Advanced Business Calculations Level 3

Model Answers Series 4 2007 (Code 3003)

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Advanced Business Calculations Level 3 Series 4 2007

How to use this booklet

Model Answers have been developed by Education Development International plc (EDI) to offer additional information and guidance to Centres, teachers and candidates as they prepare for LCCI International Qualifications. The contents of this booklet are divided into 3 elements: (1) Questions – reproduced from the printed examination paper (2) Model Answers – summary of the main points that the Chief Examiner expected to

see in the answers to each question in the examination paper, plus a fully worked example or sample answer (where applicable)

(3) Helpful Hints – where appropriate, additional guidance relating to individual

questions or to examination technique Teachers and candidates should find this booklet an invaluable teaching tool and an aid to success. EDI provides Model Answers to help candidates gain a general understanding of the standard required. The general standard of model answers is one that would achieve a Distinction grade. EDI accepts that candidates may offer other answers that could be equally valid.

© Education Development International plc 2007 All rights reserved; no part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without prior written permission of the Publisher. The book may not be lent, resold, hired out or otherwise disposed of by way of trade in any form of binding or cover, other than that in which it is published, without the prior consent of the Publisher.

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3003/4/07/MA Page 3 of 11

Advanced Business Calculations Level 3 Series 4 2007 QUESTION 1 (a) Calculate the amount (principal plus interest) when a sum of £150,000 is invested at 4% per annum simple interest for three-and-three-quarter years. (3 marks) (b) At the start of the year 2000 a house was worth £150,000. Each year for the next 6 years the house increased in value at a rate of 3.5% per annum of its value at the start of the year. Treating the increase in value as compound interest, calculate (i) the value of the house after 3 years (2 marks) (ii) the value of the house after 2½ years (2 marks) (iii) the value of the house after the first year (2 marks) (c) The value of a second house increased at the same rate of 3.5% per annum compound interest over the same 6-year period. At the end of the 6 years its value was £220,000. Giving your answer correct to the nearest £1,000, calculate the value of the house at the start of the period. (3 marks)

(Total 12 marks) MODEL ANSWER TO QUESTION 1 (a) Interest = PRT = £150,000 x 4 x 3.75 = £22,500 100 100

Amount = £150,000 + £22,500 = £172,500 (b)

(i) Value of house after 3 years = (1 + 0.035)3 x £150,000 = £166,307.68

(ii) Value of house after 2½ years = (1 + 0.035)2.5 x £150,000 = £163,471.53

(iii) Value of house after 1 year = (1 + 0.035) x £150,000 = £155,250 (c) Value of house at the start of the period = £220,000 ÷ (1 + 0.035)6

= £178,970.14 = £179,000

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QUESTION 2 £100 of 2¼% Government Stock can be bought for £88. Interest is paid half yearly. A bank invested £308,000 in the stock. (a) Calculate the nominal value of the stock bought by the bank. (2 marks) The bank held the stock for 3½ years. (b) Calculate the total interest received over this period. (2 marks) The bank purchased 120,000 5½% preference shares (nominal value £5) at £7.34. (c) Calculate the cost of the shares. (2 marks) (d) Calculate the dividend received each year. (2 marks) The bank also purchased units in a unit trust with an offer price of £450 per unit, and sold the units after 2½ years at £495 per unit. (e) Express the increase in price of the units as a percentage increase per annum (simple interest).

(3 marks)

(Total 11 marks)

MODEL ANSWER TO QUESTION 2 (a) Nominal value = £308,000 x £ 100/£88 = £350,000 (b) Interest received = £350,000 x 3.5 x 2.25% = £27,562.50 (c) Cost of the shares = 120,000 x £7.34 = £880,800 (d) Dividend = 120,000 x £5 x 5.5% = £33,000 (e) Increase in price = £495 – £450 = £45

Per annum percentage = 100% x £45 ÷ (£450 x 2.5) = 4%

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QUESTION 3 An industrial product may be manufactured by two methods of production. Using Method One, fixed costs are £6,450,000 per period and variable costs are £199 per unit. Using Method Two, fixed costs are £7,320,000 per period and variable costs are £170 per unit. (a) Calculate the level of output per period for which the total costs are the same. (4 marks) (b) State the total cost for Method One and Method Two at this output. (2 marks) (c) Using your answer to (a) above:

(i) State and explain when Method Two should be used rather than Method One. (2 marks)

(ii) Give an example, and show that it supports your answer to (i) above. (2 marks) Method Two is chosen for production, and the product is sold at £250 per unit. (d) Calculate: (i) the level of production and sales for break-even (3 marks) (ii) the total cost of production per period at this output. (2 marks)

(Total 15 marks)

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MODEL ANSWER TO QUESTION 3 (a) Output cost for Method One = 6,450,000 + 199Q

Output cost for Method Two = 7,320,000 + 170Q

Total costs are equal when Output cost M1 = Output cost M2 6,450,000 + 199Q = 7,320,000 + 170Q 29Q = 870,000 Q = 30,000

Output for which the total costs are the same is 30,000 units (b) Total cost for Method One = 6,450,000 + 199Q = 6,450,000 + 199 x 30,000 = £12,420,000 (c)

(i) Method Two should be used when output is more than 30,000 units. The variable costs are more important/have more effect at higher output.

(ii) For example, at an output of 40,000 units:

Cost for Method One = 6,450,000 + 199 x 40,000 = £14,410,000 Cost for Method Two = 7,320,000 + 170 x 40,000 = £14,120,000

Hence, for this output, which is above 30,000 units, Method Two is less costly. (d)

(i) Contribution = £250 - £170 = £80 Break-even at £7,320,000 ÷ £80 = 91,500 units per period

(ii) Total cost = £7,320,000 + 91,500 x £170 = £22,875,000

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QUESTION 4 (a) At the end of the year 2006 the current ratio for Company X was 3.55 : 1 and its current liabilities were £4,200,000. Calculate the current assets for Company X at that time. (2 marks) (b) Also at the end of the year 2006, the same company, Company X, had an acid test ratio of 2.85 : 1. Calculate the stock held by Company X at that time. (3 marks) (c) State whether you think the liquidity of Company X was healthy or not. Explain your answer. (4 marks) (d) The rate of stockturn for Company Y in the year 2006 was 11. At the start of that year the company held stock to the value of £84,000, and at the end of that year the value of stock held was £77,000. Calculate the net purchases of Company Y for that year. (4 marks)

(Total 13 marks) MODEL ANSWER TO QUESTION 4 (a) Current assets = Current ratio x current liabilities

= 3.55 x £4,200,000 = £14,910,000 (b) Current assets minus stock = Acid test ratio x current liabilities = 2.85 x £4,200,000 = £11,970,000

Stock = £14,910,000 - £11,970,000 = £2,940,000 (c) The current ratio of the company is greater than 2

The acid test ratio of the company is greater than 1 Each of these is good However, the ratios are a lot higher than these advisory targets, And therefore the assets of the company could be better used

(d) Average stock = (£84,000 + £77,000) ÷ 2 = £80,500

COGS = Rate of stockturn x average stock = 11 x £80,500 = £885,500 Net purchases = COGS – opening stock + closing stock

= £885,500 - £84,000 + £77,000 = £878,500

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QUESTION 5 A business owner is considering an investment project. The initial cost of the venture and the estimated costs and returns are as follows: £ Cost 2,400,000 Year 1 Net cash inflow 600,000 Year 2 Net cash inflow 1,000,000 Year 3 Net cash inflow 1,000,000 Year 4 Net cash inflow 700,000 The owner calculates the net present value at two discount rates, with the following results Discount rate 11% Net present value = £144,900 Discount rate 13% Net present value = £36,100 (a) Use these figures to calculate the internal rate of return. Give your answer correct to four significant figures. (4 marks) (b) Calculate the net present value of the project at a discount rate of 14%, using the following figures: Year Discount factor 1 0.877 2 0.769 3 0.675 4 0.592 (4 marks) (c) Using the net present value figures for discount rates of 13% and 14% calculate the internal rate of return. (3 marks) (f) Give two reasons why the internal rate of return calculated in part (c) is expected to be more accurate than the value calculated in part (a). (2 marks)

(Total 13 marks)

MODEL ANSWER TO QUESTION 5 (a) IRR = N1R2 – N2R1 = £144,900 x 13 – £36,100 x 11 % = 1,883,700 – 397,100 % = 13.66%

N1 – N2 £144,900 – £36,100 108,800 (b) £ Discounting Net present value factor 14% (£) Cost (2,400,000) (2,400,000) Year 1 cash inflow 600,000 0.877 526,200 Year 2 cash inflow 1,000,000 0.769 769,000 Year 3 cash inflow 1,000,000 0.675 675,000 Year 4 cash inflow 700,000 0.592 414,400 (15,400) (c) IRR = N1R2 – N2R1 = £36,100 x 14 – (£15,400) x 13 % = 505,400 + 200,200 % = 13.70%

N1 – N2 £36,100 – (£15,400) 51,500

(d) The second calculation uses figures closer to the IRR The second calculation uses interpolation, which is preferable to extrapolation.

