Income effects of alternative cost accumulation systems

Income effects of alternative cost accumulation systems Solutions to Chapter 7 questions Question 7.22 (a) Manufacturing cost per unit of output = variable cost ( 6.40) + fixed cost ( 92 000/20 000 = 4.60) = 11 Absorption costing profit statement Sales (22 000 units at 14 per unit) 308.0 Manufacturing cost of sales (22 000 units 11) 242.0 Manufacturing profit before adjustment 66.0 Overhead over-absorbed a 4.6 Manufacturing profit 70.6 Note: a The normal activity that was used to establish the fixed overhead absorption rate was 20 000 units but actual production in period 2 was 21 000 units. Therefore a period cost adjustment is required because there is an over-absorption of fixed overheads of 4 600 [(22 000 units 21 000 units) 4.60]. (b) Sales 308.0 Variable cost of sales (22 000 units 6.40) 140.8 Contribution to fixed costs 167.2 Less fixed overheads 92.0 Profit 75.2 (c) (i) Compared with period 1 profits are 34 800 higher in period 2 ( 70 600 35 800). The reasons for the change are as follows: Additional sales (7000 units at a profit of 3 per unit) 21 000 Difference in fixed overhead absorption (3000 units extra production at 4.60 per unit) a 13 800 Additional profit 34 800 Note: a Because fixed overheads are absorbed on the basis of normal activity (20 000 units) there would have been an under-recovery of 9200 (2000 units 4.60) in period 1 when production was 18 000 units. In period 2 production exceeds normal activity by 1000 units resulting in an over-recovery of 4600. The difference between the under- and over-recovery of 13 800 ( 9200 + 4600) represents a period cost adjustment that is reflected in an increase in profits of 13 800. In other words, the under-recovery of 9200 was not required in period 2 and in addition there was an over-recovery of 4600. 46 INCOME EFFECTS OF ALTERNATIVE COST ACCUMULATION SYSTEMS

(c) (ii) Additional profits reported by the marginal costing system are 4600 ( 75 200 70 600). Because sales exceed production by 1000 units in period 2 there is a stock reduction of 1000 units. With an absorption costing system the stock reduction will result in a release of 4600 (1000 units at 4.60) fixed overheads as an expense during the current period. With a marginal costing system changes in stock levels do not have an impact on the fixed overhead that is treated as an expense for the period. Thus, absorption costing profits will be 4600 lower than marginal costing profits. (a) Marginal Absorption January costing costing ( ) ( ) ( ) ( ) Sales revenue (7000 units) 315 000 315 000 Less: Cost of sales (7000 units) Direct materials 77 000 77 000 Direct labour 56 000 56 000 Variable production overhead 28 000 28 000 Variable selling overhead 35 000 196 000 Fixed overhead (7000 3) 21 000 182 000 Contribution 119 000 Gross profit 133 000 Over absorption of fixed production overhead (1) 1 500 134 500 Fixed production costs (2) 24 000 Fixed selling costs (2) 16 000 16 000 Variable selling costs 35 000 Fixed admin costs (2) 24 000 64 000 24 000 75 000 Net profit 55 000 59 500 Marginal Absorption February costing costing ( ) ( ) ( ) ( ) Sales revenue (8750 units) 393 750 393 750 Less: Cost of sales (8750 units) Direct materials 96 250 96 250 Direct labour 70 000 70 000 Variable production overhead 35 000 35 000 Variable selling overhead 43 750 245 000 Fixed overhead (8750 3) 26 250 227 500 Contribution 148 750 Gross profit 166 250 Under absorption of fixed production overhead 750 165 500 Fixed production costs (2) 24 000 Fixed selling costs (2) 16 000 16 000 Variable selling costs 43 750 Fixed admin costs (2) 24 000 64 000 24 000 83 750 Net profit 84 750 81 750 Question 7.23 INCOME EFFECTS OF ALTERNATIVE COST ACCUMULATION SYSTEMS 47

