Performance Pillar
Tuesday 1 March 2011 Instructions to candidates You are allowed three hours to answer this question paper. You are allowed 20 minutes reading time before the examination begins during which you should read the question paper and, if you wish, highlight and/or make notes on the question paper. However, you will not be allowed, under any circumstances, to open the answer book and start writing or use your calculator during this reading time. You are strongly advised to carefully read ALL the question requirements before attempting the question concerned (that is all parts and/or subquestions). ALL answers must be written in the answer book. Answers written on the question paper will not be submitted for marking. You should show all workings as marks are available for the method you use. ALL QUESTIONS ARE COMPULSORY. Section A comprises 8 sub-questions and is on pages 2 to 6. Section B comprises 6 sub-questions and is on pages 8 to 10. Section C comprises 2 questions and is on pages 12 to 15. Maths tables and formulae are provided on pages 17 to 20. The list of verbs as published in the syllabus is given for reference on page 23. Write your candidate number, the paper number and examination subject title in the spaces provided on the front of the answer book. Also write your contact ID and name in the space provided in the right hand margin and seal to close. Tick the appropriate boxes on the front of the answer book to indicate which questions you have answered.
P1 – Performance Operations
P1 – Performance Operations
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The Chartered Institute of Management Accountants 2011
SECTION A – 20 MARKS [Note: The indicative time for answering this section is 36 minutes] ANSWER ALL EIGHT SUB-QUESTIONS IN THIS SECTION
Instructions for answering Section A: The answers to the eight sub-questions in Section A should ALL be written in your answer book. Your answers should be clearly numbered with the sub-question number then ruled off, so that the markers know which sub-question you are answering. For multiple choice questions, you need only write the sub-question number and the letter of the answer option you have chosen. You do not need to start a new page for each sub-question. For sub-questions 1.6 to 1.8 you should show your workings as marks are available for the method you use to answer these sub-questions.
Question One 1.1
A documentary credit is
A
A negotiable instrument, drawn by one party on another, who by signing the document acknowledges the debt, which may be payable immediately or at some future date.
B
A document issued by a bank on behalf of a customer authorising a person to draw money to a specified amount from its branches or correspondents, usually in another country, when the conditions set out in the document have been met.
C
A series of promissory notes, guaranteed by a highly rated international bank, and purchased at a discount to face value by an exporter’s bank.
D
A form of export finance where the debt is sold to a factor, at a discount, in return for prompt cash. (2 marks)
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1.2
A company is deciding which of four potential selling prices it should charge for a new product. Market conditions are uncertain and demand may be good, average or poor. The company has calculated the contribution that would be earned for each of the possible outcomes and has produced a regret matrix as follows. Regret Matrix
Demand level
Selling price $140
$160
$180
$200
Good
$20,000
$60,000
$0
$10,000
Average
$50,000
$0
$40,000
$20,000
Poor
$0
$30,000
$20,000
$30,000
If the company applies the minimax regret criterion to make decisions, which selling price would be chosen?
A
$140
B
$160
C
$180
D
$200 (2 marks)
Section A continues on the next page
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March 2011
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Performance Operations
The following data are given for sub-questions 1.3 and 1.4 below A company operates a standard absorption costing system. Details of budgeted and actual figures for February are given below: Budget 29,000 3.0 $10.00
Production (units) Direct labour hours per unit Direct labour cost per hour
1.3
The labour rate variance for the period was:
A
$34,800 A
B
$34,800 F
C
$29,120 A
D
$31,200 A
Actual 26,000 2.8 $10.40
(2 marks)
1.4
The labour efficiency variance for the period was:
A
$58,000 F
B
$60,320 F
C
$52,000 F
D
$54,080 F (2 marks)
1.5
A company is deciding whether to launch a new product. The initial investment required is $40,000. The estimated annual cash flows and their associated probabilities are shown in the table below.
