A d d i t i o n a l S t u d y S u p p o r t M a t e r i a l C A S R I L A N K A C U R R I C U L U M 2 0 1 5 KE2 Management Accounting Information (English) This document is designed to use as an additional study support material. Students are advised to refer the content in the study text and the additional study support material under each chapter. The students who have already purchased the Executive Level KE2 Management Accounting Information study text are also advised to refer this study support material.
Contents KE2 Management Accounting Information Part A Fundamental Aspects of Cost Accounting 1 Introductory mathematics 3 4 Accounting for materials 14 6 Job, batch, contract and service costing 18 Part B Quantitative Aspects for Accounting 9 Normal distribution and sampling distributions 19 Part C Cost Accounting Systems 10 Accounting for overheads 28 11 Absorption, marginal and activity based costing 29 Part D Financial Mathematics for Business and Project Appraisal Fundamentals 12 Financial mathematics for business 32 Part F Mathematics for Business Functions 16 Mathematics for business functions 34 Part G Budgeting and Forecasting 17 Budgetary control and budgetary systems 37 18 Forecasting and Preparing Budgets 44 2
Additional Practice Questions to Chapter 1 Introductory Mathematics Heading 4: Percentages and Ratios (page 13) Percentages in a business context (Learning Outcome 2.1.1) 1. If the price of a cosmetic product is reduced by 20%, sales volume increases by 30%. Calculate the change in total revenue. A) 6% B) 12% C) 10% D) 4% Solution: (2 marks) Assume the original price is p and the original sales volume is q. Express the new price and the volume in terms of p and q respectively. Original value Change New value Price p decreases by 20% 0.80 p Volume q increases by 30% 1.30 q Revenue p q 1.04 p q When revenue increases from pq to 1.04 pq the increase would be 0.04pq and so the percentage increase is 4%. Change in total revenue = (1.04pq pq) 100% = 4% Answer: D 2. The last month telephone cost of a company was Rs. 43,200, including VAT at 8%. It has been decided to allocate 50% of these telephone costs, excluding VAT, to the Marketing Division and to allocate 25% of the remainder, excluding VAT, to the Finance Division. Compute the telephone costs to be allocated to the Finance Division. (3 marks) Solution: In the question it has been stated that apportioning of telephone cost to the departments is excluding VAT and hence we need to work out the telephone cost excluding VAT. 3
Telephone cost excluding VAT would be = 43,200 1.08 1 = Rs. 40,000 Marketing Remainder Division Rs. 20,000 Rs. 40, 000 x 50% = Rs. 20,000 Finance Division Other Divisions Answer: Rs. 5,000 Rs. 20,000 x 25% = Rs. 5,000 Rs. 15,000 3. The price of an item is Rs. 1,762.50 including VAT at 17.5%. If the price is increased by 15%, calculate the new price of the item before VAT is added. A) Rs. 1,650 B) Rs. 1,725 C) Rs. 1,950 D) Rs. 2,000 Solution: (2 marks) In the question it is mentioned that the price is increased. When price is increased, it should be noted that the price excluding VAT should be increased as there is no change in VAT. Hence, the new price before VAT would be 1,762.50 1.175 Answer: B 1.15 = Rs. 1,725 4. A trader sells a product with 30% profit margin. Compute his profit mark up as a percentage to two decimal places. A) 42.84% B) 42.85% C) 42.86% D) 42.87% Solution: (2 marks) If profit margin is 30%, the selling price and cost price would be 100% and 70% respectively. Hence the mark-up would be: 30 70 100% = 42.86% Answer: C \ 4
5. A person pays no tax on the first Rs. 500,000 of his annual earnings and then 5% tax on the next Rs. 1,000,000 and 8% on the remainder of earnings. If he/she wishes to have Rs. 2,600,000 net of tax earnings per year, calculate the gross earnings he/she needs. (3 marks) Solution: If the given net earnings are more than Rs. 1,450,000 (as per the working shown below) there should be three slabs. This means that, up to Rs. 500,000 with no tax is the first, Rs. 1,000,000 on which 5% tax is the second and the balance on which 8% tax. Up to Rs. 1,500,000 gross earnings would have Rs. 50,000 tax and the net on that would be Rs. 1,450,000. To have net earnings of Rs. 2,600,000, the balance net earnings in the third slab should be Rs. 1,150,000 for which the gross earnings would be Rs. 1,250,000. Hence the total gross earnings would be Rs. 2,750,000. Slabs Gross earning Tax Net earning Up to 500,000 500,000 - Rs. 500,000 500,000 1,500,000 1,000,000 (5%) 50,000 Rs. 950,000 Rs.1,450,000 1,500,000 + 1,250,000 (8%) 100,000 Rs.1,150,000 2,750,000 Rs.2,600,000 Answer: Rs. 2,750,000 5
Heading 4: Percentages and Ratios (Page 13) Percentages in a business context Chapter 6, Heading 3: Batch costing (Page 214) Specific and continuous order costing (Learning Outcome.2.1.1) (Learning Outcome.1.4.2) A company produces a device which is used in the manufacture of vehicles. It consists of ONE control unit made in India and TWO reinforced aluminium linkages supplied by a local supplier. Instrumentation and assembly are carried out at its factory in Sri Lanka. Other details are given below: Control Units from India The company buys in consignments of 500 units. The control price is Indian rupees 5,000, but subject to a quantity discount of 10% for orders of at least 500. Freight charges for a consignment of 500 units are Indian rupees of 750,000. Insurance is payable at the rate of 2% of the gross sum insured; the gross sum insured equals the cost of units plus freight. After landing in the Colombo Port, transport costs to the factory are Rs. 200,000, plus Rs. 300 per unit carried. (Exchange rate: Indian Rupee 1 = Sri Lankan Rupees 2.50) Aluminium linkages from a local supplier These are bought from a local supplier at Rs. 6,350 per unit. Production at the factory Other materials used in production cost Rs. 750 per device. Within the factory each production run of 500 devices requires 400 hours in Instrumentation at Rs. 1,200 per hour, 250 hours in Production at Rs. 800 per hour and 95 hours in Inspection at Rs. 1,000 per hour. On the average, Inspection which is the final stage rejects 5% of the devices as defective; these are worthless. At the current planned production levels, fixed costs are absorbed into production by adding 40% to the overall cost of labour and other materials incurred at the factory. The selling price to the trade is set so that its gross profit is 20% of the total amount invoiced to customers. Required: (a) (b) Prepare the statement of total cost of production. Calculate the unit price to the trade of the device. (Total 10 marks) (Learning Outcome 2.1.1) 6
