## Breakeven Analysis for the Three Products

The breakeven point for the products A, B & C can be obtained using the formula:

Fig 3:

Formula for calculating breakeven sales in units

 Breakeven sales in units = fixed expense ÷ contribution margin per unit (Bamber, Braun & Harrison 2008, p.366).

From this relationship, breakeven point for product A, B, and C are: 29,487; 74,537 and 59630 respectively (figure 2), with the figures rounded off to the nearest one unit. Such observations indicate that only product A would have been profitable at the expected level of activity since only product A’s breakeven units are below the expected level of production. This is reinforced by calculating the margin of safety, which is given by subtracting the breakeven units from the expected units (Bamber, Braun & Harrison 2008). The margin of safety for products A, B and C are thus 513; -29,537 and -32,630 respectively.

Product Mix Decisions with Constraining Resource (Question d)

The optimal product mix that BSN limited should produce with limitation of direct material x can be calculated by ranking the products according to the unit contribution margin per limiting material needed for each product (Bamber, Braun & Harrison 2008; Drury 2006). The product ranked first should then be allocated its full share followed by the product ranked second with any remaining units of limiting material being used to determine the number of units of the last ranked product.

Accordingly, for BSN limited, when only 30,000 kilograms of material x are available, the entity should produce 30,000 units of product A, 45,000 units of product B, and 1,622 units of product C. The additional fixed costs (£150,000) are not relevant to this decision since they do not affect the contribution margin. The number of units for product C to be produced is obtained by dividing the remainder units of direct material X by the unit usage of this material in producing product C (Bamber, Braun & Harrison 2008; Drury 2006).

Fig 4:

Optimal product mix with a constraint of direct material x

 Product A Product B Product C contribution margin per unit (£) 27.30 10.80 13.50 Material x consumption per unit (Kgs) 4.80 3.20 7.40 Contribution per material x consumption (£) 5.69 3.38 1.82 Ranking 1 2 3 Estimated sales 30000 45000 27000 Total Usage for material X 144,000.00 144,000.00 199,800.00 Available material X 300,000.00 allocate rank 1 (product A) complete share (144,000.00) Remainder 156,000.00 allocate rank 2 (product B) complete share (144,000.00) allocate remainder to rank 3 (Product C) 12,000.00 Optimal product mix (units) 30,000.00 45,000.00 1,621.62

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