High Medium Low
Probability 0.20 0.50 0.30
Year 1 $20,000 $14,000 $9,000
Year 2 $24,000 $16,000 $12,000
Year 3 $18,000 $15,000 $10,000
The company’s cost of capital is 10% per annum. You should assume that all cash flows other than the initial investment occur at the end of the year. The expected present value of the year 1 cash flows is A
$12,453
B
$(27,547)
C
$15,070
D
$13,700 (2 marks)
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1.6
JB has budgeted production for the next budget year of 36,000 units. Each unit of production requires 4 labour hours and the budgeted labour rate is $12 per hour excluding overtime. Idle time is expected to be 10% of total hours available i.e. including idle time. Due to labour shortages it is expected that 20% of the hours paid, including idle time, will be paid at an overtime rate of time and a half.
Required: Calculate the labour cost budget for the year. (3 marks)
1.7
An extract from a company’s trial balance at the end of its financial year is given below: $000 2,600 1,800 1,650 220 350 260
Sales revenue (85% on credit) Cost of sales Purchases (90% on credit) Inventory of finished goods Trade receivables Trade payables
Required: Calculate the following working capital ratios: (i) (ii) (iii)
Inventory days Trade receivables days Trade payables days (3 marks)
Section A continues on the next page
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Performance Operations
1.8
A company is preparing its annual budget and is estimating the number of units of Product A that it will sell in each quarter of Year 2. Past experience has shown that the trend for sales of the product is represented by the following relationship: y = a + bx where y = number of sales units in the quarter a = 10,000 units b = 3,000 units x = the quarter number where 1 = quarter 1 of Year 1 Actual sales of Product A in Year 1 were affected by seasonal variations and were as follows: Quarter 1: Quarter 2: Quarter 3: Quarter 4:
14,000 units 18,000 units 18,000 units 20,000 units
Required: Calculate the expected sales of Product A (in units) for each quarter of Year 2, after adjusting for seasonal variations using the additive model. (4 marks)
(Total for Section A = 20 marks)
Reminder All answers to Section A must be written in your answer book. Answers to Section A written on the question paper will not be submitted for marking. End of Section A Section B begins on page 8
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Performance Operations
SECTION B – 30 MARKS [Note: The indicative time for answering this section is 54 minutes] ANSWER ALL SIX SUB-QUESTIONS. YOU SHOULD SHOW YOUR WORKINGS AS MARKS ARE AVAILABLE FOR THE METHOD YOU USE.
Question Two
(a)
‘A zero-based budgeting system involves establishing decision packages that are then ranked in order of their relative importance in meeting the organisation’s objectives’.
Required: Explain the above statement and the difficulties that a not-for-profit organisation may experience when trying to rank decision packages. (5 marks)
(b)
A company has to decide which of three new mutually exclusive products to launch. The directors believe that demand for the products will vary depending on competitor reaction. There is a 30% chance that competitor reaction will be strong, a 20% chance that competitor reaction will be normal and a 50% chance that competitor reaction will be weak. The company uses expected value to make this type of decision. The net present value for each of the possible outcomes is as follows: Competitor reaction
Product A
Product B
Product C
$000s
$000s
$000s
Strong
200
400
600
Normal
300
600
400
Weak
500
800
500
A market research company believes it can provide perfect information on potential competitor reaction in this market.
Required: Calculate the maximum amount that should be paid for the information from the market research company. (5 marks)
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(c)
A company uses a third party delivery service to deliver goods to customers. The current average cost per delivery is $12.50. The company is trying to decide whether to establish an in-house delivery service. A number of factors could affect the average total cost per delivery for the in-house delivery service. The table below shows the possible average total costs and the probability of each one occurring: Average total cost $10.50 $10.70 $11.00 $12.10 $12.50 $12.60 $14.20 $15.60 $15.80
Probability 0.05 0.10 0.08 0.12 0.14 0.16 0.12 0.18 0.05
The expected value of the average total cost, based on the probability distribution above, is $13.
