Question

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Swan Lake Company is engaged in producing ballet shoes for children aged 3 to 6. The current yearly sales of ballet shoes are 38,750 pairs at $120 per pair. The variable costs are $80 per pair and fixed costs are $950,000 per year. Jenny, the company's owner, is not satisfied with present profit level. She is planning to put forward one of the following three proposals: Proposal 1: Increase advertising expenditure of $80,000 to promote sales. It is estimated that the sales quantity will rise by 5%. Proposal 2: Reduce the variable costs per pair to $70. A 15% drop in sales quantity is expected as the shoes will be produced with materials of lower quality. Proposal 3: Lower unit selling price by 10% which will result in 4% increase in sales quantity. The drop in selling price could be justified by 20% decrease in fixed costs and 8% decrease in variable costs per pair. Required: Calculate, for the current year: (a) (i) Unit contribution margin and contribution margin ratio; (4 marks) (ii) Break-even sales [in units and in dollars (S)]; (4 marks) (iii) Margin of safety in units; and (2 marks) (iv) Operating income. (2 marks) (b) By comparing the current operating income in (a)(iv) and new operating income under each of the three proposals, advise Jenny which proposal should be adopted. (11 marks) Discuss why it is important for management to understand cost-volume-profit analysis. (c) (7 marks) (Total 30 marks)

Answer 1

(a)

(i)Unit contribution margin -

It is the remainder after all variable costs associated with a unit of sale are subtracted from the associated revenues. It is useful for establishing the minimum price at which to sell a unit (which is the variable cost). This margin analysis can apply to the sale of either goods or services.

=(Unit Revenue - Unit variable cost)/ Revenue

= (38750*120)-(38750*80)   

=1550000

The Contribution Margin Ratio is the percentage of Contribution over Total Revenue, which can be calculated from the unit contribution over unit price or total contribution over Total Revenue

Unit contribution margin / Total Revenue

=1550000 / (38750*120)

=0.33 or 33.33% (approx.)

(ii) Break even sales-

It is the point at which total cost and total revenue are equal, i.e. "even". There is no net loss or gain.

In units= Fixed Cost / Contribution per unit

(Contribution per unit = Total revenue per unit - variable cost per unit = 40)

= $950000/40

=23750 units

in $ = Fixed Cost / Contribution margin ratio

(Contribution margin ratio is 33.33% as calculated above)

= $950000/33.33333%

= $2850000

(iii) Margin of safety in units -

The margin of safety formula is calculated by subtracting the break-even sales from the budgeted or projected sales. It the total number of sales dollars that can be lost before the company loses money.

=Budgeted Units - Break Even Units

=38750- 23750

= 15000 units

(iv) Operating Income-

Operating income is an accounting figure that measures the amount of profit realised from a business's operations, after deducting operating expenses such as wages, depreciation, and cost of goods sold.

=Total Revenue - variable cost - Fixed cost

=4650000-3100000-950000

= $600000

(b) Current Operating Income = $600000

  proposal 1 : ( 40687.5*120) - ( 40687.5*80) - $950000 - $80000

=$597500

  proposal 2 : (32937.5*120) - (32937.5*70) - $950000

=$696875

      proposal 3 : (40300*108) - (40300*73.6) - $760000

=$626320

(c) Cost Volume profit Analysis -

Cost-volume-profit (CVP) analysis is used to determine how changes in costs and volume affect a company's operating income and net income. CVP analysis can help companies determine their contribution margin, which is the amount remaining from sales revenue after all variable expenses have been deducted. The amount that remains is first used to cover fixed costs, and whatever remains afterwards is considered profit.

Management of Swan Lake Company should understand the importance of Cost volume profit analysis because the CVP analysis is very much useful to management as it provides an insight into the effects and inter-relationship of factors, which influence the profits of the firm. The relationship between cost, volume and profit makes up the profit structure of an enterprise.

Cost Volume Profit analysis helps organisations to examine their profits, costs and prices with respect to any changed that occur in sales volume. CVP is an effective tool that helps accountants to engage in decision making regarding future operations.

It is an integral part of the profit planning process of the firm.Besides it helps to evaluate the purpose and reasonableness of budgets and forecasts.

As an ultimate objective it helps management to find the most profitable combination of costs and volume.A dynamic management, therefore, uses CVP analysis to predict and evaluate the implications of its short run decisions about fixed costs, marginal costs, sales volume and selling price for its profit plans on a continuous basis.