Pricing decisions and profitability analysis Solutions to Chapter 11 questions Question 11.24 (a) (b) Computation of full costs and budgeted cost-plus selling price EXE WYE Stores Maintenance Admin ( m) ( m) ( m) ( m) ( m) Material 1.800 0.700 0.100 Other variable 0.800 0.500 0.100 0.200 0.200 Gen factory 1.440 1.080 0.540 0.180 0.360 0.560 Admin reallocation 0.224 0.168 0.112 0.056 (0.560) 0.536 Maintenance reallocation 0.268 0.134 0.134 (0.536) 0.986 Stores 0.592 0.394 (0.986) 5.124 2.976 Volume 150 000 70 000 Full cost 34.16 42.51 Mark up (25%) 8.54 10.63 Price 42.70 53.14 (i) The incremental costs for the order consist of the variable costs. The calculation of the unit variable cost is as follows: EXE WYE Stores Maintenance Admin ( m) ( m) ( m) ( m) ( m) Material 1.800 0.700 0.100 0.100 Other variable 0.800 0.500 0.100 0.200 0.200 Admin 0.080 0.060 0.040 0.020 (0.200) 0.320 Maintenance 0.160 0.080 0.080 (0.320) 0.320 Stores 0.192 0.128 (0.320) 3.032 1.468 Volume 150 000 70 000 Variable cost 20.21 20.97 The proposed selling price exceeds the incremental cost and provides a contribution towards fixed costs and profits of 14.03 ( 35 20.97) per unit thus giving a total contribution of 42 090. Given that the company has spare capacity no lost business will be involved and it appears that the order is a one-off short-term special order. Therefore the order is acceptable provided it does not have an impact 86 PRICING DECISIONS AND PROFITABILITY ANALYSIS
(b) (c) on the selling price in the existing market or utilize capacity that has alternative uses. Given that the markets are segregated the former would appear to be an unlikely event. However, if the order were to generate further regular business the longer-term cost considerations described in Chapter 11 should be taken into account in determining an acceptable long-run price. (ii) The proposed selling price is 46.76 (full cost of 42.51 plus 10%). This will generate a contribution of 25.79 ( 46.76 20.97) per unit. Un-utilized capacity is 30 000 units but the order is for 50 000 units. Therefore the order can only be met by reducing existing business by 20 000 units. The financial evaluation is as follows: Increase in contribution from existing business (50 000 units at a contribution of 25.79) 1 289 500 Lost contribution from existing business (20 000 units at a contribution of ( 53.14 20.97)) 643 400 Net increase in contribution 646 100 Before accepting the order the longer term implications should be considered. The inability to meet the full demand from existing customers may result in a significant reduction in customer goodwill and the lost contribution from future sales to these customers may exceed the short-term gain of 646 100. Also the above analysis has not considered the alternative use of the un-utilized capacity of 30 000 units. If the cost savings from reducing the capacity exceed 646 100 for the period under consideration the order will not be worthwhile. The order will also result in the company operating at full capacity and it is possible that the cost structure may change if the company is operating outside its normal production range. If the company does not rely on customer repeat orders and customer goodwill it is unlikely to be affected and the order would appear to be profitable. It is important, however, that long-term considerations are taken into account when evaluating the order. In particular, consideration should be given to the negotiation of a longer-term contract on both price and volume. See Alternative denominator level measures in Chapter 7 and Selecting the cost driver denominator level in Chapter 10 for the answer to this question. (a) For the answer to this question you should refer to Chapter 11. In particular the answer should discuss the role of cost information in the following situations: 1 a price setting firm facing short-run pricing decisions; 2 a price setting firm facing long-run decisions; 3 a price taker firm facing short-run product-mix decisions; 4 a price taker firm facing long-run decisions. Question 11.25 (b) Calculation of variable overhead absorption rates Moulding Finishing General Factory ( 000) ( 000) ( 000) Allocated overheads 1600 500 1050 Reallocation of General Factory based on machine hours 600 450 (1050) 2200 950 Machine hours 800 600 Variable overhead rate per hour 2.75 1.583 PRICING DECISIONS AND PROFITABILITY ANALYSIS 87