Required: Explain the decision that the company manager is likely to make, based on the probability distribution and the current delivery cost of $12.50 per delivery, if the manager is: (i) (ii) (iii)
Risk neutral Risk averse Risk seeking (5 marks)
(d)
A company is considering the use of without recourse factoring to manage its trade receivables. It currently has a balance outstanding on trade receivables of $180,000 and annual sales revenue of $1,095,000. It anticipates that this level of sales revenue and trade receivables will continue for at least the next year. It estimates that the use of the factoring company will result in a reduction in credit control costs of $20,000 per annum. The factoring company will charge a fee of 2.5% of invoiced sales. It will give an advance of 90% of invoiced sales and charge interest at a rate of 12% per annum.
Required: (i)
Calculate the annual cost of factoring net of credit control cost savings. (3 marks)
The company currently finances its accounts receivables with a bank overdraft at an interest rate of 15% per annum. (ii)
Calculate whether there is a financial benefit from using the factor. You should ignore bad debts. (2 marks) (Total for sub-question (d) =5 marks)
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Performance Operations
(e)
A company has surplus funds to invest for a period of 3 months. It is considering potential investment opportunities as follows: Investment 1 Purchase treasury bills issued by the country’s central bank. The treasury bills can be purchased now for a period of 91 days. The purchase price is $995 per $1,000. Investment 2 Invest in a 30 day notice bank deposit account. The account will pay a variable rate of interest of 2.5% per annum, payable quarterly.
Required: Explain the advantages AND disadvantages to the company of each of the investments. Your answer should include relevant calculations. (5 marks)
(f)
A bond has a coupon rate of 8% and will repay its nominal value of $100 when it matures in 6 years’ time. The bond’s yield to maturity is 6.58%.
Required: Explain why there may be a difference between a bond’s coupon rate and its yield to maturity. (5 marks)
(Total for Section B = 30 marks)
End of Section B Section C begins on page 12
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Performance Operations
SECTION C – 50 MARKS [Note: The indicative time for answering this section is 90 minutes] ANSWER BOTH QUESTIONS IN THIS SECTION. EACH QUESTION IS WORTH 25 MARKS. YOU SHOULD SHOW YOUR WORKINGS AS MARKS ARE AVAILABLE FOR THE METHOD YOU USE. Question Three A company sells and services photocopying machines. Its sales department sells the machines and consumables, including ink and paper, and its service department provides an after sales service to its customers. The after sales service includes planned maintenance of the machine and repairs in the event of a machine breakdown. Service department customers are charged an amount per copy that differs depending on the size of the machine. The company’s existing costing system uses a single overhead rate, based on total sales revenue from copy charges, to charge the cost of the Service Department’s support activities to each size of machine. The Service Manager has suggested that the copy charge should more accurately reflect the costs involved. The company’s accountant has decided to implement an activity-based costing system and has obtained the following information about the support activities of the service department:
Activity
Overheads per annum $000 126
Cost Driver
Customer account handling Planned maintenance scheduling Unplanned maintenance scheduling Spare part procurement
Number of customers
Other overheads
Number of planned maintenance visits
480
Number of unplanned maintenance visits
147
Number of purchase orders
243
Number of machines
600
Total overheads
1,596
The following data have also been collected for each machine size: Small photocopiers
Medium photocopiers
Large photocopiers
$0.03 60,000
$0.04 120,000
$0.05 180,000
300 4
800 6
500 12
1
1
2
500 $100 $60
1,200 $300 $80
1,000 $400 $100
Charge per copy Average number of copies per year per machine Number of machines Planned maintenance visits per machine per year Unplanned maintenance visits per machine per year Total number of purchase orders per year Cost of parts per maintenance visit Labour cost per maintenance visit
Each customer has a service contract for two machines on average. Performance Operations
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Required: (a)
