Cost-Volume-Profit Analysis (multiple product breakeven calculations):
Cost-volume-profit analysis is an extremely important topic which is examinable in Test 3 for Unisa CTA students.
One of the assumptions of cost-volume-profit analysis is that if a range of products are being sold the sales will be in accordance with a predetermined sales mix. The illustrative example below covers the most important principles to be applied when calculating the breakeven point in either units or Rands where a company sells more than one product.
ILLUSTRATIVE EXAMPLE:
Freud Limited manufactures bicycles and tricycles. The following budgeted information is available for the 2019 financial year:
Bicycles | Tricycles | |
Selling price | R1 200 | R800 |
Variable manufacturing costs | R770 | R580 |
Sales commission | R60 | R40 |
Units | Units | |
Annual demand | 15 000 | 18 000 |
Other budgeted costs for the 2019 year:
- Fixed manufacturing costs R580 000
- Fixed selling & administrative costs R320 000
REQUIRED:
(a) Calculate the breakeven point in units for the 2019 financial year.
(b) Calculate the breakeven point in Rands for the 2019 financial year.
SUGGESTED SOLUTION:
(a) Calculate the breakeven point in units for the 2019 financial year.
First write out the formula because then you know what calculations are required:
Breakeven point in units = Total fixed costs (C1) / Weighted contribution per unit (C2)
The breakeven point is the activity level where the company does not make a profit or a loss (i.e. it is the activity level where profit is R0). Therefore all income and expenses that affect profit/loss should be taken into account in this calculation. Do not ignore period costs (sales commission, selling and administrative costs) – this is a common mistake made by students!!
C1: Total fixed costs:
R580 000 + R320 000 = R900 000
C2: Weighted contribution per unit:
Bicycles | Tricycles | |
15 000 units | 18 000 units | |
Selling price | R1 200 | R800 |
Variable manufacturing costs | (R770) | (R580) |
Sales commission | (R60) | (R40) |
Contribution per unit | R370 | R180 |
Total contribution | R5 550 000 | R3 240 000 |
Total annual demand = 15 000 + 18 000 = 33 000 units
Weighted contribution per unit = (R370 x 15 000 / 33 000) + (R180 x 18 000 / 33 000) = R266.36
Alternative:
Weighted contribution per unit = Total contribution / total annual demand = (R5 550 000 + R3 240 000) / 33 000 units = R266.36 |
You can now complete this calculation:
Breakeven point in units = Total fixed costs (C1) / Weighted contribution per unit (C2)
= R900 000 / R266.36 = 3 379 units
This is the total breakeven point for the company as a whole. You should now use the same predetermined sales mix to split this between the two different products:
Breakeven point (bicycles) = 3 379 x 15 000 / 33 000 = 1 536 units
Breakeven point (tricycles) = 3 379 x 18 000 / 33 000 = 1 843 units
When calculating the breakeven point in units you should always round up to the nearest whole number! Normal rounding rules do not apply!!
(b) Calculate the breakeven point in Rands for the 2019 financial year.
First write out the formula because then you know what calculations are required:
Breakeven point in Rands = Total fixed costs [part (a)] / Contribution ratio (C1)
C1: Contribution ratio:
Bicycles | Tricycles | Total | |
15 000 units | 18 000 units | ||
Contribution per unit (part (a)) | R370 | R180 | |
Total contribution | R5 550 000 | R3 240 000 | R8 790 000 |
Total sales | R18 000 000 | R14 400 000 | R32 400 000 |
Contribution ratio = Total contribution / Total sales
= R8 790 000 / R32 400 000
= 27.13%
You can now complete this calculation:
Breakeven point in Rands = Total fixed costs [part (a)] / Contribution ratio (C1)
= R900 000 / 27.13% = R3 317 361
This is the total breakeven point for the company as a whole. You should now use the same predetermined sales mix to split this between the two different products:
Breakeven point (bicycles) = R3 317 361 x R18 000 000 / R32 400 000 = R1 842 978
Breakeven point (tricycles) = R3 317 361 x R14 400 000 / R32 400 000 = R1 474 383
PLEASE NOTE:
- When calculating the breakeven point in units [part (a)] you use the predetermined sales mix in units to split the total breakeven point between the different products.
- When calculating the breakeven point in Rands [part (b)] you use the predetermined sales mix in Rands to split the total breakeven point between the different products.
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