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A producer of pottery is considering the addition of a new plant to absorb the backlog of demand that now exists. The primary location being considered will have fixed costs of $9,200 per month and variable costs of 70 cents per unit produced. Each item is sold to retailers at a price that averages 90 cents.
a. What volume per month is required in order to break even?
b. What profit would be realized on a monthly volume of 61,000 units? 87,000 units?
c. What volume is needed to obtain a profit of $16,000 per month?
d. What volume is needed to provide a revenue of $23,000 per month?
e. Plot the total cost and total revenue lines
SOLUTION :
a.
Let the volume be x units per month to break even.
At break even,
Revenue = FC + VC. (Per month basis)
=> 0.90 x = 9200 + 0.70x
=> (0.90 - 0.70) x = 9200
=> 0.20 x = 9200
=> x = 9200 / 0.20 = 46000 units.
So,
Volume per month should be. 46000 unit to break even. (ANSWER).
b.
When volume is 61000 units :
Contribution margin per unit = 0.90 - 0.70 = 0.20 ($)
Profit will start after break even.
So,
Profit = (61000 - 46000)*0.20 = 3000 ($)
So,
Profit at 61000 units level will be $3000 .(ANSWER))
When volume is 87000 units :
Contribution margin per unit = 0.90 - 0.70 = 0.20 ($)
Profit will start after break even.
So,
Profit = (87000 - 46000)*0.20 = 8200 ($)
So,
Profit at 87000 units level will be $8200 .(ANSWER))
c.
Let volume be x units to make profit of $16000 .
Contribution margin per unit = 0.90 - 0.70 = 0.20 ($)
As Profit will start after break even.
Profit = (x- 46000)*0.20
=> 16000 = (x - 46000)*0.20
=> x = 16000/0.20 + 46000
=> x = 126000 units
So,
For making profit of $16000, volume should be 126000 units .(ANSWER))
d.
Let volume be x units to make revenue of $23000.
So, R = 23000 = 0.90 x
=> x = 23000/0.9 = 25555.56 = 25556 units.
So,
Volume should be 25556 units to have revenue of $23000 . (ANSWER)
e.
R = 0.90x
C = 9.2 + 0.70x
Where x, R and C are in thousands.
Use demos.com to see the graphs. Write expressions in the LHS boxes 1 and 2.
See the graphs on the RHS in different colours on the same grid. Point of intersection is break even point (46, 41.4) (in thousands) . So, BEP is 46000 units and both Revenue and Costs are $41400 .