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QUESTION 6 The following information relates to the business of a bankrupt trader. £ Mortgage 114,600 Cash in hand 200 Trade creditors 105,000 Machinery ? Bank overdraft ? Trade debtors 12,000 Stock 76,000 Office equipment 14,300 Vehicles 7,400 Total assets 148,700 Total liabilities 247,600 (a) Calculate the value of the machinery and the amount of the bank overdraft. (4 marks) £32,600 of the liabilities must be paid first and in full. Calculate: (b) the rate in the £ that an unsecured creditor will receive. (4 marks) (c) the amount owed to an unsecured creditor who receives £13,500 (2 marks) (d) the amount paid to an unsecured creditor who is owed £35,400. (2 marks)

(Total 12 marks) MODEL ANSWER TO QUESTION 6 (a) Total assets = £(200 + machinery + 12,000 + 14,300 + 76,000 + 7,400) Value of machinery = £148,700 – £109,900 = £38,800 Total liabilities = £(114,600 + 105,000 + overdraft) Amount of bank overdraft = £247,600 – £219,600 = £28,000 (b) Assets available for unsecured creditors = £148,700 - £32,600 = £116,100 Owed to unsecured creditors = £247,600 - £32,600 = £215,000 Rate payable = £1 x £116,100/£215,000 = £0.54 in the £ (c) Owed to unsecured creditor who receives £13,500 = £13,500 = £25,000 0.54 (d) Paid to unsecured creditor who is owed £35,400 = £35,400 x 0.54 = £19,116

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QUESTION 7 A factory machine that costs £115,000 is estimated to have a life of 5 years and a scrap value of £10,000. (a) Using the equal instalment method, prepare a depreciation schedule that shows, for each year, the annual depreciation, the accumulated depreciation and the book value at the end of each year. (5 marks) (b) Using the equal instalment method, calculate the percentage of the cost that is written off over the first 4 years. (3 marks) (c) Using the diminishing balance method of depreciation, calculate the rate of depreciation.

(4 marks)

(Total 12 marks) MODEL ANSWER TO QUESTION 7 (a) Annual depreciation = (£115,000 – £10,000) ÷ 5 = £21,000 Annual Cumulative Book value at depreciation (£) depreciation (£) end of year (£)

Initial cost 115,000 Year 1 21,000 21,000 94,000 Year 2 21,000 42,000 73,000 Year 3 21,000 63,000 52,000 Year 4 21,000 84,000 31,000 Year 5 21,000 105,000 10,000

(b) Amount written off over first 4 years = 4 x £21,000 = £84,000 Percentage to be written off over first 4 years = £84,000 x 100% = 73% £115,000 (c) £10,000 = 0.08695652 £115,000 5 08695652.0 = 0.6136 d = 1 – 0.6136 = 0.386 = 38.6%

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QUESTION 8 An index of industrial productivity has the following values over the period 2003 to 2006, with 2002 as the base year. 2002 2003 2004 2005 2006 100 105.5 108.3 120.1 127.7 (a) Calculate these indices as a chain base index. Give each answer correct to one decimal place. (6 marks) (b) Calculate the percentage increase in industrial productivity between 2004 and 2006.

(2 marks) An index of average earnings is shown below 2002 (2000=100) 2006 (2002=100) 105.7 112.9 (c) Calculate the index of average earnings for 2006 with 2000 as the base year. (2 marks) (d) Give a brief interpretation of your answer to (c) as a percentage change, stating clearly what has changed. (2 marks)

(Total 12 marks) MODEL ANSWER FOR QUESTION 8 (a) Example calculation: chain base index for 2004 = 100 x 108.3/105.5 = 102.7 2002 2003 2004 2005 2006 100 105.5 108.3 120.1 127.7 Chain base index 105.5 102.7 110.9 106.3 (b) Index for 2006 with 2004 as the base year = 100 x 127.7 ÷ 108.3 = 117.9 Percentage increase in industrial productivity between 2004 and 2006 = 17.9% (c) Index for 2006 with 2000 as the base year = 105.7 x 112.9/100 = 119.335 = 119.3 (d) From 2000 to 2006 average earnings increased by approximately 19.3%.