Average C/S Ratio

Hi everybody

The BPP study text has 2 different ways to calculate the average C/S ratio for multiple products, which give different answers, as far as I can see. I want to know if I’m missing something.

e.g. Suppose product X has selling price $50 and variable costs of $25 per unit and product Y has selling price of $30 and variable costs of $20 per unit. X and Y are manufactured in the ratio 2: 5. Overall the fixed costs are $150,000. Find the breakeven sales revenue

X’s contribution per unit = $50 – $25 = $25
Y’s contribution per unit = $30 – $20 = $10

Method 1:

The first way is to find average contribution per mix and average revenue per mix and divide them.
Contribution per mix = 2 x $25 + 5 x $10 = $50 + $50 = $100
Revenue per mix = 2 x $50 + 5 x $30 = $100 + $150 = $250
Average C/S Ratio = Contribution per mix / Revenue per mix = $100 / $250 = 0.4

Breakeven Sales Revenue = Fixed Costs / Average C/S Ratio = $150,000 / 0.4
= $375,000

Method 2:

The second way is if we are given the C/S ratio for individual products and the fixed costs, as in the question at the bottom of page 78 of the BPP text.
C/S ratio for X = $25 / $50 = 0.5 or 50%
C/S ratio for Y = $10 / $30 = 0.33 or 33 1/3 %, to avoid rounding errors

So if the question instead had stated that X and Y are manufactured in the ratio 2:5, where X has a C/S ratio of 20% and Y has a C/S ratio of 33 1/3 % and fixed costs are $150,000, then, following the textbook, we would calculate

Average C/S ratio = [ (2 x 50%) + (5 x 33 1/3 %) ] / (2 + 5)
Average C/S ratio = (8/3) / 7 = 8 / 21 {leaving as fraction to avoid rounding errors}

Already, the average C/S ratio calculated with this method differs from the one calculated in the first method. The difference is not due to rounding since exact decimals and fractions were used throughout.

Breakeven Sales Revenue = FIxed costs/ Average C/S ratio = $150,000 / (8/21)
= $393,750.

Method 3:
Using the method which does not involve the C/S ratio at all:
Breakeven # of mixes = Fixed cost / contribution per mix = $150,000 / $100 = 1,500
Breakeven # of X’s = 1,500 x 2 = 3,000
Breakeven # of Y’s = 1,500 x 5 = 7,500
Breakeven sales revenue = 3,000 x $50 + 7,500 x $30 = $375,000

Check Back:
3,000 X’s and 7,500 Y’s cost 3,000 x $25 + 7,500 x $20 + $150,000 = $375,000

So methods 1 and 2 give the same, (apparently) correct answers.

Clearly, method 2 is the odd one out.
Am I skipping a step in method 2, or is it just wrong?