PAper F2 Revision Notes
June 2009 Examinations
FORMULAE SHEET
a=
b=
r=
Regression analysis
∑y b∑x n n∑xy-∑x∑y n∑x2 -(∑x)2 x ∑xy-∑x∑y (
a=
∑y b∑x n n
∑y b∑x a= n∑xy-∑x∑y n n 2 n∑x2 -(∑x) ∑y b∑x a= nn∑xy-∑x∑y n b= n∑xy-∑x∑y 2 n∑x -(∑x)2 r= 2 n∑xy-∑x∑y (n∑xb=-(∑x)2 )(n∑y 2 -(∑y)2 ) n∑x2 -(∑x)2 x∑xy-∑x∑y r= 2 2C0D (n∑x -(∑x)2 )(n∑y 2 -(∑y)2 ) = Economic order x∑xy-∑x∑y quantity Ch r= 2 (n∑x -(∑x)2 )(n∑y 2 -(∑y)2 ) 2C0D = 2C0D Ch = 2C0D D Ch (1-= ) C h R batch Economic 2C0Dquantity = D Ch (12C DR) 0 = D Ch (1- ) R b=
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PAper F2 Revision Notes
June 2009 Examinations
OVERHEAD ALLOCATION AND ABSORPTION Jones Ltd has allocated overheads between departments as follows: Dept $ A 336,000 B 210,000 Repairs 42,000 Maintenance 28,000 In addition there are general overheads of $308,000 which should be apportioned: A: 40%;
B: 30%;
Repairs: 20%;
Maintenance: 10%.
A & B are production departments. The repairs and maintenance service production department as follows:
Repairs Maintenance
A 60% 40%
B 40% 40%
Repairs – 20%
Maintenance – –
Budgeted labour hours: A: 40,000 hrs; B: 8,000 hrs Budgeted machine hours: A: 5,000hrs; B: 60,000 hrs (a)
Calculate an overhead absorption rate for each production dept.
(b) Smith Ltd has budgeted overheads of $200,000 and budgeted labour hours of 50,000. Actual hours worked were 48,000 and actual overheads were $205,000.
Calculate the amount of over or under absorption of overheads
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PAper F2 Revision Notes
June 2009 Examinations
OVERHEAD ABSORPTION - SERVICE DEPARTMENTS After allocating and apportioning overheads, the total overheads for each department are: X Y Stores Canteen 280,000 196,000 84,000 56,000 Stores and Canteen are service departments, and are used by other departments as follows: X Y Stores Canteen Stores 80% 10% – 10% Canteen 60% 36% 4% – Reallocate the service department costs
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PAper F2 Revision Notes
June 2009 Examinations
BREAKEVEN ANALYSIS Skully Ltd has produced the following (summarised) P&L A/C for 2002: $ $ Sales (20 000 units) 560,000 Production costs: Variable 252,000 84,000 Fixed 336,000 Gross Profit 224,000 Non-production costs: Variable 84,000 84,000 Fixed 168,000 Net Profit $56,000 (a)
What was breakeven sales volume for 2002?
(b) What was the margin of safety in 2002? (c)
What is C/S ratio in 2003
(d) Draw (i) profit volume chart (ii) breakeven chart for 2002
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PAper F2 Revision Notes
June 2009 Examinations
PROCESS COSTING A
In process X, 8,000 units were started during the month. There is a normal loss of 10% of input. All losses are sold for $1 p.u. Actual units completed during the month were 7300u. Costs incurred during the month: Materials: $20,000 Labour and overheads: $3,840 (There was no W.I.P at start or end of month) Write up the Process account and Loss account for the month B In process Y, 6,000u were started during the month. W.I.P. at the start of month: 400u [Materials 100% complete: $1,600 Labour 30% complete: $240] W.I.P. at the end of month: 600u [ Materials 100% complete Labour 60% complete] Expenditure during the month: Materials: $30,000 Labour: $18,120 (There were no losses during the month) Write up the process account, using FIFO
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PAper F2 Revision Notes
June 2009 Examinations
JOINT COSTS AND BY-PRODUCTS Jackson Ltd produces 2 products (& a by-product) in a joint process. During 2001, production was as follows: A B By-product
10,000 kg 40,000 kg 10,000 kg
S.P. (per kg) $10 $14 $1.40
The costs incurred in the process are $560,000 Product A needs a further $3 per kg to be spent before it is ready for sale. For products A & B, calculate the stock value per kg splitting the joint costs (i)
on the basis of weight
(ii) on the basis of sales value
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PAper F2 Revision Notes
June 2009 Examinations
LINEAR PROGRAMMING Mulder Ltd manufactures 2 products - X & Y with the following unit costings:
Selling price Variable costs Contribution Labour usage Material usage Maximum demand:
X 20 14 $6 2 hrs 5 kg 3,000 u
Y 15 5 $10 4 hrs 3 kg 12,000 u
If labour hours are restricted to a maximum of 8,000 hours, and material is restricted to a maximum of 13,000kg, what is the optimum production schedule?
