Question

Sultan Ltd plans to manufacture crockery sets and the following information is applicable: Estimated sales for the 14 000 units at R80 each 2016 year Estimated costs for the 2016 year Direct material R24 unit per Direct labour R4 per unit Factory overheads (all fixed) R48 000 per annum 30% of sales Selling expenses R78 000 per annum Administrative expenses (all fixed) Required: 3.1 Calculate the break-even quantity. 3.2 Calculate the break-even value using the break - even quantity. 3.3 Calculate the break-even value using the marginal income ratio. 3.4 Calculate the selling price per unit if the profit per unit is R4. 3.5 Calculate the new break-even quantity and value if selling price is increased by 10%

Answer 1

3.1 Break-even quantity:

• Fixed costs = R48 000 + R78 000 = R126 000
• Contribution R80 - R24 - R8 - 30% of R80 = R24
• So, Break-even quantity = 5250 [i.e., R126 000 / R24]

3.2 Break-even value using break-even quantity:

• Break-even value = Break-even quantity x Selling prince per unit = R420 000 [i.e., 5250 x R80]

3.3 Break-even value using marginal income ratio:

• Marginal income = Contribution = R24
• Sales = R80
• Marginal Income ratio = R24 / R80 = 30%
• Break-even value = Fixed Cost / Marginal Income Ratio = R126 000 / 30% = R420 000.

3.4 Selling price per unit if Profit per unit is R4:

• Let X be the Selling price.
• So, Sales = 14 000X.
• Contribution = 30% of Sales = R4 200X
• Profit = Contribution - Fixed Cost = R4 200X - R126 000
• This is same as Profit per unit x Quantity = R4 x 14 000 = R56 000
• So, R4 200X - R126 000 = R56 000
• This gives X as R43.33.

3.5 Break-even quantity if Selling price is increased by 10%:

• New selling price = R88.
• New contribution per unit = R88 - R24 - R8 - 30% of R88 = R29.6
• Break-even quantity = Fixed cost / Contribution per unit = R126 000 / 29.6 = 4 256.76. This can be rounded up to 4 257.

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