Calculation of fixed overhead absorption rates Moulding Finishing General Factory ( 000) ( 000) ( 000) Allocated overheads 2500 850 1750 Reallocation of General Factory based on machine hours 1050 700 (1750) 3550 1550 Machine hours 800 600 Variable overhead rate per hour 4.4375 2.583 (c) Calculation of full manufacturing cost Direct material 9.00 Direct labour 10.00 (2 5) 16.50 (3 5.50) 26.50 Variable overheads 11.00 (4 2.75) 4.75 (3 1.583) 15.75 Variable manufacturing cost 51.25 Fixed overheads 17.75 (4 4.4375) 7.75 (3 2.583) 25.50 Full manufacturing cost 76.75 Prices based on full manufacturing cost 25% mark up = 95.94 30% mark up = 99.78 35% mark up = 103.61 Minimum prices based on short-term variable cost and incremental cost are as follows: Variable cost = 51.25 Incremental cost = 59.60 ( 51.25 plus specific fixed costs of 8.35) The specific fixed cost per unit is calculated by dividing the fixed costs of 167 000 by the estimated sales volume (10% 200 000). The cost information is more likely to provide a general guide to the pricing decision but the final pricing decision will be influenced by the prices of competitors products ( 90 100). The full cost prices indicate prices within a range of 96 104. The variable/incremental price indicates a minimum short-run price that may be appropriate if the company wishes to pursue a price skimming policy. Given that the product is an improvement on competitors, a price in the region of 100 would seem to be appropriate but the final decision should be based on marketing considerations drawing off the knowledge of the marketing staff. The role of the cost information has been to indicate that a price within this range should provide a reasonable margin and contribution to general fixed costs. Question 11.26 (a) Presumably the question is intended to indicate that if competitors increase their prices by 6% and the company maintains its current price then this is equivalent to a price reduction by the company of 6%. An estimated price reduction of 6% and a price elasticity of demand of 1.5 would be expected to increase demand by 9%. To predict costs for the next period it is necessary to analyse the costs into their fixed and variable elements. The high low method can be used by comparing the changes in costs between the periods with the changes in activity. However, the current period costs must be deflated by the inflation factor so that they are expressed in the current prices for the previous period. 88 PRICING DECISIONS AND PROFITABILITY ANALYSIS
Current period s costs adjusted to previous period s prices 1036 ( 1077.4/ 1.04. Applying the high low method: Units Costs (000) ( 000) Current period 106 1036 Previous period 100 1000 6 36 Variable cost per unit Increase in costs ( 36 000)/Increase in activity (6000 units) 6 per unit Fixed costs 1 000 000 (100 000 units 6) 400 000 Costs have increased by 4% from the previous to the current period and by a further 6% from the current to the next period: Variable cost per unit next period 6 (1.04) (1.06) 6.6144 Fixed costs next period 400 000 (1.04) (1.06) 440 960 Budgeted profit at a selling price of 13 Sales (106 000 1.09 a 13) 1 502 020 Variable costs (106 000 1.09 a 6.6144) 764 228 Contribution 737 792 Less fixed costs 440 960 Profit 296 832 Note a It is assumed that sales volume and production increase by 9% as a result of the price increase by competitors. (b) Budgeted profit assuming that the selling price is increased by 6% Sales (106 000 13 (1.06)) 1 460 680) Variable costs (106 000 6.6144) (701 126) Contribution 759 554) Fixed costs 440 960) 318 594) If the selling price is increased to match that of the competitors it is assumed that demand will remain unchanged. (c) The report should indicate that on the basis of the information specified in parts (a) and (b) the price should be increased by 6%. (d) It is assumed that: (i) Total market volume will remain unchanged and that the sales of the company will not decline as a result of both the firm and its competitors increasing prices by 6%; (ii) The estimate of the elasticity of demand is correct; (iii) All costs are affected by the same rate of inflation; (iv) All other factors remain constant so that sales will not be influenced by changes in advertising, customer preferences and general economic conditions. PRICING DECISIONS AND PROFITABILITY ANALYSIS 89
