Calculate the break-even point in units, sales revenue, profit, margin of safety, and selling price needed to achieve a specific profit.

Selling price per unit = $168 Total variable costs per unit =$120 Total Fixed Costs = Depreciation + Rent and rates + Insurance

$$\text{Total Fixed Costs} = 100,000 + 68,000 + 120,000 = 288,000$$

Contribution margin per unit = Selling price per unit - Total variable costs per unit

$$\text{Contribution Margin per unit} = 168 - 120 = 48$$

a) (i) units,

$$\text{Break-even Point (units)} = \frac{\text{Total Fixed Costs}}{\text{Contribution Margin per unit}}$$ $$\text{Break-even Point (units)} = \frac{288,000}{48} = 6,000$$

a) (i) units: $\boxed{\text{6,000 units}}$

a) (ii) sales revenue.

$$\text{Break-even Point (sales revenue)} = \text{Break-even Point (units)} \times \text{Selling Price per unit}$$ $$\text{Break-even Point (sales revenue)} = 6,000 \times 168 = 1,008,000$$

a) (ii) sales revenue: \boxed{\1,008,000}$

b) If the firm decides to start by making and selling 13 000 units per annum, calculate at this level of activity,

b) (i) profit,

Total Sales Revenue = 13,000 units $\times$ $168/unit =$2,184,000
Total Variable Costs = 13,000 units $\times$ $120/unit =$1,560,000
Total Contribution = Total Sales Revenue - Total Variable Costs

$$\text{Total Contribution} = 2,184,000 - 1,560,000 = 624,000$$

Profit = Total Contribution - Total Fixed Costs

$$\text{Profit} = 624,000 - 288,000 = 336,000$$

b) (i) profit: \boxed{\336,000}$

b) (ii) margin of safety as a percentage,

Margin of Safety (units) = Actual Sales Units - Break-even Sales Units

$$\text{Margin of Safety (units)} = 13,000 - 6,000 = 7,000 \text{ units}$$

Margin of Safety as a percentage = $\frac{\text{Margin of Safety (units)}}{\text{Actual Sales Units}} \times 100\%$

$$\text{Margin of Safety as a percentage} = \frac{7,000}{13,000} \times 100\% \approx 53.85\%$$

b) (ii) margin of safety as a percentage: $\boxed{53.85\%}$

b) (iii) the selling price needed to achieve a profit of $1 402 000,

Target Profit = $1,402,000 Required Total Contribution = Target Profit + Total Fixed Costs

$$\text{Required Total Contribution} = 1,402,000 + 288,000 = 1,690,000$$

Required Contribution per unit = $\frac{\text{Required Total Contribution}}{\text{Sales Units}}$

$$\text{Required Contribution per unit} = \frac{1,690,000}{13,000} = 130$$

New Selling Price per unit = Required Contribution per unit + Variable Cost per unit

$$\text{New Selling Price per unit} = 130 + 120 = 250$$

*b) (iii) the selling price needed to achieve a profit of $1 402 000:*$\boxed{$250}$

b) (iv) the percentage change in selling price to achieve the result identified in (iii) above.

Percentage Change = $\frac{\text{New Selling Price} - \text{Original Selling Price}}{\text{Original Selling Price}} \times 100\%$

$$\text{Percentage Change} = \frac{250 - 168}{168} \times 100\% = \frac{82}{168} \times 100\% \approx 48.81\%$$

b) (iv) the percentage change in selling price: $\boxed{48.81\%}$

c) State five assumptions underlying cost-volume-profit (break-even) analysis.

c) Assumptions:

• All costs can be clearly classified as either fixed or variable.
• The selling price per unit remains constant regardless of the volume sold.
• Variable costs per unit remain constant regardless of the volume produced.
• Fixed costs remain constant within the relevant range of activity.
• The sales mix remains constant for multi-product companies.
• Production equals sales, meaning there is no change in inventory levels.