Workings: (1) Fixed production overhead has been unitized on the basis of a normal monthly activity of 8000 units (96 000 units per annum). Therefore monthly production fixed overhead incurred is 24 000 (8000 3). In January actual production exceeds normal activity by 500 units so there is an over-absorption of 1500 resulting in a period cost adjustment that has a positive impact on profits. In February production is 250 units below normal activity giving an under-absorption of production overheads of 750. (2) With marginal costing fixed production overheads are treated as period costs and not assigned to products. Therefore the charge for fixed production overheads is 24 000 per month (see note 1). Both marginal and absorption costing systems treat non-manufacturing overheads as period costs. All of the nonmanufacturing overheads have been unitized using a monthly activity level of 8000 units. Therefore the non-manufacturing fixed overheads incurred are as follows: Selling = 16 000 (8000 2) Administration = 24 000 (8000 3) (b) In January additional profits of 4500 are reported by the absorption costing system. Because production exceeds sales by 1500 units in January there is a stock increase of 1500 units. With an absorption costing system the stock increase will result in 4500 (1500 units 3) being incorporated in closing stocks and deferred as an expense to future periods. With a marginal costing system changes in stock levels do not have an impact on the fixed overhead that is treated as an expense for the period. Thus, absorption costing profits will be 4500 higher than marginal costing profits. In February sales exceed production by 1000 units resulting in a stock reduction of 1000 units. With an absorption costing system the stock reduction will result in a release of 3000 (1000 units at 3) fixed overheads as an expense during the current period. Thus, absorption costing profits are 3000 lower than marginal costing profits. (c) (i) Contribution per unit = Selling price ( 45) unit variable cost ( 28) = 17 Break-even point (units) = Annual fixed costs ( 64 000)/unit contribution ( 17) = 3765 units Break-even point ( sales) = 3765 units 45 selling price = 169 424 The above calculations are on a monthly basis. The sales value of the annual break-even point is 2 033 100 ( 169 425 12). (ii) Required contribution for an annual profit of 122 800 = Fixed costs ( 64 000 12) + 122 800 = 899 800 Required activity level = Required contribution ( 899 800) Unit contribution ( 17) = 52 400 units (d) See Cost volume profit analysis assumptions in Chapter 8 for the answer to this question. Question 7.24 (a) Preliminary calculations January June July December ( ) ( ) Production overheads 90 000 30 000 (Over)/underabsorbed (12 000) 12 000 78 000 42 000 Change in overheads 36 000 Change in production volume (units) 12 000 48 INCOME EFFECTS OF ALTERNATIVE COST ACCUMULATION SYSTEMS

Production variable overhead rate per unit 3 Fixed production overheads ( 78 000 (18 000 3)) 24 000 Distribution costs 45 000 40 000 Decrease in costs 5 000 Decrease in sales volume (units) 5 000 Distribution cost per unit sold 1 Fixed distribution cost ( 45 000 (15 000 1)) 30 000 Unit costs are as follows: ( ) ( ) Selling price 36 Direct materials 6 Direct labour 9 Variable production overhead 3 Variable distribution cost 1 19 Contribution 17 Note that the unit direct costs are derived by dividing the total cost by units produced Marginal costing profit statement January June July December Sales 540 360 Variable costs at 19 per unit sold 285 190 Contribution 255 170 Fixed costs: Production overhead 24 24 Selling costs 50 50 Distribution cost 30 30 Administration 80 184 80 184 Profit 71 (14) (b) Marginal costing stock valuation per unit = 18 per unit production variable cost Absorption costing stock valuation per unit = 20 per unit total production cost January June July December Absorption costing profit 77 (22) Fixed overheads in stock increase of 3000 units 6 Fixed overheads in stock decrease of 4000 units (8) Marginal costing profit 71 14 (c) Absorption gross profit per unit sold = Annual gross profit ( 400 000)/Annual production (15 000 units) = 16 Profit from January June 77 Reduction in sales volume (5000 16) (80) Difference in overhead recovery ( 12 000 over recovery and 12 000 under recovery) (24) Reduction in distribution cost 5 (22) INCOME EFFECTS OF ALTERNATIVE COST ACCUMULATION SYSTEMS 49

Question 7.25 (d) Fixed cost 184 000 2 = 368 000 Contribution per unit 17 Break-even point 21 647 units (Fixed costs/contribution per unit) (e) See Some arguments in support of variable costing in Chapter 7 for the answer to this question. (a) Budgeted fixed overheads ( 300 000) Fixed overhead rate per unit = = 7.50 Budgeted production (40 000 units) Absorption Costing (FIFO) Profit Statement: Sales (42 000 72) 3024 Less cost of sales: Opening stock (2000 30) 60 Add production (46 000 52.50 a ) 2415 2475 Less closing stock (6000 52.50) 315 2160 864 Add over-absorption of overheads b 27 Profit 891 Notes: a Variable cost per unit = 2070/46 000 = 45 Total cost per unit = 45 + 7.50 Fixed overhead = 52.50 b Overhead absorbed (46 000 7.50) = 345 000 Actual overhead incurred = 318 000 Over-recovery 27 000 Marginal Costing (FIFO) Profit Statement: Sales 3024 Less cost of sales: Opening stock (2000 25) 50 Add production (46 000 45) 2070 2120 Less closing stock (6000 45) 270 1850 Contribution 1174 Less fixed overheads incurred 318 Profit 856 Reconciliation: Absorption profit exceeds marginal costing profit by 35 000 ( 891 000 856 000). The difference is due to the fixed overheads carried forward in the stock valuations: ( ) Fixed overheads in closing stocks (6000 7.50) 45 000 Less fixed overheads in opening stocks (2000 5) 10 000 Fixed overheads included in stock movement 35 000 Absorption costing gives a higher profit because more of the fixed overheads are carried forward into the next accounting period than were brought forward from the last accounting period. 50 INCOME EFFECTS OF ALTERNATIVE COST ACCUMULATION SYSTEMS

