Finance Lecture Notes by DynamiteKegs

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									                 Advanced Management Accounting and Finance
            Lecture notes Managerial Accounting 2009 (Weeks 1 to 11)

The risk of going nowhere is the greatest risk of all
If it is to be, it is up to me (Fat is not the spoon’s fault)

Course guidelines

        First learn all the principles, concepts and techniques of each topic to enable you to identify problems
        and solve these successfully.

Many students fail because they spot test/exam topics.

Assessment & DP: Of 3 tests 2 form 50% of the year mark, and 50% from a trial examination. If the DP is
met the final exam counts 70% of the final mark and the DP 30%.

                                  MANAGEMENT ACCOUNTING

                                Introduction, Cost Terms & Concepts

 COST ACCUMULATION                    DECISION MAKING                   PLANNING & CONTROL

 Cost Assignment (Int.)               CVP Analysis (Int. & Adv.1)       Budgeting Process (Int.)

 Job Costing (Int.)                   Relevant Costing (Int. &          Standard Costing (Int. &
                                      Adv.2)                            Adv.5&6)
 Process Costing (Int)
                                      Activity-Based Costing (Int.      Divisional Performance
 Joint & By Products (Adv 1)          & Adv.3)                          (Adv.7)

 Absorption/Variable Costing          Pricing & Profitability (Adv4)    Transfer Pricing (Adv.8)
 (Int. & Adv. 1)
                                      Risk & Uncertainty (Adv.4)        Strategic Management
                                      Cost Estimation (Adv.10)
 Key: Int. = Intermediate
      Adv. =Advanced                  Linear Programming

Preliminary: Introduction, cost terms, cost assignment and job costing (Drury 1 – 4)

Chapter 1

Cost accounting: “…cost accumulation for inventory valuation, reporting and profit measurement…”

Management accounting: Providing information for internal users to facilitate management’s decision making
(figure 1.1 p9), planning, control and performance evaluation.

Overall goal: Maximise shareholder value by wealth creation (i.e. earning returns in excess of investors’ required
returns/WACC= W eKe+W dKd.

Emphasis on customer satisfaction brings new management approaches (total quality management {TQM},
benchmarking, value chain analysis and continuous improvement – see later Study Weeks).

Chapter 2 – Cost classification depends on the 3 main costing purposes:

Costing Purpose                                              Cost Object                                    Cost Classifications
Inventory                                                    Products                                       Categories of production cost:
valuation and                                                                                                      Direct material & labour
profit measure-                                                                                                    Manufacturing overhead
ment (pp 30 – 32)                                                                                                  Period or product cost
Decision-making                                              Decision alternatives                          Cost behaviour – Variable, Fixed, Semi-fixed (stepped)
(pages 32 – 40)                                              e.g.:                                              Semi-variable (mixed)
                                                             - make/buy                                     Relevant (unavoidable) cost / irrelevant cost (avoidable)
                                                             - continue product/not                             Sunk/Allocated cost
                                                             - labour or automation                             Opportunity cost
                                                                                                            Incremental (marginal) cost
Control &             Product                                                                               Controllable / non-controllable cost/income
performance           Customer                                                                              Who is responsible for controlling the cost?
evaluation (p41)      Department etc.
Draw a graph depicting the following scenarios (y-axis = Cost and x-axis = Volume):
i   A publisher pays a book royalty of R2 per copy to a maximum royalty of R10 000,
ii A church pays no electricity until it uses more than 50 KW per month, when it has to pay a flat amount of R500
    for that month,
iii An enterprise pays sales commission of 4% on sales that exceed R15 000 per month,
iv An enterprise pays a basic salary of R2 000 plus 4% commission on sales that exceed R15 000 per month,
v Monthly materials cost R10 000 for the first 400 kilograms and R20/Kg thereafter,
vi An enterprise pays a bonus of R5 for every unit produced after the first 1000 units per month,
vii An enterprise pays its maintenance staff a fixed salary for maintaining 3 of its 9 machines each.
Cost behaviour - Graph solutions
i   A publisher pays a book royalty of R2 per copy to a maximum royalty of R10 000,
ii Pays no electricity until 50 KW pm or more is used, when a flat amount of R500 is due for that month,
                     12000                                                                                             600
                     10000                                                                                             500
                     8000                                                                                              400


                     6000                                                                         Series1              300                                                                                          Series1

                     4000                                                                                              200

                     2000                                                                                              100
                                 1   2   3       4   5   6     7     8    9   10 11 12 13                                                  1          2       3       4       5         6        7         8

                                                             Books                                                                                                    Kilowatt

iii                  An enterprise pays sales commission of 4% on sales that exceed R15 000 per month,
iv                   An enterprise pays a basic salary of R2 000 plus 4% commission on sales that R15 000 per month,
                     250                                                                                                                   2300
       Basic & Com

                                                                                                                             Basic & Com

                     150                                                                                    Series1
                                                                                                                                           2100                                                                       Series1
                     100                                                                                                                   2050
                      50                                                                                                                   1950
                       0                                                                                                                   1850
                             1       3       5       7   9      11       13   15   17   19   21                                                   1       3   5   7       9   11   13       15   17   19       21
                                                               Sales                                                                                                          Sales

v                    Monthly materials cost R10 000 for the first 400 kilograms and R20/Kg thereafter,
vi                   An enterprise pays a bonus of R5 for every unit produced after the first 1000 units per month,

             30000                                                                                        1200

             25000                                                                                        1000

             20000                                                                                        800

             15000                                                                      Series1           600                                                       Series1
             10000                                                                                        400
             5000                                                                                         200
                0                                                                                           0
                     1       2   3   4       5     6    7    8   9       10 11 12                                1   2   3   4   5   6   7   8   9   10   11   12
                                                 Kilograms                                                                           Units

vii An enterprise pays its maintenance staff a fixed salary for maintaining 3 of its 9 machines each.


             10000                                                                                Series1


                         1       2       3          4        5       6      7       8   9

Chapter 3 – Cost Assignment
Direct costs: Easily traced and allocated to cost objects/products
Indirect costs (i.e. overheads): Allocated using arbitrary (e.g. labour hours) or cause-and effect (e.g. ABC
labour/machine hours, m , Kilowatt) allocation bases. ABC provides more accurate cost allocations.

Main purposes of product costing: Inventory valuation/profit measurement (primary focus) and decision making
(incorrectly viewed as secondary purpose) e.g. Asset depreciation forms part of full product cost for inventory
valuation, but is ignored (sunk cost) for decision making purposes (e.g. discontinue a product line).

Cost systems design: Costing systems depend on the significance of indirect costs (costly errors), the
complexity of the manufacturing environment and the cost versus benefit of the cost system.

Plant-wide vs. departmental overhead rates: Diverse product range and varying production times require multiple
departmental or cost centre/pool overhead rates (not blanket/plant wide). Thus overheads to service cost
centres→production cost centres→predetermined/normal overheard absorption rate (budgeted cost/budgeted
activity) →products/services/customers (e.g. based on machine/labour hours or ABC)

Reallocating service centre costs:
   • Repeated distribution - Allocate and reallocation service costs to service and production departments
       until immaterial or calculate final costs by simultaneous equation/reciprocal method (e.g. a’s reciprocal
       cost = own cost (R) +0,1b and b’s = own cost + 0,2a)
   • Specified order of closing (step-down) – allocate from highest service cost to lowest. Once allocated
       service dept. costs remain nil.
   • Direct allocation method - Ignore inter-service department allocations. Allocate costs in any order to
       production departments only. This is the simplest but least accurate method.

Under- and over-recovery of overheads: Actual overheads and activity differ from budget. Predetermined rate
= Budgeted cost/Budgeted activity (hours/units)

Example absorption costing based on unit produced
Machine centre ‘X’     Production Overhead Control Account
                               R’000                                                                                                     R’000
Actual overheads incurred      4 500     Absorbed overhead (R4,3m/2m)2,1m                                                                4 515
(CB, etc)
*Over-absorbed OH period          15     (budgeted rate x actual hours/units)
gain not in inventory
                                 4 515                                                 4 515

*Actual cost and actual hours/units differed from budget giving a net favourable variance of R0,015m split into:
    • expense variance = Bud.cost(R4,3m)–Act.cost(R4,5m)=R0,2m Unfav.
    • volume variance(VC) = (Act.–Bud.hrs/units)bud.rate=(2,1–2m)R4,3m/2m =R0,215m Favourable
    • volume variance(AC) = (Std – Bud hrs/units)bud rate

When the FOAR is based on production (machine or labour) hours as opposed to product units,
production overheads are charged to WIP at the FOAR x STD hours for actual production units (not at
actual hours). See AC and VC fro example

Non-manufacturing overheads: Selling, administration and distribution costs are period costs and excluded from
stock values, but part of product cost for decision making purposes.

Chapter 4 – Job Costing (assessed at level 2)

See Example 4.2 (p115–123) for recording of typical transactions. Exhibit 4.3 on p116 summarises the transactions.
Figure 4.1 on p133 illustrates the flow of accounting entries.

Ignore pages 123 (Interlocking accounting) – 132 (up to the summary).

Chapter 5 – Process costing (assessed at level 2)

Direct and indirect (depreciation/supervision) costs are allocated to a process not separate products. Pooled cost
per output unit (e.g. kilogram or litre) =Total production cost in period/ number of full units of output in period

FIFO-cost excludes the costs of BWIP. Weighted average cost includes BWIP.
Assuming only full units: Process cost per unit (R10) = Total process cost R120000/normal or expected
output 12 000
   • Normal (expected) losses – reduces normal/expected output (to 10 000)(Cost pu rises to R12) and scrap
       value is deducted from total process cost to reduced cost pu,
   • Abnormal (unexpected) losses are valued at normal output cost (R12 after normal losses). Arise from
       inefficiencies and excluded from inventory values with costs written off separately in the income statement.
       Abnormal scrap value is deducted from total abnormal losses cost.
   • Abnormal (unexpected) gains are valued at normal output cost. Assume maximum production of 12 000
       litres, normal losses of 2 000 litres and actual output of 11 000 litres, thus abnormal gains of 1 000 litres (11
       000 – [12 000 – 2 000]). Cost per unit (R11) = Total cost less normal scrap value / Expected output =
       (R120 000 – [R5x2000 normal losses]) /10000 litres)
       Abnormal gain is R6 000 (R11 000 gains [1 000 litres x R11 cost per unit] less scrap value of R5 000 [1 000
       x R5]).

Partially completed WIP: Convert to equivalent full units = physical units x percentage completion e.g. 2 000 units
only 60% (partially) complete equals 1 200 (2000 x 60%) equivalent full units

If raw material is added at the start of the process all WIP are full units (100% complete once in the process) in the
current period. Conversion costs (CC) are normally incurred evenly during a process and WIP units share in current
conversion costs to the extent (percentage) of their completion (say 60%) in the current period.

See the equivalent unit calculation and alternative set out (using the data in Example 5.2 on page 164) in your lecture

Partially complete BWIP: Equivalent full units (EFU)              Material        Conversion
 Weighted average value - 100% of physical units                    2 000             2 000
 FIFO value – % of physical units completed in current period      0 (0%)      800 (40%)
Do the Process Costing Question in the study notes

Advanced Managerial Accounting 2009

Chapter 6 – Joint and by-products (assessed at level 2)

Joint products have significant relative sales value.
By-products have minor sales value.
Joint costs has little value in decision-making (based on decision relevant cost/revenue principles)

At split-off point joint products could be sold or processed further. Further processing costs (after split-off =
separable costs [attributable or traceable to a specific product]). See Figure 6.1 on page 199.

Allocating joint costs: IAS 2 (AC108.12) - Conversion costs must be allocated between joint products on a
rational and consistent basis (e.g. relevant total sales value at completion or split-off). By-products are viewed as
immaterial and valued at net realisable value (deducted from the cost of the main/joint products).

    Rational bases to allocate joint costs at split off include:
    • Physical measures (used 75% of time) is suitable when outputs are solids, liquids or gas. This
        method ignores MV. Profit/loss margins will differ and the lower of cost and NRV may apply.
        Assume the total joint cost to split-off point is R1 million to produce 50 Kg Gold and 30 Kg Silver.
        Physical method: Gold: 50/80xR1m= R,625m Silver: 30/80xR10m=R,375m
    • Relative market values (recognises earnings potential). It provides more meaningful results
        when external or market prices are not available.
        • Total sales value at split off if determinable/saleable (could use joint cost as a basis for the setting of
           selling prices - circular thinking?) - Gross margins are equal, separable further processing costs are
           ignored and identification of unprofitable products at split-off are ignored.
           If joint cost to split-off is R1m for 50Kg Gold (SP R40000/Kg) and 30Kg Silver (SP R22000/Kg).
           Cost: Gold:50x40000=R2m/2,66 x R1m=R0,752m Sales R2m Profit R1,248 (62,4%)
           Silver:30x22000=R,66m/2,66m x R1m=R0,248 Sales R0,66m Profit R0,412 (62,4%)
        • Net realisable value (after separable costs) – Sales values and further processing costs are more
           readily available. Gross margins of different joint products will differ under this method.
           Assume joint cost is R1 million to produce 50Kg Gold (SP R40000/Kg) and 30Kg Silver (SP
           R22000/Kg). Each product requires further purifying after split-off costing R300/Kg.
           NRV: Gold:R2m-(50x300) = R1,985m                  Silver: R0,66m-(30x300) = R0,651m
            Joint cost: Gold: R1,985m/2,636m xR1m=R0,753m                  Silver: R0,651m/2,636m xR1m=R0,247
        • Constant gross profit % method - Joint costs allocation ensures joint products (after further
           processing) earn the same gross margin as the total joint production. The method unrealistically
           assumes a uniform relationship between the cost and sales value for all products.
            Assume the same information immediately preceding:
            Total Sales R2,66m Total cost R1+(80x300)=R1,024m Total Gross profit R1,636m (GP% 61,5)
                                                                      Gold              Silver
                 Sales                                                R2m               R0,66m
                 Joint cost (Balance)       COS              38,5% { -0,755             -0,245 (Total R1m)
                 Own separable cost (50x300)                         { -0,015           -0,009
                 Gross profit                                61,5% R1,23m               R0,406m (61,5%)

By-products: No joint production costs to split-off are allocated to by-products. Processing costs of by-products
beyond split-off are charged to them. By-product revenues or net revenues (after deducting separable costs)
should be deducted from joint process costs before allocation to joint products .

A joint process may produce material (waste) or residue that has no or a negative (i.e. disposal cost) sales value.
Waste is not included in inventory.

Left over material (scrap or off cuts) from a joint process may have minor sales value which, net of any realisation
cost, are also deducted from joint process costs.

Further processing decisions: Joint products should be processed further after split off if incremental revenues
exceed incremental/separable costs (i.e. attributable or traceable to a specific product). Further processing
decisions should incorporate capital budgeting procedures (i.e. Net present value – study week 17) when the time
value of money is significant and relevant qualitative aspects (e.g. customer/employee satisfaction) should also
be considered.

See the joint and by-product costing question in the study material.

Chapter 7 – Absorption and variable costing (assessed at level 3)

QE 2009 P2Q3: Discuss, with reasons, whether or not direct labour expense is a fixed manufacturing overhead
• Variable costs are defined as cost items that vary according to different levels of activity (production in the
   present scenario).
• Labour costs have traditionally being regarded as variable on the assumption that management can retrench
   workers in the event that production levels decline. In practice, downsizing and retrenching workers is not a
   unilateral decision and negotiations are required with unions and others before wide-scale retrenchments can be
   implemented. Retrenchments and downsizing are not an everyday occurrence. To assume that labour costs are
   variable because of the potential to reduce these may be inappropriate.
• Labour costs are incurred irrespective of production activity and, in the short term, labour costs are fixed in nature
   provided production is within normal capacity/relevant levels.
• Overtime costs are certainly variable in nature.
• The company forecast to have excess production personnel in 2008. If this transpired it would be inaccurate to
   assume production personnel was a variable cost and be misleading from a decision making perspective.
• Direct labour is a fixed cost as it can only be reduced through the drastic and unusual occurrence of retrenching
   labour. At worst, direct labour is a short term fixed cost.
• The wage rate would be variable, but the number of employees would be fixed.
• If there was an alternative use for employees, the labour costs would be variable.

Absorption costing
Under- and over-recovery of overheads: Actual overheads and activity differ from budget. Predetermined rate
= Budgeted cost/Budgeted activity (hours/units)

Example absorption costing based on unit produced
Machine centre ‘X’     Production Overhead Control Account
                               R’000                                                   R’000
Actual overheads incurred      4 500     Absorbed overhead (R4,3m/2m)2,1m              4 515
(CB, etc)                                hrs
*Over-absorbed OH period          15     (budgeted rate x actual hours/units)
gain not in inventory
                               4 515                                                   4 515

*Actual cost and actual hours/units differed from budget giving a net favourable variance of R0,015m split into:
    • expense variance = Bud.cost(R4,3m)–Act.cost(R4,5m)=R0,2m Unfav.
    • volume variance(VC) = (Act.–Bud.units)bud.rate=(2,1–2m)R4,3m/2m =R0,215m Favourable
    • volume variance(AC) = (Std – Bud units)bud rate

When the FOAR is based on production (machine or labour) hours as opposed to product units,
production overheads are charged to WIP at the FOAR x STD hours for actual production units (not at
actual hours).

Example: From the absorption costing information given below, calculate the over/under recovery of fixed production
overheads in Department P, divided into an expenditure and volume variance:
                                                       Budgeted          Actual
       Annual production of product A                  17 000 units      17 500 units
       Annual production of product B                  19 500 units      18 500 units

        Standard machine hours per unit of A           3 hours
        Standard machine hours per unit of B           2 hours
        Total machine hours                           90 000 hours 88 000 hours
        Fixed production overheads for the year       R5 490 000     R5 400 000
Fixed production overheads are recovered per machine hour.

Suggested solution:
FOAR: Budgeted FC 5 490 000 / 90 000 budgeted hrs = R61 per hour
Under recovery:
   Actual FO - (Std hrs x FOAR) = R5,4m – ({17500x3}+{18500x2})61= R59 500 F
FO Expenditure variance: Budget – Actual = R5,49m – R5,4 = R90 000 F
FO Volume variance: Bud hrs - Std hrs for Act Prod)FOAR
 = (90000 - [{17500x3} +{18500x2}])61 = (90000-89500)61 = R30 500 U
Or balancing amount : 90 000 – 59 500 = 30 500 U

If a variable costing system was in use above, there would be no under/over recovery of fixed production overheads
and there would be no volume variance. The fixed overhead Expenditure variance would be:
                  Budget – Actual = R5,49m – R5,4 = R90 000 F

Variable costing
Variable or marginal or direct costing, assigns only variable production costs to products/inventory.
The difference between the profits of these two costing systems is fixed production overheads in opening and
closing inventory.

Assume UKZN Limited manufactures and sells 66 centimetre television sets. