Marginal Costing: Practical Questions and Solutions

Written by True Tamplin, BSc, CEPF®

Updated on July 22, 2022

Question 1

A company produces 500 units at a variable cost of $200 per unit. The price is $250 per unit and there are fixed expenses of $12,000 per month.

For this question, calculate Break-even point in terms of both units and sales. Also, show the profit at 90% capacity.

Solution

(i) BEP (units) = Fixed Expenses / C = ($542,000 + $252,000) / 6 = 792,000 / 6 = 132,000 units BEP (Sales) = 132,000 x 20 = $2640,000

(ii) Sales for examining profit = $60,000 BEP (units) = (Fixed Exp. + Desired Profit) / C = (792,000 + 60,000) / 6 = 852,000 / 6 = 142,000 units BEP Sales = 142,000 x 20 = $2,840,000

Question 2

For a company, sales are $80,000, variable costs are $4,000, and fixed costs are $4,000. Calculate the following: (i) PVR, (ii) BEP (Sales), (iii) Margin of Safety, and (iv) Profit.

Solution

(i) PVR = (C / $) x 100 = (4,000 x 100) / 8,000 = 50% C = 8,000 - (4,000) = $4,000

(ii) BEP (Sales) = Fixed Cost / PVR = (4,000 x 100) / 50 = $8,000

(iii) MOS = Actual Sales - BEP Sales = 8,000 - 8,000 = Nil

OR

MOS = Profit / PVR = 0 / 8,000 = Nil (iv) Profit = Sales - Variable Cost - Fixed Cost = 8,000 - 4,000 - 4,000 = Nil

Question 3

From the following information, find out PVR and sales at BEP.

  • Variable cost per unit = $15
  • Sales per unit = $20
  • Fixed expenses = $54,000

What should the new selling price be if BEP for units is reduced to 6,000 units?

PVR = (C x 100) / S

Thus, = ((20 - 15) x 100) / 20 PVR = 25% BEP (Sales) = Fixed expenses / PVR = (54,000 x 100) / 25 = $216,000

(iii) New selling price if BEP is brought down to 6,000 units: New SP = (Fixed Exp. + Variable Cost ) / New BEP (units) = (54,000 + 15) / 6,000 = $24

Solution

Question 4

Calculate (i) PVR, (ii) BEP, and (iii) Margin of Safety based on the following information:

  • Sales = $100,000
  • Total cost = $80,000
  • Fixed cost = $20,000
  • Net profit = 80,000

Solution

(i) PVR = (C x 100) / S C = Sales - Variable Cost 100,000 - 60,000 = 40,000 Variable cost = Sales - Profit - Fixed Cost (100,000 - 20,000 - 20,000) = 60,000 Thus, PVR =  (C / S) x 100 = (40,000 / 100,000) x 100 = 40%

(ii) BEP = Fixed Exp. / PVR = 20,000 / 40% = (20,000 x 100) / 40 = $50,000

(iii) Margin of Safety = Present Sales - Break-Even Sales = 1,00,000 - 50,000 = 50,000 Profitability = (40 x 50,000) / 100 = $20,000

Question 5

The National Company has just been formed. They have a patented process that will make them the sole suppliers of Product A.

During the first year, the capacity of their plant will be 9,000 units, and this is the amount they will be able to sell. Their costs are:

  • Direct labor = $15 per unit
  • Raw materials = $5 per unit
  • Other variable costs = $10 per unit
  • Fixed costs = $240,000

There are two parts to this question:

(a) If the company aims to make a profit of $210,000 for the first year, what should the selling price be? What is the contribution margin at this price?

(b) If, at the end of first year, the company aims to increase its volume, how many units will they have to sell to realize a profit of $760,000 given the following conditions?

  • An increase of $100,000 in the annual fixed costs will increase their capacity to 50,000 units
  • Selling price is at $70 per unit and no other costs change
  • $500,000 is invested in advertising

Solution

(a) Calculation of selling price Direct labor (9,000 x 15) = $135,000 Raw materials (9,000 x 5) = $45,000 Other variable costs (9,000 x 10) = $90,000 Total variable costs (PU 30) = 270,000 Add: Fixed Cost = 240,000 Profit = 210,000 Total sales value of 9,000 units @ $80 per unit = 720,000

(b) Sales in units (Fixed expenses + Desired profit) / (Sales - Variable cost) Thus, Fixed Expenses = 2,40,000 (given) + 1,00,000 (extra) + 50,000 (advertisement cost) = 840,000 + Desired Profit (760,000) = $1,600,000 = 1,600,000 / (70 - 30) = 40,000 units

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About the Author

True Tamplin, BSc, CEPF®

True Tamplin is a published author, public speaker, CEO of UpDigital, and founder of Finance Strategists.

True is a Certified Educator in Personal Finance (CEPF®), author of The Handy Financial Ratios Guide, a member of the Society for Advancing Business Editing and Writing, contributes to his financial education site, Finance Strategists, and has spoken to various financial communities such as the CFA Institute, as well as university students like his Alma mater, Biola University, where he received a bachelor of science in business and data analytics.

To learn more about True, visit his personal website, view his author profile on Amazon, or check out his speaker profile on the CFA Institute website.