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Cost and Decision-Making Analysis

The formula for calculating the contribution margin is as follows: Contribution margin= Fixed cost per unit – Variable cost per unit. This provides sufficient information to facilitate the calculation of break-even point in total sales dollars. The formula for calculating the break-even point in total sales dollars is as follows: B/E point (in total sales dollars) = Fixed Cost ? P/V ratio In a multiproduct environment the assumption is that the sales mix remains constant (Globusz n.d; unf.edu n.d.). The sales mix is referred to as the relative proportion of each product sold to the total sales value. This can be expressed in the form of a ratio or in the form of a percentage. The contribution per unit for each product is calculated as follows: Contribution = selling price – variable cost Cv = SPv – VCv = $1.65 – $1.25 = $0.40 Cm = SPm – VCm = $1.50 - $0.70 = $0.80 Cn = SPn – VCn = $0.85 - $0.25 = $0.60 The subscripts v, m and n relates to Velcro, Metal and Nylon respectively. Contribution based on the relative weight in the sales mix = Contribution per unit x quantity. Piedmont Fasteners normally produce as total of 700,000 units of clothing fasteners consisting of 100,000 units from Velcro, 200,000 units from Metal and 400,000 units of nylon. Therefore, in this case the ratio is 1:2:4 The Weighted contribution (WC) is calculated as follows: WCv = $0.40 x (1/7 x 700,000) = $0.40 x 100,000 = $40,000 WCm = $0.80 x (2/7 x 700,000) = $0.80 x 200,000 = $160,000 WCn = $0.60 x (4/7 x 700,000) = $0.60 x 400,000 = $240,000 The quantities represent 1/7th, 2/7th and 4/7th Sales = units sold (Q) x selling price per unit (SP) Sales = Qv x SPv + Qm x SPm + Qn x SPn Sales = (100,000 x $1.65) + (200,000 x $l.50) + 400,000 x $0.85) = $165,000 + $300,000 + $340,000 = $805,000 The weighted P/V ratio is calculated as follows: P/V = ($440,000 ? $805,000) x 100 = .55 = 55% B/E = $400,000 ? .55 = $727,273 The breakeven total sales in dollars is equal to $727,273 Of this 1/7th would relate to the sale of Velcro, 2/7th to the sale of metal and 4/7th to the sale of nylon. This would be $103,896 from the sale of Velcro; $207792 from the sale of metal; and $415,585 from the sale of nylon. The weighted average was used because each product has a different selling price and a different variable cost. Additionally, the quantities of these products that are normally sold are also different. Using weights allow for the relative proportions of each product sold to be taken into consideration. Solution to Question 2 Part (a) The break-even point in units for each product can be calculated taking into consideration that certain fixed costs relate to each of these products only while a certain portion relates administration, salaries and rent. Since we do not know the proportion of these we assume that they are equal. The following formula will be used to calculate the break even point in units for the three types of fasteners. B/E in units = Fixed cost/contribution The fixed cost for each product = specific fixed cost + proportion of common fixed cost The fixed cost for Velcro fasteners = $20,000 + (1/3 x $240,000) = $100,000 The $20,000 relates to the cost that would be avoided if Velcro fasteners are not produced. The fixed cost for Metal fasteners = $80,000 + (1/3 x $240,000) = $160,000 The $80,000 relates to additional cost incurred when metal fasteners are produced The fixed cost for Nylon fasteners = $60,000 + (1/3 x $240,000) = $140,000 The break-even for each type of fastener is as follows: B/Ev =
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