Calculate the annual profit per machine for each of the three sizes of machine, using the current basis for charging the costs of support activities to machines. (4 marks)
(b)
Calculate the annual profit per machine for each of the three sizes of machine using activity-based costing. (14 marks)
(c)
Explain the potential benefits to the company of using an activity-based costing system. (7 marks) (Total for Question Three = 25 marks)
Section C continues on the next page
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Performance Operations
Question Four A bus operator has been experiencing a fall in passenger numbers over the past few years as a result of intense competition from other transport providers. The company directors are concerned to improve profit and are considering two possible alternatives. Passenger volume last year was 20,000 passengers per day. The average fare was $2 per passenger per day and variable costs per passenger per day were $0.50. If no investment is made the current passenger volume, average fares and variable costs will remain the same on current routes for the next five years. The company operates a full service for 365 days of the year. Project 1 The company hired a management consultant, at a cost of $50,000, to review the company’s fare structure. The consultant recommended that the company reduce fares by 10% which will result in a 20% increase in passenger volume in the first year. In order to maintain this level of passenger numbers, fares will remain at the reduced rate for years 2 to 5. The increase in passenger numbers will result in the need for four new buses costing $250,000 each. The new buses will be depreciated on a straight line basis over their useful life of 5 years. They will have no residual value at the end of their useful life. Other annual fixed costs, including advertising costs, will increase by $100,000 in the first year and will remain at that level for the life of the project. Variable costs will remain at $0.50 per passenger per day for the life of the project. Project 2 Increase the number of buses to enable new routes to be opened. The new buses are expected to cost $5,000,000 in total and have a useful life of five years with no residual value. Fixed costs, including straight line depreciation, are expected to increase by $3,500,000 in the first year, as a result of opening the new routes. Fixed costs will remain at the higher level for the life of the project. Additional working capital of $1,000,000 will also be required. The passenger numbers for year 1 on the new routes are predicted as follows: Passenger numbers per day 6,000 9,000 12,000
Probability 50% 30% 20%
It is expected that passenger numbers will increase by 3% per annum for the following four years. The average fare per passenger for year 1 will be $2 and will remain at that level for the life of the project. Variable costs will remain at $0.50 per passenger per day for the life of the project. Additional Information Taxation and inflation should be ignored. The company uses a cost of capital of 8% per annum.
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Required: (a) (i)
Advise the management of the company which project should be undertaken based on a financial appraisal of the projects. You should use net present value (NPV) to appraise the projects. (13 marks)
(ii)
Explain TWO other major factors that should be considered before a final decision is made. (4 marks)
(b)
Calculate the sensitivity of the choice between Project 1 and Project 2 to a change in passenger numbers for Project 2. (4 marks)
(c)
Company D is planning its capital investment programme for next year. It is considering four potential projects all of which have a positive net present value. The initial investment, internal rate of return (IRR) and net present value (NPV), based on a cost of capital of 12%, are given below for each project. Project A B C D
Investment $000 50 40 20 30
NPV at 12% $000 13.6 15.2 10.2 12.3
IRR 12.6% 10.3% 13.1% 11.2%
Funding for the company is restricted to $110,000. The projects are independent and divisible i.e. part of a project can be undertaken.
Required: Prioritise the projects and determine how much funding should be allocated to each project. (4 marks) (Total for Question Four = 25 marks)
(Total for Section C = 50 marks)
End of question paper
March 2011
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Performance Operations
Maths tables and formulae are on pages 17 to 20
Performance Operations
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March 2011
PRESENT VALUE TABLE
(
Present value of $1, that is 1+ r payment or receipt.
)竏地 where r = interest rate; n = number of periods until
Periods (n) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1% 0.990 0.980 0.971 0.961 0.951 0.942 0.933 0.923 0.914 0.905 0.896 0.887 0.879 0.870 0.861 0.853 0.844 0.836 0.828 0.820
2% 0.980 0.961 0.942 0.924 0.906 0.888 0.871 0.853 0.837 0.820 0.804 0.788 0.773 0.758 0.743 0.728 0.714 0.700 0.686 0.673
3% 0.971 0.943 0.915 0.888 0.863 0.837 0.813 0.789 0.766 0.744 0.722 0.701 0.681 0.661 0.642 0.623 0.605 0.587 0.570 0.554
4% 0.962 0.925 0.889 0.855 0.822 0.790 0.760 0.731 0.703 0.676 0.650 0.625 0.601 0.577 0.555 0.534 0.513 0.494 0.475 0.456
Interest rates (r) 5% 6% 0.952 0.943 0.907 0.890 0.864 0.840 0.823 0.792 0.784 0.747 0.746 0705 0.711 0.665 0.677 0.627 0.645 0.592 0.614 0.558 0.585 0.527 0.557 0.497 0.530 0.469 0.505 0.442 0.481 0.417 0.458 0.394 0.436 0.371 0.416 0.350 0.396 0.331 0.377 0.312
7% 0.935 0.873 0.816 0.763 0.713 0.666 0.623 0.582 0.544 0.508 0.475 0.444 0.415 0.388 0.362 0.339 0.317 0.296 0.277 0.258
8% 0.926 0.857 0.794 0.735 0.681 0.630 0.583 0.540 0.500 0.463 0.429 0.397 0.368 0.340 0.315 0.292 0.270 0.250 0.232 0.215
9% 0.917 0.842 0.772 0.708 0.650 0.596 0.547 0.502 0.460 0.422 0.388 0.356 0.326 0.299 0.275 0.252 0.231 0.212 0.194 0.178
10% 0.909 0.826 0.751 0.683 0.621 0.564 0.513 0.467 0.424 0.386 0.350 0.319 0.290 0.263 0.239 0.218 0.198 0.180 0.164 0.149
Periods (n) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
11% 0.901 0.812 0.731 0.659 0.593 0.535 0.482 0.434 0.391 0.352 0.317 0.286 0.258 0.232 0.209 0.188 0.170 0.153 0.138 0.124
12% 0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404 0.361 0.322 0.287 0.257 0.229 0.205 0.183 0.163 0.146 0.130 0.116 0.104
13% 0.885 0.783 0.693 0.613 0.543 0.480 0.425 0.376 0.333 0.295 0.261 0.231 0.204 0.181 0.160 0.141 0.125 0.111 0.098 0.087
14% 0.877 0.769 0.675 0.592 0.519 0.456 0.400 0.351 0.308 0.270 0.237 0.208 0.182 0.160 0.140 0.123 0.108 0.095 0.083 0.073
Interest rates (r) 15% 16% 0.870 0.862 0.756 0.743 0.658 0.641 0.572 0.552 0.497 0.476 0.432 0.410 0.376 0.354 0.327 0.305 0.284 0.263 0.247 0.227 0.215 0.195 0.187 0.168 0.163 0.145 0.141 0.125 0.123 0.108 0.107 0.093 0.093 0.080 0.081 0.069 0.070 0.060 0.061 0.051
17% 0.855 0.731 0.624 0.534 0.456 0.390 0.333 0.285 0.243 0.208 0.178 0.152 0.130 0.111 0.095 0.081 0.069 0.059 0.051 0.043
18% 0.847 0.718 0.609 0.516 0.437 0.370 0.314 0.266 0.225 0.191 0.162 0.137 0.116 0.099 0.084 0.071 0.060 0.051 0.043 0.037
19% 0.840 0.706 0.593 0.499 0.419 0.352 0.296 0.249 0.209 0.176 0.148 0.124 0.104 0.088 0.079 0.062 0.052 0.044 0.037 0.031
20% 0.833 0.694 0.579 0.482 0.402 0.335 0.279 0.233 0.194 0.162 0.135 0.112 0.093 0.078 0.065 0.054 0.045 0.038 0.031 0.026
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Performance Operations
Cumulative present value of $1 per annum, Receivable or Payable at the end of each year for n years
1− (1+ r ) − n r
Periods (n) 1 2 3 4 5
1% 0.990 1.970 2.941 3.902 4.853
2% 0.980 1.942 2.884 3.808 4.713
3% 0.971 1.913 2.829 3.717 4.580
4% 0.962 1.886 2.775 3.630 4.452
Interest rates (r) 5% 6% 0.952 0.943 1.859 1.833 2.723 2.673 3.546 3.465 4.329 4.212
7% 0.935 1.808 2.624 3.387 4.100
8% 0.926 1.783 2.577 3.312 3.993
9% 0.917 1.759 2.531 3.240 3.890
10% 0.909 1.736 2.487 3.170 3.791
6 7 8 9 10
5.795 6.728 7.652 8.566 9.471
5.601 6.472 7.325 8.162 8.983
5.417 6.230 7.020 7.786 8.530
5.242 6.002 6.733 7.435 8.111
5.076 5.786 6.463 7.108 7.722
4.917 5.582 6.210 6.802 7.360
4.767 5.389 5.971 6.515 7.024
4.623 5.206 5.747 6.247 6.710
4.486 5.033 5.535 5.995 6.418
4.355 4.868 5.335 5.759 6.145
11 12 13 14 15
10.368 11.255 12.134 13.004 13.865
9.787 10.575 11.348 12.106 12.849
9.253 9.954 10.635 11.296 11.938
8.760 9.385 9.986 10.563 11.118
8.306 8.863 9.394 9.899 10.380
7.887 8.384 8.853 9.295 9.712
7.499 7.943 8.358 8.745 9.108
7.139 7.536 7.904 8.244 8.559
6.805 7.161 7.487 7.786 8.061
6.495 6.814 7.103 7.367 7.606
16 17 18 19 20
14.718 15.562 16.398 17.226 18.046
13.578 14.292 14.992 15.679 16.351
12.561 13.166 13.754 14.324 14.878
11.652 12.166 12.659 13.134 13.590
10.838 11.274 11.690 12.085 12.462
10.106 10.477 10.828 11.158 11.470
9.447 9.763 10.059 10.336 10.594
8.851 9.122 9.372 9.604 9.818
8.313 8.544 8.756 8.950 9.129
7.824 8.022 8.201 8.365 8.514
Periods (n) 1 2 3 4 5
11% 0.901 1.713 2.444 3.102 3.696
12% 0.893 1.690 2.402 3.037 3.605
13% 0.885 1.668 2.361 2.974 3.517
14% 0.877 1.647 2.322 2.914 3.433
Interest rates (r) 15% 16% 0.870 0.862 1.626 1.605 2.283 2.246 2.855 2.798 3.352 3.274
17% 0.855 1.585 2.210 2.743 3.199
18% 0.847 1.566 2.174 2.690 3.127
19% 0.840 1.547 2.140 2.639 3.058
20% 0.833 1.528 2.106 2.589 2.991
6 7 8 9 10
4.231 4.712 5.146 5.537 5.889
4.111 4.564 4.968 5.328 5.650
3.998 4.423 4.799 5.132 5.426
3.889 4.288 4.639 4.946 5.216
3.784 4.160 4.487 4.772 5.019
3.685 4.039 4.344 4.607 4.833
3.589 3.922 4.207 4.451 4.659
3.498 3.812 4.078 4.303 4.494
3.410 3.706 3.954 4.163 4.339
3.326 3.605 3.837 4.031 4.192
11 12 13 14 15
6.207 6.492 6.750 6.982 7.191
5.938 6.194 6.424 6.628 6.811
5.687 5.918 6.122 6.302 6.462
5.453 5.660 5.842 6.002 6.142
5.234 5.421 5.583 5.724 5.847
5.029 5.197 5.342 5.468 5.575
4.836 4.988 5.118 5.229 5.324
4.656 7.793 4.910 5.008 5.092
4.486 4.611 4.715 4.802 4.876
4.327 4.439 4.533 4.611 4.675
16 17 18 19 20
7.379 7.549 7.702 7.839 7.963
6.974 7.120 7.250 7.366 7.469
6.604 6.729 6.840 6.938 7.025
6.265 6.373 6.467 6.550 6.623
5.954 6.047 6.128 6.198 6.259
5.668 5.749 5.818 5.877 5.929
5.405 5.475 5.534 5.584 5.628
5.162 5.222 5.273 5.316 5.353
4.938 4.990 5.033 5.070 5.101
4.730 4.775 4.812 4.843 4.870
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FORMULAE PROBABILITY A ∪ B = A or B. A ∩ B = A and B (overlap). P(B | A) = probability of B, given A. Rules of Addition If A and B are mutually exclusive: If A and B are not mutually exclusive:
P(A ∪ B) = P(A) + P(B) P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
Rules of Multiplication If A and B are independent: If A and B are not independent:
P(A ∩ B) = P(A) * P(B) P(A ∩ B) = P(A) * P(B | A)
E(X) = ∑ (probability * payoff)
DESCRIPTIVE STATISTICS Arithmetic Mean
x =
∑x n
x=
∑ fx ∑f
(frequency distribution)
Standard Deviation
SD =
∑( x − x ) 2 n
SD =
∑ fx 2 − x 2 (frequency distribution) ∑f
INDEX NUMBERS Price relative = 100 * P1/P0
Price:
Quantity:
Quantity relative = 100 * Q1/Q0
P ∑ w ∗ 1 Po ∑w
x 100
Q ∑ w ∗ 1 Qo x 100 ∑w
