Question

A producer of plastic mugs 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 $12,000 per month and variable costs of 60 cents per unit produced. Each item is sold to retailers at a price that averages 82 cents. (please Show work)

a) What sales volume per month is required in order for the producer to break even? b) What profit would be realized on a monthly volume of 54,000 units?

c) What volume is needed to obtain a profit of $19,000 per month?

d) What volume is needed to provide a revenue of $35,000 per month?

e) Plot the total cost and total revenue lines.

Answer 1

Solution: Here, we are given the information as mentioned below:

TFC = Total Fixed Cost = $12,000

VC = Variable Cost Per Unit = 0.60 $, and

SP = Selling Price per Unit = 0.82 $

Let's answer the given questions one by one as mentioned below:

Answer a) Here, we have to find the sales volume per month such that the producer reaches the break-even, i.e. a point where Total Revenue = Total Cost.

We will apply the formula of Break Even Quantity (Q) as mentioned below:

Where TFC = Total Fixed Cost = $12,000, and C = Contribution Per Unit = SP - VC = 0.82 - 0.60 = 0.22

Hence,

(Rounded to the whole number, because the unit can not be produced in decimals)

Answer b) We will find the profit realized on a monthly volume of 54,000 units, by applying the following formula

Profit = (C X Q) - TFC

Where  C = Contribution Per Unit = SP - VC = 0.82 - 0.60 = 0.22, TFC = Total Fixed Cost = $12,000, and Q = Monthly Sales Volume = 54000 Units

Hence, Profit = (0.22 X 54000) - 12000 = -120 $ (Loss)

Answer c) We will find the volume needed to obtain a profit of $19,000 per month, by applying the following formula:

Where Required Profit = 19000 $, TFC = Total Fixed Cost = $12,000, and C = Contribution Per Unit = SP - VC = 0.82 - 0.60 = 0.22

Hence,

(Rounded to the whole number, because the unit can not be produced in decimals)

Answer d) We will find the volume needed to provide a revenue of $35,000 per month, by applying the following formula:

Total Revenue = SP X Q

Where Total Revenue = 35000 $, SP = Selling Price Per Unit = 0.82, Q = Required Sales Volume = ?

Hence, 35000 = 0.82 X Q

Thus, Q = 35000 / 0.82 = 42683 Units (Rounded to the whole number, because the unit can not be produced in decimals)