Solution: Note: Since there are two different currencies involved initially, two columns are suggested, one for each. Cost of producing a batch of 500 devices (a) Indian Rs. Cost of 500 control units (from India) Basic cost of units (500 x 5,000) 2,500,000 Less: Discount (10%) (250,000) Sri Lankan Rs. 2,250,000 Freight 750,000 3,000,000 Insurance (2% of 3,000,000) 60,000 3.060,000 Total cost of importing 500 devices in SLR (3,060,000 X 2.50) 7,650,000 Transport charges (200,000 + (500 X 300) 350,000 8,000,000 Cost of 1,000 aluminium linkages (1,000 x 6,350) 6,350,000 Sri Lankan Cost incurred at the factory Rs Other Material (500 x 750) 375,000 Labour - Instrumentation (400 x 1,200) 480,000 Production (250 x 800) 200,000 Inspection (95 x 1,000) 95,000 Total cost of other materials and labour 1,150,000 Overheads 460,000 Total cost of production 15,960,000 (b) No. of good units produced = 95% of 500 = 475 devices Cost per unit = 15,960,000 475 = Rs. 33,600 Selling price = 33,600 0.8 = Rs. 42,000 7
Heading 6: Errors (page 28) Variations under addition, subtraction, multiplication and division (Learning Outcome 2.2.1) The accountant of a small company which produces a single product prepares the budget for the forthcoming year. She is uncertain about certain factors. Therefore, her estimates given below are subject to a margin of error. Margin of error Sales volume (in units) 400,000 5% Selling price (Rs) 80 10% Material cost per unit (Rs) 20 20% Labour cost per unit (Rs) 30 10% Fixed costs per annum (Rs) 3,000,000 5% Required: Compute the maximum error in next year s a) Contribution per unit; (5 marks) b) Annual contribution; (3 marks) c) Annual profit; in each of the above cases state the maximum error in relative terms (%) and interpret the results. (2 marks) (Total 10 marks) Solution: Material cost per unit = Rs. 20 ± 20% = Rs. 20 ± Rs. 4 = Rs. 16 Rs. 24 Labour cost per unit = Rs. 30 ± 10% = Rs. 30 ± Rs. 3 = Rs. 27 Rs. 33 Variable cost per unit = Rs. 43 Rs. 57 Selling Price per unit = Rs. 80 ± 10% = Rs. 80 ± Rs. 8 = Rs. 72 Rs. 88 Contribution per unit = Rs. 15 Rs. 45 8
a) The contribution per unit can also be expressed as follows: Contribution per unit = Rs. 15 - Rs. 45 = Rs. 30 ± Rs. 15 = Rs. 30 ± 50% Interpretation: When the selling price is subject to ± 10% error and the material and labour cost per unit is subject to errors of ± 20% and ± 10% respectively then contribution per unit will be subject to an error of ± 50%. b) Sales Volume = 400,000 ± 5% = 400,000 ± 20,000 = [380,000 420,000] units Contribution per unit = [Rs. 15 Rs. 45] Hence total contribution would be between = Rs. 5,700,000 Rs. 18,900,000 = Rs. 12,000,000 ± 6,900,000 = Rs. 12,000,000 ± 57.5% The maximum error in total contribution would be 57.5%. Interpretation: When the sales volume is subject to ± 5% error and the contribution per unit is subject to an error of ±50% error, the maximum error in the total contribution would be ± 57.5%. c) Total contribution is [Rs. 5,700,000 Rs. 18,900,000] Fixed overhead = Rs. 3,000,000 ± 5% = Rs. 3,000,000 ± Rs. 150,000 = Rs. 2,850,000 Rs. 3,150,000 Hence, annual profit would be [Rs. 2,550,000 - Rs. 16,050,000]. This could be expressed as Rs. 9,000,000 ± Rs. 7,050,000 = Rs. 9,000,000 ± 78.3% Interpretation: When all the variations happen in the factors as mentioned in the question the profit will be subject to a maximum error of ± 78.3%. 9
Heading 7: The arithmetic mean Heading 8: The Variance and the standard deviation Mean and standard deviation (Learning Outcome 2.3.1) At the close of business on the last working day of each month, the manager of a branch of a bank requires his staff to produce a brief summary of the corporate account balances. These monthly figures are intended to form the basis of the manager s quarterly report which is then used by the head office for planning purposes. To provide this information, the accounts of all corporate customers are examined. The details for one month are shown in the table below. Account balance (Rs. million) Class mid-point (x) Class frequency (f) 0 to less than 20 10 20 to less than 40 40 40 to less than 60 30 60 to less than 80 15 80 to less than 100 5 Total 100 fx fx 2 Required: a) Record the values in the missing places of the table. b) Calculate the arithmetic mean of the account balance. c) Calculate the standard deviation of the account balance to 2 d.p. d) Interpret the values obtained in (b) and (C) above. (3 marks) (2 marks) (2 marks) (3 marks) (Total 10 marks) 10
Solution: a) Account balance (Rs. million) Class mid-point x Class frequency (f) fx fx 2 0 to less than 20 10 10 100 1,000 20 to less than 40 30 40 1,200 36,000 40 to less than 60 50 30 1,500 75,000 60 to less than 80 70 15 1,050 73,500 80 to less than 100 90 5 450 40,500 Total 100 4,300 226,000 b) Mean x = fx f = 4300 100 = Rs. 43 million c) σ = fx2 f x 2 = 226,000 100 43 2 = Rs. 20.27 million d) Interpretation: Mean balance of Rs. 43 million: On average, a corporate customer keeps a deposit of Rs. 43 million with the bank. Standard deviation of Rs. 20.27 million: Customers individual account balances are, on average, dispersed from the mean by Rs. 20.27 million. 11