TIME SERIES Additive Model Series = Trend + Seasonal + Random Multiplicative Model Series = Trend * Seasonal * Random
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FINANCIAL MATHEMATICS Compound Interest (Values and Sums) Future Value S, of a sum of X, invested for n periods, compounded at r% interest S = X[1 + r]
n
Annuity Present value of an annuity of £1 per annum receivable or payable for n years, commencing in one year, discounted at r% per annum:
PV =
1 1 1 − r [1 + r ] n
Perpetuity Present value of £1 per annum, payable or receivable in perpetuity, commencing in one year, discounted at r% per annum: PV =
1 r
LEARNING CURVE b
Yx = aX
where: Yx = the cumulative average time per unit to produce X units; a = the time required to produce the first unit of output; X = the cumulative number of units; b = the index of learning. The exponent b is defined as the log of the learning curve improvement rate divided by log 2. INVENTORY MANAGEMENT Economic Order Quantity 2C o D
EOQ =
Ch
where:
Co Ch D
= = =
cost of placing an order cost of holding one unit in inventory for one year annual demand
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LIST OF VERBS USED IN THE QUESTION REQUIREMENTS A list of the learning objectives and verbs that appear in the syllabus and in the question requirements for each question in this paper. It is important that you answer the question according to the definition of the verb. LEARNING OBJECTIVE Level 1 - KNOWLEDGE What you are expected to know.
Level 2 - COMPREHENSION What you are expected to understand.
VERBS USED
DEFINITION
List State Define
Make a list of Express, fully or clearly, the details/facts of Give the exact meaning of
Describe Distinguish Explain
Communicate the key features Highlight the differences between Make clear or intelligible/State the meaning or purpose of Recognise, establish or select after consideration Use an example to describe or explain something
Identify Illustrate Level 3 - APPLICATION How you are expected to apply your knowledge.
Apply Calculate Demonstrate Prepare Reconcile Solve Tabulate
Level 4 - ANALYSIS How are you expected to analyse the detail of what you have learned.
Level 5 - EVALUATION How are you expected to use your learning to evaluate, make decisions or recommendations.
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Analyse Categorise Compare and contrast
Put to practical use Ascertain or reckon mathematically Prove with certainty or to exhibit by practical means Make or get ready for use Make or prove consistent/compatible Find an answer to Arrange in a table
Construct Discuss Interpret Prioritise Produce
Examine in detail the structure of Place into a defined class or division Show the similarities and/or differences between Build up or compile Examine in detail by argument Translate into intelligible or familiar terms Place in order of priority or sequence for action Create or bring into existence
Advise Evaluate Recommend
Counsel, inform or notify Appraise or assess the value of Advise on a course of action
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Performance Pillar
Operational Level Paper
P1 – Performance Operations
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