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PAper F2 Revision Notes
June 2009 Examinations
LINEAR PROGRAMMING CONSTRAINTS: Labour: 2x + 4y ≤ 8.000 Material: 5x + 3y ≤ 13.000 Demand: x ≤ 3000; y ≤ 12.000 Non-negativity: x ≥0; y ≥ 0 OBJECTIVE: Maximise contribution: C = 6x+10y
y 4333
Demand For x
A
The demand for y constraint is obviously redundant
Material
2000
C
Labour
1500 Objective
E
B
2500 2600
D 4000
[Contribution line: if C = $15.000, then: x=0; y=1500 y=0; x=2500 BUT use any value for C - slope will be the same]
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x
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PAper F2 Revision Notes
June 2009 Examinations
LINEAR PROGRAMMING Optimum production schedule occurs at point E on the graph At point E: and (1) x 2.5 gives: (3) – (2) gives
Substitute for y in (1):
2x + 4y = 8,000 (1) 5x + 3y = 13,000 (2) 5x + 10y = 20,000 (3) 7y = 7000 y = 1000 2x + 4000 = 8000 2x = 4000 x = 2000
Optimum production schedule: Produce 2000 units of product X and 1000 units of product Y
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PAper F2 Revision Notes
June 2009 Examinations
STOCK CONTROL X plc needs to purchase 1,800 units a year. The purchase price of each unit is $25.
Delivery costs per order: Stock holding costs p.a. (as %age of purchase cost):
(a)
$32 18 % p.a.
Calculate the optimum order quantity, and the total costs p.a. at that order quantity.
(b) Y Plc has minimum demand of 20 units per day, average demand of 30 units per day, and maximum demand of 40 units per day. The lead time varies between 10 and 15 days. (i)
What should the reorder level be?
(ii) If the reorder quantity is 1,200 units, what will be the maximum stock level?
– buffer (or safety) stock
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PAper F2 Revision Notes
June 2009 Examinations
VARIANCE ANALYSIS COST CARD Selling price Materials (5kg at $4 per kg Labour (3 hrs at $3 per hr) Fixed overheads (3hrs at $2 per hr) Standard profit Budgeted production: Budgeted sales:
$ p.u. 40 20 9 6 35 $5p.u.
5,600 units 5,000 units
No opening stock. Actual results: Sales: 5,200 units for $218,400 Production costs (for production of 5,500 units): Materials (27,200 kg) Labour (18,000 hours paid and worked) Fixed overheads
$ 112,000 55,800 30,000
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PAper F2 Revision Notes
June 2009 Examinations
REGRESSION Units x 100 200 300 400 500 600 700 (a)
Costs ($’000’s) y 40 45 50 65 70 70 80
xy
x2
y2
Calculate the regression line
(b) Calculate the coefficient of correlation (c)
Calculate the coefficient of determination
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PAper F2 Revision Notes
June 2009 Examinations
RELEVANT COSTING Example 1 500 kg of material are needed for a special contract. There are 200 kg in stock, which was purchased for $2 per kg.. The current purchase price is $2.20 per kg.. The material is in regular use. What is the relevant cost?
Example 2 600 kg of material are needed for a special contract. There are 400 kg in stock, which was purchased for $5 per kg. The current purchase price is $7 per kg, and the current realisable value is $6 per kg. The company has no other use for this material. What is the relevant cost?
Example 3 A contract needs 200 hours of labour. Labour is paid $8 per hour, and the company has spare capacity. What is the relevant cost?