Question 11.27 (a) The following represents the quantity of sales that would be required to break even for a range of selling prices within each of the three selling price categories: Selling Variable Unit Break-even Break-even price costs a contribution point b % share of (units) market Category 1 Low selling price 600 850 0 Not applicable Medium selling price 825 917.50 0 Not applicable High selling price 1050 985 65 8462 38 Category 2 Low selling price 1450 1105 345 1594 27 Medium selling price 1675 1172.5 502.5 1095 18 High selling price 1900 1240 660 833 14 Category 3 Low selling price 2500 1420 1080 509 68 Medium selling price 2750 1495 1255 438 58 High selling price 3000 1570 1430 385 51 Notes a (30% selling price) 670 variable cost. b ( 550 000 fixed costs)/unit contribution. The average market share per manufacturer in category 1 is 5500 units. AB Ltd would have to sell 8462 units (that is, capture a 38% share of the market) at the maximum price within the range in order to break even. It is likely that there will be a significant demand in the category 1 market for a lower-quality and lower-priced product. It may therefore be unwise to enter the category 1 market. The average market share per manufacturer in the category 2 market is 1200 units. Given that AB will be able to enter the market with a product of advanced technology and distinctive design, it is likely that it will be able to sell the breakeven sales volume of 1594 units (that is, obtain a market share of 27%) at the lowest selling price within the range. At the medium and high selling prices the break-even sales volume is below the average sales volume per manufacturer. For the category 3 market the average market share per manufacturer is 375 units. This is in excess of the break-even point for the three prices considered in the above analysis. The company would also have to obtain a market share in excess of 50% in order to break even. The technology in this market is also advanced, and consequently competition will be more intensive. It is therefore suggested that the company market the product within a selling price range of 1450 1900. (b) The question does not provide any details of demand information within each price range, and it is therefore questionable whether or not it is possible to recommend a price from the data given. AB s product incorporates some of the most advanced techniques available, together with a very distinctive design, and it is therefore likely that a large market share will be obtained at selling prices at the lower end of the price range. Assuming that a 50% market share could be obtained at a 1500 selling price, 40% at 1700, 30% at 1800 and 20% at 1900, the profits would be as follows: Selling price 1500 1700 1800 1900 3000 units (50%) 590 000 2400 units (40%) 698 000 1800 units (30%) 512 000 1200 units (20%) 242 000 90 PRICING DECISIONS AND PROFITABILITY ANALYSIS
Note that the above figures have been calculated as follows: demand (70% of selling price 670 variable cost) 550 000 fixed costs Assuming that the above estimates of demand were correct, a selling price of 1700 would be recommended. (a) The answer should include a discussion of the following points: the benefits and limitations of cost-plus pricing; price skimming and price penetration policies; pricing based on demand estimates approximating economic theory. A detailed description of each of the above approaches is provided in Chapter 11. You will find an explanation of the approach involving demand estimates in the sections relating to economic theory and pricing non-customized products in Chapter 11. (b) (i) To increase demand by one unit, price must be reduced by 0.01 ( 10/1000) so that: Selling price = 750 0.10x Marginal revenue = 750 0.02x Marginal cost = 320 At the optimum output level where MR = MC: 320 = 750 0.02x x = 21 500 Selling price = 750 21 500 (0.01) = 535 Therefore the maximum annual profit is: Total contribution (21 500 unit contribution ( 535 320) = 4 622 500 Less fixed costs (15 000 80) = 1 200 000 = 3 422 500 (b) (ii) Current contribution = 4 622 500 Contribution from exporting to L = [(930 0.60) 300] 25 000 = 6 450 000 Based on the above information R Ltd. should sell all of the output to L. However, if the exchange rate falls below h1 = 0.521 R Ltd. will be worse off. This rate is calculated as follows: Required unit contribution = 4 622 500/25 000 = 184.90 Required selling price in UK currency = 484.90 ( 300 variable cost + 184.90) The exchange rate can fall to h1 = 0.521 ( 484.90/[h]930) before R Ltd. will be worse off. Also note that if the exchange rate falls to h1 = 0.25 the following negative contribution will be generated: ((h930 0.25) 300) 25 000 = 1 687 500 The above items can now be plotted on the graph (see Figure 11.28). Question 11.28 PRICING DECISIONS AND PROFITABILITY ANALYSIS 91
