• Document: Calculate the total variable cost per unit. (2 marks) Calculate the selling price of the product that will maximise the company s profits.
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P2 May 2011 Exam Solutions SECTION A – 50 MARKS Question One (a) (i) Calculate the total variable cost per unit. (2 marks) (ii) Calculate the selling price of the product that will maximise the company’s profits. (4 marks) (i) The direct material and labour costs are completely variable. This can be determined by dividing the combined costs of labour and material costs by the respective activity level in the forecast, which will result in the same cost per unit at all activity levels. For example at activity level 100,000 units material and labour costs added together are \$800,000, and therefore cost per unit = \$8 per unit. This is the same rate at activity levels 160,000 and 200,000 units if you compare them with their respective combined material and labour costs. Overhead costs however are not completely variable and must be analysed between fixed overheads and variable overheads. We need to use the “high-low method” to find the variable overheads. Units Overhead cost (\$) 200,000 1,460,000 100,000 800,000 100,000 580,000 \$580,000 / 100,000 = \$5.80. Total variable cost per unit = \$8 + \$5.80 = \$13.80. -1- P2 May 2011 Exam Solutions (ii) 1. Determine the price function or demand function The price or demand function formula is: P = a - bx P = Price a = Price at which demand would be zero (i.e. the “p” when x=0) b = The gradient of the demand curve x = Quantity sold at that price (P) P = 25 b = 1 /25,000 = 0.00004 x = 150,000 a=? In order to determine the price function we need to first find the value of “a”. Substitute all known values into the price function formula to determine “a”. 25 = a – 0.00004 (150,000) 25 = a – 6 25 + 6 = a 31 = a Now we can construct the price function: P = 31 – 0.00004x 2. Determine the marginal revenue function (MR) The MR function is the price function itself, but it will have twice the value of whatever the ‘b’ value is, within the price function. Therefore: MR = 31 – 2(0.00004)x MR = 31 – 0.00008x 3. Determine the marginal cost function (MC) Marginal cost is given in the question as \$13.80. -2- P2 May 2011 Exam Solutions 4. Equate MR = MC to obtain the units sold to maximise profits MR = MC 31 – 0.00008x =13.80 -0.00008x = 13.80 - 31 -0.00008x = -17.20 x = -17.20 / -0.00008 x = 215,000 Therefore we sell 215,000 units when we maximise our profits. 5. Use the price function to determine the selling price that would maximise profits We can substitute in 215,000 units into the price function we created before to determine the selling price that will maximise profits. P = 31 – 0.00004x P = 31 – 0.00004 (215,000) P = 31 – 8.6 P = 22.4 The selling price that will maximise profits is \$22.40. (b) Explain TWO reasons why the company might decide NOT to use this optimum selling price. (4 marks) Exam tip: Please note that the question only asks for two reasons however we have provided a selection of possible reasons. Any two would suffice. The optimum selling process is derived from the price function or demand function. The main problem with using the price function is that the quality of the market research to determine the demand function has to be very good, for it to have any real value; otherwise it may give unrealistic predictions. It also assumes that price and quantity are the only factors in determining demand, but we must be mindful of other factors which are just as important such as quality, advertising, the availability of substitutes, brand loyalty, fashion, and the cost of complimentary products. It is difficult to estimate the demand curve. The price function assumes that there is a linear or straight line relationship between price and demand in reality this may not be true. It is difficult to determine the price at which demand would be zero in other words the maximum price that can be charged. -3- P2 May 2011 Exam Solutions It is difficult to ascertain the variable costs accurately without detailed knowledge of cost curves this may not be available. Question Two For each of the (i) Growth; and (ii) Maturity stages of the new product’s life cycle explain the likely changes that will occur in the unit selling prices AND in the unit production costs, compared to the preceding stage. (10 marks) (i) Growth stage Unit selling prices Due to the very short expected life cycle, during the growth stage as competition begins to enter the market, PT will have to reduce its selling price; in order to stay competitive as substitutes will be being produced by competitors. These substitutes would have been created by manufacturers purchasing PT’s product and reverse engineering the product. This approach will aim to sustai

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