Heading 10: Indices terminology (page 42) Heading 13: Weighted index numbers (page 47) Index numbers (Learning Outcome.2.6.1) The following table shows the average wholesale price and production quantities of various products supplied by a manufacturing firm over the years 2014 and 2015. Price per tonne (Rs. 000) Item 2014 2015 Weights Alpha 250 300 6 Beta 360 400 1 Gamma 250 200 3 Required: a) Calculate the weighted aggregate price index for 2015 using 2014 as the base point. (4 marks) b) Calculate the weighted average relative index. (4 marks) c) State the difference between the methods used in (a) and (b) above. (2 marks) (Total 10 marks) Solution: (a) Price per tonne (Rs. 000) Item 2014 2015 Weights p 0 p 1 w p 0 w p 1 w Alpha 250 300 6 1,500 1,800 Beta 360 400 1 360 400 Gamma 250 200 3 750 600 Total 2,610 2,800 Weighted aggregate price index = p 1 w p 0 w 100 = 2,800 2,610 100 = 107 approximately 12
The overall increase in prices, using the standard weights given, between 2014 and 2015, is approximately 7% (107% - 100%). b) Price relative weights I = p 1 p 0 100 w I w Alpha Beta Gamma 300 250 400 360 200 250 100 = 120 6 720 100 = 111 1 111 100 = 80 3 240 10 1,071 Weighted average of price relative = 1,071 10 = 107 (approximately) The overall increase in prices, using the standard weights provided, between 2014 and 2015, is approximately 7%. c) The difference between weighted aggregate method and the weighted average method is, the weights are provided first and then the index is calculated. Whereas with the weighted average method, the index is calculated first and then the weights are provided. Both show the overall increase in prices, taking the weights given into account. 13
Additional Practice Questions to Chapter 4 Accounting for Materials Heading 7: FIFO (first in, first out) Heading 8: LIFO (last in, first out) Heading 9: AVCO (cumulative weighted average pricing) Material and inventory control - Profit differences under FIFO, LIFO and AVCO (Learning Outcome.1.2.2) David Ltd is a dealer in washing machines. Assume that it buys and sells a standard size of machines. On 01 April 2015, the company had a stock of 240 machines at purchase price of Rs. 40,000. During the month of April 2015, the shipments received and the quantities issued to retailers are summarised and given below: Shipments received (Purchased): 06 April 250 machines at Rs. 41,000 12 April 200 machines at Rs. 41,500 22 April 270 machines at Rs. 42,000 Issued to retailers (Sales): 09 April 400 machines at Rs. 50,000 27 April 500 machines at Rs. 50,000 David Ltd had a stock of 60 washing machines in the store at the end of April 2015. Required: Calculate the profits obtained for the month of April 2015 under the stock valuation methods of FIFO, LIFO and the monthly AVCO. (Total 10 marks) 14
Solution: Initially estimate the value of closing under the three methods. Using FIFO, Date Receipts Issues Balance Rs. 000 01/04 240 x 40,000/- 9,600 06/04 250 x 41,000/- 240 x 40,000/- 250 x 41,000/- 19,850 09/04 240 x 40,000/- 160 x 41,000/- 90 x 41,000/- 3,690 12/04 200 x 41,500/- 90 x 41,000/- 200 x 41,500/- 11,990 22/04 270 x 42,000/- 90 x 41,000/- 200 x 41,500/- 270 x 42,000/- 23,330 27/04 90 x 41,000/- 200 x 41,500/- 210 x 42,000/- 60 x 42,000/- 2,520 Under FIFO the closing stock is valued at Rs. 42,000 each, this being the price of the last batch obtained on 22 April. Hence value of closing stock would be Rs. 2,520,000. 15
Using LIFO, Date Receipts Issues Balance Rs. 000 01/04 240 x 40,000/- 9,600 06/04 250 x 41,000/- 240 x 40,000/- 250 x 41,000/- 19,850 09/04 250 x 41,000/- 150 x 40,000/- 90 x 40,000/- 3,600 12/04 200 x 41,500/- 90 x 40,000/- 200 x 41,500/- 11,900 22/04 270 x 42,000/- 90 x 40,000/- 200 x 41,500/- 270 x 42,000/- 23,240 27/04 270 x 42,000/- 200 x 41,500/- 30 x 40,000/- 60 x 40,000/- 2,400 The value of closing stock is Rs. 40,000 each and hence the value of closing stock would be Rs. 2,400,000. Using AVCO, Rs. 000 Opening stock 240 machines 9,600 Purchases 250 machines 10,250 200 machines 8,300 270 machines 11,340 960 machines 39,490 The unit cost per washing machine is Rs. 41,135 to the nearest Re. (Rs. 39,490,000/960) and hence the value of closing stock would be Rs. 2,468,100 (60 machines x Rs. 41,135 per machine). (For ease of calculation it has been rounded to the nearest Rs. 000) 16
Trading Account for the month of April 2015 (in Rs. 000): FIFO LIFO AVCO Sales (900 x Rs. 50,000) 45,000 45,000 45,000 Opening stock 9,600 9,600 9,600 Purchases 29,890 29,890 29,890 39,490 39,490 39,490 Closing stock 2,520 2,400 2,468 Cost of sales 36,970 37,090 37,022 Gross profit 8,030 7,910 7,978 17
Additional Practice Questions to Chapter 6 Job, batch, contract and service costing Heading 4: Contract costing (Page 216) Specific and continuous order costing (Learning Outcome 1.4.2) A contract has been signed by a company for Rs. 8 million during the financial year 2015/2016. The contractor incurs Rs. 3.6 million during the year and expects to incur another Rs. 2.4 million to complete the job. The customer has agreed to pay 80% of jobs approved and certified. Calculate the profit to be recognised. A) Rs. 1.20 million B) Rs. 1.50 million C) Rs. 1.80 million D) Rs. 2 million (2 marks) Solution: Estimated profit = Contract price {Expenditure incurred up to the point + Expected amount to be incurred in the balance period} = 8 {3.6 + 2.4} = Rs. 2 million Profit to be recognised = 2 3.6 6 = Rs. 1.2 million Note: Customer s agreement to pay only 80% of the jobs approved and certified is ignored in computation of profit as per LKAS 11. Answer: A 18