Example 4 A contact needs 300 hours of labour. Labour is paid $6 per hour. There is no spare capacity, and the labour would have to be transferred from other work producing units that earn a contribution of $14 per unit and take 2 hours per unit to produce. What is the relevant cost?
SUNK COSTS OPPORTUNITY COSTS
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PAper F2 Revision Notes
June 2009 Examinations
Labour costs Ratios: Production Volume Ratio =
Expected hours to make output Hours budgeted
Capacity Ratio =
Actual hours worked Hours budgeted
Efficiency Ratio =
Expected hours to make output Actual hours worked
Piecework:
Pay workers per unit produced
Labour Turnover Rate =
Employees Replaced Average Number of Employees
Example Firm had 200 employees at start of the year, and 160 at the end of the year. During the year 50 employees had left. Answer Number of employees fell by 40, so if 50 left 10 must have been replaced. Average number of employees 200 +160 Average number of employees = = 180 2 Labour turnover rate =
10 × 100% = 5.56% 180
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PAper F2 Revision Notes
June 2009 Examinations
Marginal and Absorption costing Z Ltd produces desks for which the standard cost card is as follows: $ pu Materials 10 Labour 6 Variable overheads 4 Fixed overheads 3 $23 During January, Z Ltd produced 50,000 desks and sold 45,000. The profit was calculated at $220,000, using absorption costing What would the profit be using marginal costing?
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PAper F2 Revision Notes
June 2009 Examinations
Key Factor Analysis (1) XX produces 3 products: Selling price Materials Labour Variable overheads Contribution p.u. Maximum demand
A 42 10 12 8 30 $12 1,000
B 56 18 16 10 44 $12 1,000
C 51 14 12 10 36 $15 1,000
Labour is paid $4 per hour, and there is a maximum 8,000 hours available. How many units of each should be produced to maximise profit?
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PAper F2 Revision Notes
June 2009 Examinations
Key Factor Analysis (2) YY makes 2 products: Materials Labour Variable overheads Units required
F 8 5 3 16 2,000
G 4 10 4 18 2,000
Labour is paid $5 per hour, and there are only 5,000 hours available. The units may be purchased from a supplier at costs of F:$22p.u., and G: $26p.u. How many units of each should be produced, and how many purchased from the supplier, in order to minimise costs?
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PAper F2 Revision Notes
June 2009 Examinations
VARIANCES – MATERIALS Standard cost of materials:
20 kg at $4 per kg = $80 per unit
During the month we produced 5000 units. We purchased 120,000 kg of material and paid $500,000 We used 105,000 kg in production (the other 15,000 kg are in inventory)
Materials expenditure (price) variance:
Materials usage variance:
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PAper F2 Revision Notes
June 2009 Examinations
VARIANCES – LABOUR Standard cost of labour:
8 hours at $3 per hr = $24 per unit
During the month we produced 6000 units. We paid for 52,000 hours of labour at the rate of $3.20 per hour. We worked 49,500 hours.
Labour rate of pay variance:
Labour idle time variance:
Labour efficiency variance:
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PAper F2 Revision Notes
June 2009 Examinations
VARIANCES – VARIABLE OVERHEADS Standard cost of variable overheads:
6 hours at $2 per hr = $12 per unit
During the month we produced 1,200 units. We worked for 7100 hours, and paid $13,900 for variable overheads.
Variable overhead expenditure variance:
Variable overhead efficiency variance:
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PAper F2 Revision Notes
June 2009 Examinations
VARIANCES – FIXED OVERHEADS Our company uses absorption costing, and budgeted to produce and sell 8,000 units. Standard cost of fixed overheads:
4 hours at $3 per hr = $12 per unit
During the month we produced 9,000 units. We worked for 35,000 hours, and paid $100,000 for fixed overheads.
Total fixed overhead variance:
Fixed overhead expenditure variance:
Fixed overhead volume variance:
Fixed overhead capacity variance:
Fixed overhead efficiency variance:
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PAper F2 Revision Notes
June 2009 Examinations
VARIANCES – SALES We budgeted to sell 10,000 units. The standard selling price is $20 per unit. The standard costs are: Variable costs $12 per unit Fixed costs $ 5 per unit The actual sales were 12,000 units at a selling price of $19 per unit Absorption costing:
Sales price variance:
Sales volume variance:
Marginal costing:
Sales price variance:
Sales volume variance:
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