(b) Absorption Costing (AVECO) Profit Statement: Sales 3024 Opening stock plus production (48 000 51.56 a ) 2475 Less closing stock (6000 51.56) 309 2166 858 Add over-absorption of overheads 27 Profit 885 Marginal Costing (AVECO) Profit Statement: Sales 3024 Less cost of sales Opening stock plus production (48 000 44.17 b ) 2120 Less closing stock (6000 44.17) 265 1855 Contribution 1169 Less fixed overheads 318 Profit 851 Notes: a With the AVECO method the opening stock is merged with the production of the current period to ascertain the average unit cost: Opening stock (2000 30) + Production cost ( 2 415 000) = 2 475 000 Average cost per unit = 2 475 000/48 000 units b Average cost = (Production cost ( 2 070 000) + Opening stock (50 000))/48 000 units. Reconciliation: Difference in profits ( 885 851) 34 Fixed overheads in closing stocks (309 265) 44 Less fixed overheads in opening stock (2000 5) 10 Fixed overheads included in stock movement 34 The variations in profits between (a) and (b) are 6000 for absorption costing and 5000 for marginal costing. With the FIFO method all of the lower cost brought forward from the previous period is charged as an expense against the current period. The closing stock is derived only from current period costs. With the AVECO method the opening stock is merged with the units produced in the current period and is thus allocated between cost of sales and closing stocks. Therefore some of the lower cost brought forward from the previous period is incorporated in the closing stock at the end of the period. (a) It is assumed that opening stock valuation in 2001 was determined on the basis of the old overhead rate of 2.10 per hour. The closing stock valuation for 2001 and the opening and closing valuations for 2002 are calculated on the basis of the new overhead rate of 3.60 per hour. In order to compare the 2001 and 2002 profits, it is necessary to restate the 2001 opening stock on the same basis as that which was used for 2002 stock valuations. We are informed that the 2002 closing stock will be at the same physical level as the 2000 opening stock valuation. It should also be noted that the 2001 opening stock was twice as much as the 2000 equivalent. The 2000 valuation on the revised Question 7.26 INCOME EFFECTS OF ALTERNATIVE COST ACCUMULATION SYSTEMS 51

basis would have been 130 000, resulting in a 2001 revised valuation of 260 000. Consequently, the 2001 profits will be 60 000 ( 260 000 200 000) lower when calculated on the revised basis. From the 2001 estimate you can see that stocks increase and then decline in 2002. It appears that the company has over-produced in 2001 thus resulting in large opening stocks at the start of 2002. The effect of this is that more of the sales demand is met from opening stocks in 2002. Therefore production declines in 2002, thus resulting in an under recovery of 300 000 fixed overheads, which is charged as a period cost. On the other hand, the under recovery for 2001 is expected to be 150 000. The reconciliation of 2001 and 2002 profits is as follows: ( ) 2001 profits 128 750 Difference in opening stock valuation for 2001 (60 000) Additional under recovery in 2002 (150 000) Budgeted loss for 2002 (81 250) (b) To prepare the profit and loss accounts on a marginal cost basis, it is necessary to analyse the production costs into the fixed and variable elements. The calculations are: 2000 2001 2002 ( ) ( ) ( ) Total fixed overheads incurred 600 000 600 000 600 000 Less under recovery 300 000 150 000 300 000 Fixed overheads charged to production 300 000 450 000 300 000 Total production cost 1 000 000 975 000 650 000 Proportion fixed 3/10 6/13 (450/975) 6/13 Proportion variable (balance) 7/10 7/13 7/13 Profit and loss accounts (marginal cost basis) Actual 2000 Estimated 2001 Budget 2002 ( ) ( ) ( ) ( ) ( ) ( ) Sales 1 350 000 1 316 250 1 316 250 Opening finished goods stock at marginal cost 70 000 a 140 000 a 192 500 b Variable factory cost 700 000 a 525 000 b 350 000 b 770 000 a 665 000 a 542 500 b Closing finished goods stock at marginal cost 140 000 a 630 000 192 500 b 472 500 70 000 b 472 500 720 000 843 750 843 750 Fixed factory cost 600 000 a 600 000 a 600 000 b Administrative and financial costs 220 000 a 220 000 a 220 000 b 820 000 820 000 820 000 Profit/(loss) ( 100 000) 23 750 23 750 (c) Notes a 7/10 absorption cost figures given in the question. b 7/13 absorption cost figures given in the question. The under absorption of overhead may be due to the fact that the firm is operating at a low level of activity. This may be due to a low demand for the firm s products. The increase in the overhead rate will cause the product costs to increase. When cost-plus pricing is used the selling price will also be increased. An increase in 52 INCOME EFFECTS OF ALTERNATIVE COST ACCUMULATION SYSTEMS