Additional Practice Questions to Chapter 9 Normal Distribution and Sampling Distributions Sub Heading 6.4: Estimation of parameters: Confidence intervals (Page 325) Sampling technique Confidence interval (Learning Outcome 2.5.1) 1. The Municipal Council of a city is considering how it should change a derelict site to a peoples leisure centre. Three proposals have been put forward by its board members, for which the Council decides to ascertain people s opinion through a sample survey. The sample includes 900 people of the city population. Preferences expressed by the sample are as follows: Number of people Public Park 360 Performing Art Centre 240 Cricket Ground 300 Required: i) Calculate the confidence interval & ii) Interpret the results in each case in the situations given below. a) The proportion of the city population that prefers the Cricket Ground at 95% level. (5 marks) b) The number of the city population that prefers the Performing Art Centre at 99% level, assuming a city population of 500,000 people. (5 marks) (Total 10 marks) Solution: a) i. Confidence interval for population proportion at any given level is P = p ± Z SEP The proportion of people in the sample who prefer Cricket Grounds is 300 900 = ⅓. p = ⅓ P = p ± Z SEP SEP = ⅓ ⅔ 900 = 0.0157 (approx.) and at 95% level Z = 1.96 19
P = ⅓ ± 1.96 0.0157 Hence, P = 0.303 0.364 P = 30.3% - 36.4% ii.interpretation: We are 95% certain that between 30.3% and 36.4% of the city population prefer a Cricket Ground built in that land. b) i. P = p ± Z SEP The proportion of people in the sample that prefers Performing Art Centre 240 is = 4. 900 15 p = 4 15 SEP = 4 15 11 15 900 P = p ± Z SEP P = 4 ± 2.58 0.0147 15 = 0.0147 (approx.) and at 99% level Z = 2.58 Hence, P = 0.2287 0.3046 P = 22.87% - 30.46% So, the number of people in the city population that prefers Performing Art Centre is as follows: = (22.87% - 30.46%) 500,000 = 114,350 152,300 ii.interpretation: We are 99% sure that between 114,350 and 152,300 in the city population go for Performing Art Centre. 20
2. The number of enquiries received at a five star hotel tend to be normally distributed with a mean of 45 calls per hour with a standard deviation of 9 calls per hour. Required: a) Calculate the probability that the average number of calls per hour over a 9-hour period is (i) Over 50 (ii) Under 37 (iii) Between 42 and 49 (5 marks) b) Calculate the 95% confidence limits for the average number of calls received per hour over the 9-hour period. (3 marks) c) Explain, briefly the advantages and disadvantages of working with sample data (2 marks) (Total 10 marks) Solution: The sampling distribution of sample means is normally distributed with mean (x ) = 45 calls and the standard error of mean (SEM) = 9 9 = 3 calls a) P (sample mean exceeds 50) = P (x > 50) = P (Z > 50 45 ) 3 = P (Z > 1.67) = 0.5 0.4525 = 0.0475 45 50 21
37 45 P (sample mean is under 37) = P (x < 37) = P (Z < 37 45 ) 3 = P (Z < - 2.67) = 0.5 0.4962 = 0.0038 42 45 49 P (sample mean lies between 42 and 49) = P (42 < x < 49) = P ( 42 45 < Z < 49 45 ) 3 3 = P (-1.00 < Z < 1.33) = 0.3413 + 0.4082 = 0.7495 b) The 95% confidence interval for the average number of calls received in a 9-hour period would be: μ = x ± Z SEM = 45 ± 1.96 = 45 ± 6 = (39 51) calls 9 9 c) Advantages: less expensive and less time consuming Disadvantages: may be less reliable and not accurate 22
Sub Heading- 7.2 Breakeven analysis Page No. 329 The word point needs to be corrected as Profit. Corrected profit/volume chart is given below. Profit 23
Sub Heading 6.4: Estimation of parameters: Confidence intervals (Page 325) Sampling technique Confidence interval (Learning Outcome 2.5.1) Chapter 18 Forecasting for budgeting (Learning Outcome 7.2.2) Lankan Automobiles PLC Lankan Automobiles PLC operates a chain of garages in three major cities, Colombo, Kandy and Galle. The company s business include car hire, servicing, repairs and petrol sales. It operates for 50 weeks a year, closing for one week in December from Christmas to New Year and another one week in April for Sinhala & Tamil New Year. Car Servicing Departments Lankan Automobiles PLC is concerned about the number of errors which seems to be made on customers service bills in the pricing of replacement items such as oil filters, engine oil, brake shoes, fan and A/C belts etc. The car servicing departments of the three garages in Colombo, Kandy and Galle had an internal audit last week. The internal audit included 100% investigation on 10% of its invoices in the last month. Some of the findings of the internal audit were as follows: Colombo Kandy Galle Number of invoices checked 144 64 49 Number of items on invoices 444 135 90 Number of items with error 40 15 10 Average (mean) value of error +Rs. 800 +Rs. 200 - Rs. 120 Standard deviation Rs. 84 Rs. 40 Rs. 35 (A plus mean value shows over charging and a minus under charging) Hire Cars Two types of fleets are used for this service, Maruti Suzuki Swift (S) and Maruti Suzuki Ritz (R). The new vehicle of both types cost the same. The company has 5 cars of each type. The Management Accountant of the firm has already obtained a relationship between the age (X) of a vehicle in months and its market value (Y) in Rs. million for each type of fleet using the least squares method of regression analysis. Given below are age and market value of each vehicle of each type. 24
Type S: Vehicle: 1 2 3 4 5 Age (X) in months 6 10 9 15 18 Market Value(Y) in 2.7 2.5 2.6 2.2 2.1 (Rs. Mn) Correlation coefficient (r) = - 0.99 Regression equation: Y = 3.04 0.05 X X = 11.6 Y = 2.42 Type R: Vehicle: 1 2 3 4 5 Age (X) in months 7 8 12 4 18 Market Value(Y) in 2.5 2.4 2.1 2.8 2.0 (Rs. Mn) Correlation coefficient (r) = - 0.94 Regression equation: Y = 2.91 0.06 X X = 9.8 Y = 2.36 Required: a) i. Graph the scatter diagrams of the two types of fleet (S and R), include the regression lines. ii. Interpret the regression lines and graphs. (10 marks) b) Assess, for the service departments, 95% confidence limits for the following and interpret the results. i. The percentage of items with error in the Colombo Garage. ii. The mean of monthly value of errors in the Galle Garage (5 marks) (5 marks) (Total 20 marks) 25
