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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

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


 


 


Solutions

Expert Solution

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 . 



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