Contribution 8m 7m 6m exporting to L = 6 450 000 5m 4m do not export to L = 4 622 500 3m 2m 1m 1m 2m 10p 20p 30p 40p 50p 52p 60p 70p 80p c = exchange rate exporting to L = 1 687 500 3m 4m exporting to L = 2 850 000 5m Figure Q11.28 (c) Purchase Outlay Capital Tax Net cash Discount Present Year allowances savings flow factor value on capital allowances a 0 (1 000 000) (1 000 000) 1.000 (1 000 000) 1 (250 000) 37 500 37 500 0.893 33 488 2 (187 500) 65 625 65 625 0.893 52 303 3 (140 625) 49 219 49 219 0.712 35 044 4 (421 875) 84 375 84 375 0.636 53 663 5 63 281 63 281 0.567 35 880 (1 000 000) (789 622) Lease Payments Tax cash flow Net cash flow Discount Present Year factor value 0 (300 000) 45 000 (255 000) 1.000 (255 000) 1 (300 000) 90 000 (210 000) 0.893 (187 530) 2 (300 000) 90 000 (210 000) 0.797 (167 370) 3 (300 000) 90 000 (210 000) 0.712 (149 520) 4 45 000 45 000 0.636 28 620 (730 800) therefore, leasing is the least cost option with savings of 58 822. 92 PRICING DECISIONS AND PROFITABILITY ANALYSIS
(a) Note a Capital allowances cannot be claimed if the machine is hired. The tax saving for year 2 is (0.30 250 000 0.5) + (0.30 187 500 0.5) (i) If the selling price is 200, demand will be zero. To increase demand by one unit, selling price must be reduced by 1/1000 units or 0.001. Hence the maximum selling price attainable for an output of x units is: P 200 0.001x At an output level of 100 000 units, P 200 0.001 10 000 100 per unit Total contribution at an output level of 100 000 units 100 000 ( 100 50) 5 000 000 Less fixed costs (100 000 25) 2 500 000 Profit 2 500 000 (ii) Profit is maximized where MC MR MC 50 per unit variable cost (given) MR dtr dx TR x (200 0.001x) 200x 0.001x 2 Question 11.29 dtr 200 0.002x dx Therefore optimum output is where 50 200 0.002x (i.e. where MC MR). And so 150 0.002x That is, x 75 000 units At an output level of 75 000 units, the selling price is 200 ( 0.001 75 000) 125. Therefore profit at 75 000 units: Contribution (75 000 75) 5 625 000 Less fixed costs 2 500 000 3 125 000 (b) (i) Revised fixed costs 3 000 000. The optimal output level will not be affected by a change in fixed costs. Therefore the selling price should not be changed. Profit will decline by 500 000. (ii) Revised marginal cost 60. The new optimum is where 60 200 0.002x 0.002x 140 Therefore x 70 000 units At this output level, P 200 0.001 70 000 130 PRICING DECISIONS AND PROFITABILITY ANALYSIS 93
(c) Profit before advertising expenditure: Total contribution [70 000 ( 130 60)] 4 900 000 Less fixed costs 3 000 000 Profit 1 900 000 After the introduction of the advertising expenditure: P 210 0.001x TR x (210 0.001x) 210x 0.001x 2 Therefore MR 210 0.002x The revised optimum output is where 60 210 0.002x 0.002x 150 x 75 000 The optimum price at this output level is where P 210 0.001 75 000 135 Total contribution [75 000 ( 135 60)] 5 625 000 Revised fixed costs 4 000 000 Profit 1 625 000 Therefore profits will decline by 275 000 if the advertising campaign is undertaken. (d) The original budgeted output of 100 000 units was higher than the optimum output level. The solution to (a) (ii) indicates that the optimum output level is achieved by reducing production to 75 000 units and increasing the selling price to 125. Beyond an output level of 75 000 units, marginal cost per unit is in excess of marginal revenue. This is because selling price is reduced in order to expand output. Consequently, marginal revenue declines and is less than marginal cost. This means that profits decline when output is in excess of 75 000 units. This analysis is based on the following assumptions: (i) The demand schedule can be predicted accurately. (ii) Marginal cost per unit is constant at all output levels. (iii) Fixed costs are constant throughout the entire output range. The analysis also showed that the change in fixed costs had no effect on the MR and MC function, so that the optimum output level and price did not change. When MC increases, the effect is to decrease output level and increase price. The effect of the advertising campaign is to shift the demand curve to the right, thus causing sales demand to be higher at each selling price or the selling price to be higher at each demand level. However, the increased advertising costs are in excess of the additional revenue, thus resulting in a reduction in profits. 94 PRICING DECISIONS AND PROFITABILITY ANALYSIS