Market value in Rs. Million Market value in Rs. Million KE2 - Additional Study Support Material Solution: a) i. Scatter Diagram of Type S 2.8 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2 Y = 3.04-0.05 X 0 2 4 6 8 10 12 14 16 18 20 Age of vehcile in months Scatter Diagram of R 2.9 2.8 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2 Y = 2.91-0.06 X 0 2 4 6 8 10 12 14 16 18 20 Age of vehicle in months 26
ii. Interpretation: If we notice the two scatter diagrams, we can notice that the relationship between age and market value is stronger for type S than type R as the points are closer to the regression lines and also the value of r shows it. The regression line of type S {Y = 3.04 + 0.05 X} indicates that a brand new vehicle of this type would cost Rs. 3,040,000 and the market value drops by Rs. 50,000 every month. Similarly the regression line of type R {Y = 2.91 0.06 X} shows that a brand new vehicle of this type would cost Rs. 2,910,000 and the market value drops by Rs. 60,000 every month. b) i. The percentage of items with error in the invoices of Colombo Garage Error rate for the Colombo garage = 40 444 100% = 9% The 95% confidence interval for error rate in the Colombo Garage would be: 0.09 0.91 = 0.09 ± 1.96. 144 = 0.09 ± 1.96 * 0.02385 = 0.09 ± 0.05 (to 2 d.p) = 0.04-0.14 = 4% - 14% We are 95% certain that the true error rate in the invoices of the Colombo Garage is between 4% and 14%. ii. The mean monthly value of errors in the Galle Garage μ = x ± Z. SEM μ = 120 ± 1.96 35 μ = 110 130 49 We are 95% certain that the invoices with error have, on average under charged between Rs. 110 and Rs. 130. 27
Additional Contents to Chapter 10 Accounting for Overheads Heading 7: Over and under absorption of overheads (Page 364) Absorption costing and marginal costing Accounting of under/over-absorbed overheads (Learning Outcome 3.1.2) The accounting treatment of under/over absorption of overheads could be done in one of the following ways: a) Using supplementary rates: It is calculated by dividing the under or over absorbed amount by the amount absorbed and expressed as a percentage. Under absorption is adjusted by the plus percentage and over absorption by the minus percentage. b) By writing off to the Costing P & L Account: The amount of under or over-absorption at the end of the accounting period is transferred to the Costing Profit and Loss Account. Since the under or over absorbed is transferred directly to Costing P & L, it will distort the value of stock by the amount of under or over-absorption of overheads. c) Under or over absorption will be taken in the accounts in to the subsequent Year. 28
Additional Contents to Chapter 11 Absorption, marginal and activity based costing Heading 7: Calculating product costs using ABC (Page 389) The steps involved in ABC (Learning Outcome 3.2.2) An ABC system would be developed by analysing the causes of overhead costs as a function of the support activities carried out within the organisation. These cost drivers are then used to apportion costs in a meaningful way to the different products produced in a multi-product organisation. Steps involved with ABC approach: Let us explain the steps with activity based costing approach taking a simple example given below: Example: A company produces four products, AYE, BEE, CEE and DEE. The standard cost card of the 4 products is shown below: AYE BEE CEE DEE Rs Rs Rs Rs Material 1,200 1,500 800 1,000 Labour (at Rs. 600 per hour) 1,800 1,500 900 1,200 Production overhead absorbed 1,500 1,250 750 1,000 Standard cost per unit 4,500 4,250 2,450 3,200 Quantity produced (in units) 8,000 6,000 10,000 5,000 In the above cost card, production overhead has been absorbed on the basis of labour hours. The accountant of the firm is keen to introduce ABC since there is great diversity in the product range. He has identified only two major cost pool for production overhead. They are Machine set-ups and quality assurance for which the cost drivers are identified as purchase orders and number of batches produced. The cost associated with the above cost pools are as follows: Quality assurance Rs. 12,000,000 Machine set-up Rs. 20,000,000 Rs. 32,000,000 29
Further relevant information on the four products are as follows: AYE BEE CEE DEE Number of purchase orders 800 700 900 600 Number of batches produced 80 40 80 50 Required: Calculate the activity based standard cost of production per unit for the four products. Solution: If we consider the steps mentioned in Chapter 11, heading 7 Step 1: Step 2: Step 3: Step 4: Identify the major production related activities and the cost of these activities In this example the production related activities are quality assurance and machine set-up. Identify the cost drivers. It provides an explanation of the size of the cost pool. The cost drivers for the two production related activities have been identified as number of purchase orders and number of batches produced. Record the cost of each activity into cost pools Cost pools are quality assurance and machine set-ups for which the amounts are Rs. 12 million and Rs. 20 million. Charge support overheads to products on the basis of their usage of the activity. Calculate a cost driver rate for each activity cost pool in the same way as an overhead is calculated with the traditional approach and then use the rates to products to arrive at an activity based product cost. Cost driver rate: - Quality assurance = - Machine set-up = Rs.12,000,000 = Rs. 4,000 3,000 orders Rs.20,000,000 = Rs. 80,000 250 set ups 30
