I need by tuesday finance hw
tedy.r
week_09_example_problems.docWeek 09 Example Problems
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.
|
Quantity |
Total Revenue |
Variable Costs |
Fixed Costs |
Total Costs |
Profits (Loss) |
|
0 |
|
|
|
|
|
|
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 |
Total Revenue |
Variable Costs |
Fixed Costs |
Total Costs |
Profits (Loss) |
|
0 |
0 |
0 |
$5,000 |
$5,000 |
($5,000) |
|
500 |
$5,000 |
$2,500 |
$5,000 |
$7,500 |
($2,500) |
|
1,000 |
$10,000 |
$5,000 |
$5,000 |
$10,000 |
0 |
|
1,500 |
$15,000 |
$7,500 |
$5,000 |
$12,500 |
$2,500 |
|
2,000 |
$20,000 |
$10,000 |
$5,000 |
$15,000 |
$5,000 |
|
2,500 |
$25,000 |
$12,500 |
$5,000 |
$17,500 |
$7,500 |
|
3,000 |
$30,000 |
$15,000 |
$5,000 |
$20,000 |
$10,000 |
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.
