Output (T-shirts) Total Cost (R) Total Revenue (R) 0 18,000 0 200 27,000 19,000 360 34,200 34,200 500 40,500 47,500 600 45,000 57,000 Solaris Print Solution...

(a) Definition of margin of safety [2]

The margin of safety is the amount by which a business's current or actual sales exceed its break-even level of output. It is usually expressed in units or as a percentage of current sales. A larger margin of safety means the business can absorb a greater fall in sales before it starts making a loss. [2]

(b) Break-even output and margin of safety [6]

Contribution per T-shirt:

Contribution = Selling price - Variable cost = R95 - R45 = R50 [1]

Break-even output:

Break-even = Fixed costs / Contribution per unit = R18,000 / R50 = 360 T-shirts [2]

This can be verified from the table: at 360 T-shirts, total cost (R34,200) equals total revenue (R34,200).

Margin of safety:

Margin of safety = Actual sales - Break-even output = 500 - 360 = 140 T-shirts [2]

This means Naledi's sales could fall by 140 shirts (or 28% of current output) before the business reaches its break-even point and stops making a profit. [1]

(c) Two limitations of break-even analysis [6]

1. Assumes all output is sold at a constant price [3]: Break-even analysis assumes that every T-shirt produced is sold and that the selling price remains fixed at R95. In reality, Solaris Print Solutions may need to offer discounts for bulk school orders or reduce prices during quiet periods to win contracts. This would lower the actual contribution per shirt and make the break-even point higher than the calculated 360 units.
2. Assumes costs divide neatly into fixed and variable [3]: The model treats all costs as either purely fixed or purely variable. In practice, some costs are semi-variable. For example, staff overtime during busy school-uniform seasons increases wage costs above the fixed salary base, but not in direct proportion to output. This makes the neat linear total cost line an oversimplification that may understate or overstate actual costs at different output levels.

(Other valid limitations: it is a static, short-term tool that does not account for seasonal demand fluctuations; it does not consider cash flow timing; it ignores external factors such as competition.)

(d) Evaluation: should Naledi invest in the new printing machine? [6]

With the new machine:

• New contribution per shirt = R95 - R35 = R60
• New break-even output = R25,000 / R60 = 417 shirts (rounded up from 416.7)
• This is higher than the current break-even of 360 shirts, meaning the business needs to sell more just to cover costs.

Profit comparison at current sales of 500 shirts:

• Current profit = (500 x R50) - R18,000 = R25,000 - R18,000 = R7,000
• New profit with machine = (500 x R60) - R25,000 = R30,000 - R25,000 = R5,000

At 500 shirts per month, the new machine actually reduces profit by R2,000.

Break-even between the two options:

The two approaches produce equal profit when:

50Q - 18,000 = 60Q - 25,000

25,000 - 18,000 = 60Q - 50Q

7,000 = 10Q

Q = 700 shirts per month

Below 700 shirts, the current setup is more profitable. Above 700 shirts, the new machine becomes more profitable because its higher contribution per unit (R60 vs R50) more than compensates for the higher fixed costs.

Conclusion: At the current sales volume of 500 shirts per month, Naledi should not invest in the new machine. It increases the break-even point (from 360 to 417), reduces monthly profit (from R7,000 to R5,000), and increases financial risk. However, if Naledi is confident that sales will grow significantly - for example, by winning new school contracts or expanding into corporate merchandise - and can sustain volumes above 700 shirts per month, the investment becomes worthwhile in the longer term. The decision should be deferred until there is clear evidence that demand will reach and sustain that level. [6]