Marginal Costing: Dwyer Ltd - Leaving Cert Accounting - Question 8 - 2006

To find the fixed cost per unit, the formula is:

$Fixed\ Cost\ per\ unit = \frac{Total\ Fixed\ Costs}{Number\ of\ Units}$

Thus:

$Fixed\ Cost\ per\ unit = \frac{48,000}{30,000} = €1.60\ per\ unit$

To compute the variable cost per unit, we use:

$Variable\ Cost\ per\ unit = \frac{Total\ Variable\ Costs}{Number\ of\ Units}$

This leads to:

$Variable\ Cost\ per\ unit = \frac{180,000}{30,000} = €6\ per\ unit$

The contribution per unit is calculated as:

$Contribution\ per\ unit = Selling\ Price - Variable\ Cost$

Substituting the known values:

$Contribution\ per\ unit = 20.00 - 6.00 = €14\ per\ unit$

The break-even point in units is found using:

$Break-even\ point\ in\ units = \frac{Fixed\ Costs}{Contribution\ per\ unit}$

Therefore:

$Break-even\ point\ in\ units = \frac{48,000}{14} \approx 3,429\ units$

The margin of safety in units is given by:

$Margin\ of\ Safety\ in\ units = Actual\ Sales\ in\ units - Break-even\ Sales\ in\ units$

Thus:

$Margin\ of\ Safety = 30,000 - 3,429 = 26,571\ units$

To find the required sales quantity, we use:

$Required\ Sales = \frac{Fixed\ Costs + Target\ Profit}{Contribution\ per\ unit}$

Calculating gives:

$Required\ Sales = \frac{48,000 + 160,000}{14} \approx 14,858\ units$