Question

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

 

 

Answer 1

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 . 

Answer 2

Fixed cost (FC) = 9200 per month

Variable cost (VC) = 70 cents per unit

Selling price (SP) = 90 cents per unit

a) For break even, Total cost = Total revenue

For break even quantity "Q", Total cost = FC + Q*VC

Total revenue = Q*SP

So, 9200 + Q*0.70 = Q*0.90

Q = 46000 units

b)

Profit = Total revenue - Total cost = Q*SP - (FC + Q*VC)

Q = 61000

Profit = 61000*0.9 - (9200 + 61000*0.7) = 3000 $

Q = 87000

Profit = 87000*0.9 - (9200 + 87000*0.7) = 8200 $

c) For Profit = 16000, let quantity be Q

16000 = Q*0.9 - (9200 + Q*0.7)

16000 - 9200 = Q*0.2

Q = 126000

d) For revenue of 23000, let quantity be Q

Revenue = SP*Q

23000 = 0.9*Q

Q = 115000