AYE BEE CEE DEE Quality assurance Rs.4,000 800 8,000 Rs.4,000 700 6,000 Rs.4,000 900 10,000 Rs.4,000 600 5,000 Machine set-up Rs. 80,000 80 8,000 Rs. 80,000 40 6,000 Rs. 80,000 80 10,000 Rs. 80,000 50 5,000 Rs. Rs. Rs. Rs. 400 467 360 480 800 533 640 800 1,200 1,000 1,000 1,280 AYE BEE CEE DEE Rs. Rs. Rs. Rs. Material 1,200 1,500 800 1,000 Labour (at Rs. 600 per hour) 1,800 1,500 900 1,200 Activity based production overhead 1,200 1,000 1,000 1,280 Standard cost per unit 4,200 4,000 2,700 3,480 31
Additional Practice Questions to Chapter 12 Financial Mathematics for Business Amortisation Schedule (Learning Outcome 4.1.1) An Amortisation Schedule is a statement which shows the outstanding amount of a loan, period by period. The amount of repayment can be either calculated in which case every repayment from the first to the final is the same and it covers the principal amount and the interest, or as agreed by the two parties in which case every payment is the same except for the final payment which is the balance due on the loan at the end. Question: Spotlight PLC is a firm which deals with N-Computing. N-computing is where one server machine is used by more than one users at a time through N- Computing units, thus it reduces the power consumption and the capital cost. ABC Ltd, a small company, wishes to buy an 8-user N-computing set for Rs. 250,000. ABC Ltd has agreed to pay a deposit of Rs. 100,000 and to set off the balance payment by instalments of Rs. 50,000 per year, payable at the end of each year. Interest is charged on the outstanding balance at 10% per year. Required: a) Draw up a schedule of the payments until the debt is paid off. (3 marks) b) State the number of full payments of Rs. 35,000 is made and the value of the final payment (1 marks) c) State the amount paid in total for the computer (1 marks) ABC Ltd is facing a financial crisis at present and therefore is unable to pay a big annual instalment of Rs. 50,000 for the next four years. Spotlight PLC has decided to help ABC Ltd to obtain the N-computing units immediately but pay for it after 4 years with no interest. ABC Ltd management has requested the Accountant to open a reserve fund account so that it can deposit a fixed amount every quarter for 16 quarters, the first one now. The reserve fund will earn compound interest of 2% per quarter. At the end of 4 years ABC Ltd can withdraw the whole amount and settle the due. d) Calculate the amount of quarterly deposits. (5 marks) (Total 10 marks) 32
Solution: a) Year Amount at the Beginning (Rs.) Interest payable (Rs.) Installments (Rs.) Amount at the end (Rs.) 1 150,000 15,000 (50,000) 115,000 2 115,000 11,500 (50,000) 76,500 3 76,500 7,650 (50,000) 34,150 4 34,150 3,415 (37,565) NIL b) There are 3 full payments of Rs. 50,000 and the final payment is Rs. 37,565. c) Total amount paid for the computer, Rs. 100,000 + (3 * Rs. 50,000) + Rs. 37,565 = Rs. 287,565 d) Assume that each quarterly investment deposit is Rs. A then 250,000 = A 1.02 (1.0216 1) (1.02 1) A = (250,000 0.02) {1.02 (1.02 16 1)} A = Rs. 13,150 (approx.) 33
Additional Practice Questions to Chapter 16 Mathematics for Business Functions Heading 8: The profit-maximising price/output level Average cost minimisation (Learning Outcome 6.2.1) 1. On a certain ferry it has been observed that the running costs per km, C are directly proportional to the square of the sailing speed. It can be considered as C = k x 2, where k is a constant and x is the sailing speed. From experience and it is known that C = Rs. 27,000 per km when the speed is 30 km per hour. In addition, there are other costs of Rs. 1,000 per hour, regardless of the ferry speed. Every week the ferry makes 10 journeys of 81 km up and down. Required Assess the following requirements: a) A mathematical expression for the cost of a journey of 60 km at x km per hour in terms of x. (4 marks) b) The most economical sailing speed for the ferry and the total cost for that journey at that speed. (6 marks) (Total 10 marks) Solution: a) Total weekly cost = Running costs + Other costs To estimate the running cost, the constant k should be identified. This is possible from the equation C = k x 2 27,000 = k (900), and hence, k = 30 This implies running costs are = 30 x 2 Other costs depend upon the sailing time. When the ferry sails at x km per hour time taken for a journey (up and down) would be 81 x hours and so other costs per journey = 81,000 Therefore weekly other costs would be Total weekly costs (C) = 30 x 2 + 810,000 x x 810,000 x 34
b) Minimise the total weekly costs: C = 30 x 2 + 810,000 x dc 810,000 = 30x dx x 2 At turning points, dc 810,000 = 0 and so 30x dx x 2 = 0 This implies that 30 x 3 = 810,000 x 3 = 27,000 x = 30 km per hour The turning point is minima as d2 C dx > 0 Hence, the most economical speed is 30 km per hour. When x = 30 total weekly cost would be 30 (30 2 ) + 810,000 30 = Rs. 54,000 per week. 2. Covering L.O 6.2.1 a) The costs of a company consist of variable costs, semi-variable costs and fixed costs. The relationship of capacity utilisation to costs can be expressed as: AC = 125 U + 32 + 300 where AC is the average cost per unit in Rs. U2 and U is the capacity utilisation proportion. Required Calculate the percentage capacity utilisation which will give the least cost per unit. (5 marks) b) The cost of producing a product is described by the function given below. C = 1280 560 x + 0.2x 2 (in Rs. 000) i. Calculate the level of production which minimises the average cost. (3 marks) ii. Calculate the cost of producing the 151 st unit. (2 marks) (Total 10 marks) 35