selling price may result in a further decline in demand. Cost-plus pricing ignores price/demand relationships. For a more detailed discussion of the answer required to this question see section on Limitations of cost-plus pricing in Chapter 11. (d) For an answer to this question see section on Reasons for using cost-based pricing formulae in Chapter 11 and Some arguments in favour of absorption costing in Chapter 7. Note that SSAP 9 requires that absorption costing (full costing) be used for external reporting. (a) Sales for the second six-monthly period have increased for department A, but profit has declined, whereas sales for department B have declined and profit has increased. This situation arises because stocks are valued on an absorption cost basis. With an absorption costing system, fixed overheads are included in the stock valuations, and this can result in the amount of fixed overhead charged as an expense being different from the amount of fixed overhead incurred during a period. The effect of including fixed overheads in the stock valuation is shown below: Question 7.27 1 July 31 December 1 January 30 June Department Department Department Department A B A B Fixed overheads brought forward in opening stock of finished goods a 36 112 72 96 Fixed overheads carried forward in closing stock of goods b 72 96 12 160 Profit increased by 36 64 Profit reduced by 16 60 Net profit as per absorption costing profit and loss account 94 50 53 83 Profit prior to stock adjustment 58 66 113 19 Notes a Stocks are valued at factory cost with an absorption costing system. The opening stock valuation for department A for the first six months is 60 000 based on a product cost of 20 per unit. Therefore opening stock comprises 3000 units. Fixed manufacturing overheads are charged to the product made in department A at 12 per unit. Consequently, the stock valuation includes 36 000 for fixed overheads. The same approach is used to calculate the fixed overheads included in the opening stock valuation for the second period and department B. b Closing stock for department B (first period) 6000 units ( 120 000/ 20). Fixed overheads included in closing stock valuation 72 000 (6000 units 12). The same approach is used to calculate fixed overheads included in the remaining stock valuations. Comments During the first six months for department A, stocks are increasing so that the stock adjustment results in a reduction of the fixed overhead charge for the period of 36 000. Fixed manufacturing overheads of 132 000 have been incurred during the period. Therefore the total fixed manufacturing overhead charge for the period is 96 000. In the first period for department B stocks are declining and the stock adjustment will result in an additional 16 000 fixed manufacturing overheads being included in the stock valuation. Consequently, the fixed manufacturing INCOME EFFECTS OF ALTERNATIVE COST ACCUMULATION SYSTEMS 53

overhead charge for the period is 320 000 ( 304 000 16 000). When stocks are increasing, the stock adjustment will have a favourable impact on profits (department A, period 1), and when stocks are declining, the stock adjustment will have an adverse impact on profits (department B, period 1). In the second period stocks decline in department A and the stock adjustment will have an adverse impact on profits, whereas in department B stocks increase and this has a favourable impact on profit. When the two periods are compared, the stock adjustment has an adverse impact on the profits of department A and a favourable impact on the profits of department B. With an absorption costing system, profit is a function of sales and stock movements, and these stock movements can have an adverse impact on profits even when sales are increasing. (b) Departmental profit and loss accounts (marginal costing basis) 1 July 31 December 1 January 30 June Department Department Department Department A B A B Sales revenue 300 750 375 675 Variable manufacturing costs: Direct material 52 114 30 132 Direct labour 26 76 15 88 Variable overheads 26 76 15 88 Variable factory cost of production 104 266 60 308 Add opening stock of finished goods 24 98 48 84 128 364 108 392 Less closing stock of finished goods 48 84 8 140 Variable factory cost of goods sold 80 280 100 252 Total contribution 220 470 275 423 Less: Fixed factory overheads 132 304 132 304 Fixed administrative and selling costs 30 100 30 100 Net profit 58 66 113 19 54 INCOME EFFECTS OF ALTERNATIVE COST ACCUMULATION SYSTEMS