.00 = 1,666 units
Second scale: $4,000/ $6.50 – $4.30 = 1,818 units
b. Earnings = total revenue – total costs
TR $6.50(5,000) = $32,500
Earnings under the two alternatives:
1. $32,500 – $2,500 – $5(5,000) = $5,000
2. $32,500 – $4,000 – $4.30(5,000) = $7,000
Sales of 7,000 units clearly call for a use of the second scale of operation, with the use of higher fixed costs but lower costs per unit.
c. At sales of 2,000 and scale of operation with
TC = $2,500 + $5.00(2,000)
Then earnings are:
$6.50(2,000) – $2,500 – $5(2,000) = $500
Since $1,250 of the expenses is non-cash depreciation, the cash flow from operations is:
Earnings
$500
Depreciation
$1,250
Total
$1,750
At sales of 2,000 and scale of operation with
TC = $4,000 + $4.30(2,000)
Then earnings are:
$6.50(2,000) – $4,000 – $4.30(2,000) = $400
Since $2,000 of the expenses is non-cash depreciation, the cash flow from operations is
Earnings
$400
Depreciation
$2,000
Total
$2,400
Either scale of operation generates positive cash flow.
d. Year 1
6.50(3,000) – $4,000 – $4.30(3,000) = profit
$19,500 – $4,000 – $12,900 = $2,600
Year 2
6.50(3,500) – $4,000 – $4.30(3,500)
$22,750 – $4,000 – $15,050 = $3,700
6.50(4,000) – $4,000 – $4.30(4,000)
$26,000 – $4,000 – $17,200 = $4,800
With 4,000 of sales scale of production #1, would go:
$26,000 – $2,500 – $5(4,000) = $3,500. The second scale that gives a $4,800 profit is the one to use.
Adapted from:
Mayo, H. (2007). Basic finance: An introduction to financial institutions, investments & management. United States: Thomson South-Western.
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