Solution: a) AC = 125 U + 32 U + 3 2 dac 64 = 125 - du U 3 At turning point 125-64 U 3 = 0 U3 = 0.512 Hence, at the minimum point of AC, U = 0.8 as d2 AC is always positive. 2 The average cost is minimised when 80% of the capacity is utilised. U b) (i) Since the cost function is C = 1,280 560 x + 0.2x 2, the average cost function would be: 1,280 AC = - 560 + 0.2 x x dac dx = - 1,280 x 2 + 0.2 At turning points dac dx 0.2x 2 = 1,280 = 0. This implies - 1,280 x 2 + 0.2 = 0 x = 80 Units is the minima as the second derivative is positive. (ii) MC = - 1,280 x 2 + 0.2 When x = 150 MC = - 1,280 1502 + 0.2 = 0.143 (3 dp) Cost of producing the 151 st unit equals Rs. 143 (approx.) 36
Additional Practice Questions to Chapter 17 Budgetary Control and Budgetary Systems Heading 4: Functional budgets (Page 591) Preparing functional budgets (Learning Outcome 7.3.1) Rainbow PLC Rainbow PLC is a manufacturing firm which produces two products, CEE and DEE, which are used by households. The budget for the forthcoming financial year from 01 April 2016 to 31 March 2017 is to be prepared by its Management Accountant. The expected Balance Sheet as at 01 April 2016 is given below: Balance Sheet as at 01 April 2016 Rs. 000 Rs. 000 Non-Current Assets Land & Buildings 170,000 Plant & Machinery 70,000 Less: Accumulated depreciation (15,000) 55,000 Current Assets Inventory - Raw material 6,440 - Finished goods 9,160 Debtors/ Receivables 8,195 Bank 1,205 25,000 TOTAL ASSETS 250,000 EQUITY & LIABILITIES Capital 200,000 Current Liabilities Creditors 32,600 Taxation 17,400 50,000 250,000 37
Further information is given below: 1. The two Products CEE DEE Demand for the two products 4,000 units 5,000 units Selling price per unit Rs. 7,500 Rs. 7,000 Finished goods as at 01.04 16 800 units 600 units Factory cost per finished good Rs. 6,800 Rs. 6,200 Finished goods expected at 31.03.17 500 units 400 units Machine hours required for each unit - in the Machining Department 30 minutes 20 minutes - in the Finishing Department 15 minutes 10 minutes Raw material requirement per unit CEE DEE - Raw material X 1.00 Kg 1.50 Kg - Raw material Y 2.50 Kg 2.00 Kg Labour hours per unit 5 hours 4 hours 2. Raw Materials X Y Opening stock as at 01.04.16 2,400 Kg 3,600 Kg Closing stock expected 1,500 Kg 2,400 Kg Budgeted raw material price per kg Rs. 1,200 Rs. 1,000 The budgeted raw material price is same as the actual price of opening stock. 3. The standard direct labour hour rate is Rs. 500 per hour. 4. Factory overheads are absorbed on the basis of machine hours Machining Finishing Rs. Rs. Indirect wages 95,000 32,000 Power 295,000 91,500 Maintenance and running costs 24,600 24,800 General expenses 35,400 41,700 450,000 190,000 5. Depreciation is charged at 5% straight line on plant and machinery. You may assume that the ratio of the value of the plant & machinery in the Machining and Finishing departments is 6:1. 38
6. Selling and distribution expenses are expected to be Rs. 322,000. 7. There is neither opening nor closing work in progress and inflation should be ignored. Required: Prepare the following budgets for the year ended 31 st March 2017 for Rainbow PLC. a) Sales budget (2 marks) b) Production budget (in units) (1 marks) c) Plant utilization budget (2 marks) d) Materials usage budget (3 marks) e) Labour budget (2 marks) f) Factory overhead budget (2 marks) g) Materials purchase budget (2 marks) h) Cost of goods sold budget (3 marks) i) Budgeted profit and loss account (3 marks) (Total 20 marks) Solution a) Sales budget Product Sales volume Selling price Sales value Units Rs. Rs. 000 CEE 4,000 7,500 30,000 DEE 5,000 7,000 35,000 65,000 b) Production budget (in units) CEE DEE Sales volume 4,000 5,000 Increase or (decrease) in finished goods stock (300) (200) Production requirement 3,700 4,800 39
c) Plant utilization budget Products Units Machining Finishing Hours Total Hours Total per unit hours per unit hours CEE 3,700 ½ 1,850 ¼ 925 DEE 4,800 ⅓ 1,600 ⅙ 800 3,450 1,725 d) Materials usage budget Raw material X Raw material Y Required for production Kg Kg CEE 1.0 kg 3,700 3,700 2.5 kg 3,700 9,250 DEE 1.5 kg 4,800 7,200 2.0 kg 4,800 9,600 10,900 18,850 e) Labour budget Product Production Hours Total Rate per Total labour Units Per unit hours hour cost (Rs. 000) CEE 3,700 5 18,500 500/- 9,250 DEE 4,800 4 19,200 500/- 9,600 18,850 f) Factory overhead budget Machining Rs.000 Finishing Rs.000 As per allocated and apportioned 450 190 Depreciation (5%) 3,000 500 3,450 690 Total machine hours [As per above (c)] 3,450 hours 1,725 hours Absorption rate per machine hour Rs. 1,000 Rs. 400 40
g) Materials purchase budget Raw material X Raw material Y Kg Kg Closing stock required 1,500 2,400 Production requirements 10,900 18,850 12,400 21,250 Opening stock 2,400 3,600 Purchase requirement 10,000 17,650 Purchase price per kg Rs. 1,200 Rs. 1, 000 Purchase cost (in Rs. 000) 12,000 17,650 Note: Cost of finished goods values are given in the question so the students can use them in calculation. The working of the above is shown here for students reference. Cost of finished goods CEE DEE Rs. 000 Rs. 000 Direct material X 1.20 1.80 Y 2.50 2.00 Direct labour 2.50 2.00 Production overhead Machining 0.50 0.33 Finishing 0.10 0.07 Factory cost per unit 6.80 6.20 h) Cost of goods sold budget CEE DEE Units Rs. 000 Units Rs. 000 Opening stock 800 5,440 600 3,720 Add-Cost of production 3,700 25,160 4,800 29,760 4,500 30,600 5,400 33,480 Less-Closing stock 500 3,400 400 2,480 Cost of sales 4,000 27,200 5,000 31,000 41
i) Budgeted profit and loss account CEE DEE Total Rs. 000 Rs. 000 Rs. 000 Sales 30,000 35,000 65,000 Less: Cost of sales 27,200 31,000 58,200 Gross profit 2, 800 4,000 6,800 Less: Selling & Administration expenses 322 Net profit before taxation 6,478 Note: There will be no under or over absorbed production overhead in a budgeted profit or loss account. 42
Heading 13: Rolling budgets (Page 626) Budgeting Rolling budgets (Learning Outcme.7.1.2) A rolling budget is a new, revised set of financial plans for the next accounting period used to replace the prior one in a continuous budgeting system. In other words, it s a newly updated budget that takes the place of the old version when it expires. Explain the steps involved in preparing rolling budgets by giving an example of your own. The process of preparing a rolling budget can be explained using an example given below: Assume that a company has prepared a budget for the year 2016 (January December) by the end of 2015. It has been broken down into suitable periods (for instance quarterly). At the end of first quarter, (31 March 2016), a comparison is made between that quarter s actual and the budget. The variations between the two is analysed and the necessary corrective measures are taken into account for the remaining period of the year. Then the first quarter of 2016 budget will be dropped and a budget for a further quarter (first quarter of 2017) will be added to the budget, making the budget for 4 quarters from April 2016 to March 2017. This process will be repeated at the end of every new quarter. If a shorter period (for example monthly) is considered it will be comparatively more tedious. State the advantages and disadvantages of rolling budgets. Advantages: More accurate Up to date Always a budget is available for one year that extends in to the future The impact of uncertainty would be small as it concerns with short periods It becomes a budget which is concerned with current developments Disadvantages: When budgetary targets keep on changing, it may demotivate the employees Since more time will be spent on preparing budgets, time available for control over actual results and other important matters may get curtailed More expensive time consuming 43
Additional Practice Questions to Chapter 18 Forecasting and Preparing budget Heading 11: Sales forecasting: time series analysis (Page 673) Forecasting for budgeting Calculating forecast information (Learning Outcome. 7.2.4) CORNETT LTD CORNETT Ltd is an ice cream manufacturing company. It is preparing budgets for the next six months, starting from April to September. To obtain the sales forecast for the six months, the accountant likes to collect past 12 months sales record and analyse the relationship between the trend in sales volume and the month. He believes that the relationship between the above is linear. The results shown below are sales volume (in 000 cases) for the last 12 Months. Month X Apr May June July Aug Sept Oct Nov Dec Jan Feb Mar Sales Volume Y (000 cases) 7 6 5 6 4 4 3 2 2 4 8 9 X = 78, Y = 60 X 2 = 650 XY = 393 Past experience has shown that the average seasonal variations for the sales of ice creams are: Month Apr May June July Aug Sept Oct Nov Dec Jan Feb Mar Sales Variation (%) +10 +5 +5 +5-5 -10-10 -15-20 +5 +10 +20 The standard cost of production per case is Rs. 4,500 and a standard selling price is Rs. 7,000 per case. Each case uses 3 kg of ingredients and it is company policy to have stock of ingredients at the end of each month to cover 40% of the next month s production (To make calculations easy you may round it off to the nearest 10 kg). The opening stock of ingredients as at 1 April is 7,000 kg. There are 1,080 cases of finished ice cream in stock on 1 April and it is policy to have stocks of finished ice cream at the end of each month to cover 20% of sales next month. 44
Required: a) Calculate the least squares regression equation for the trend in sales volume, assuming the relationship between the sales volume and month is linear. (4 marks) b) Calculate the sales forecast for the quarter (April June), assuming the multiplicative (or proportional) model of a time series. (For ease of calculations you may round it off to the nearest 10 cases) (3 marks) c) Prepare a production budget (in cases) for the quarter (April June). (5 marks) d) Prepare ingredients purchase budget for the quarter (April June). (5 marks) e) Assess the budgeted gross profit for the quarter (April-June). (3 marks) (Total 20 marks) Solution: a) If the least square regression equation of Sales volume on month is Y = a + b X, then the regression coefficients a and b are given as follows: b = b = n XY X Y n X 2 ( X) 2 {(12 393) (78 60)} {(12 650) 78 2 } b = 0.02 Interpretation: b = 0.02 indicates that, on average, the trend in sales volume increases by 20 cases every month Hence, a would be a = Y b X a = 60 78 0.02 12 12 a = 4.87 Interpretation: a = 4.87 indicates that the sales volume in March last year were 4,870 cases. Therefore the TREND in sales volume is given by: Trend = 4.87 + 0.02 X 45
b) The trend for the quarter (April June) Trend (000 cases) April - 4.87 + 0.02 (13) = 5.13 = 5,130 cases May - 4.87 + 0.02 (14) = 5.15 = 5,150 cases June - 4.87 + 0.02 (15) = 5.17 = 5,170 cases Sales forecast for the quarter (April September): Trend Seasonal factor Sales forecast (1 + SV 100 ) (to the nearest 10 cases) April - 5,130 1.10 = 5,640 cases May - 5,150 1.05 = 5,410 cases June - 5,170 1.05 = 5,430 cases July - 5,190 1.05 = 5,450 cases August - 5,210 0.95 = 4,950 cases c) Production budget (in cases) April May June July Forecast sales (in cases) 5,640 5,410 5,430 5,450 Cases in closing stock 1,082 1,086 1,090 990 6,722 6,496 6,520 6,440 Cases in opening stock 1,080 1,082 1,086 1,090 Budgeted production 5,642 5,414 5,434 5,350 d) Ingredients purchase budget (in kg) April May June July Required for budgeted Production (@ 3 kg per case) 16,926 16,242 16,302 16,050 Quantity in closing stock 6,500 6,520 6,420 23,426 22,762 22,722 Quantity in opening stock 7,000 6,500 6,520 Budgeted quantity to be 16,426 16,262 16,202 purchased 46
e) Budgeted gross profit (Rs. 000) April May June Total Rs. 000 Rs. 000 Rs. 000 Rs. 000 Sales: 5,640 7,000 39,480 5,410 7,000 37,870 5,430 7,000 38,010 39,480 37,870 38,010 115,360 Cost of sales: 5,640 4,500 25,380 5,410 4,500 24,345 5,430 4,500 24,435 74,160 Gross profit 14,100 13,525 13,575 41,200 47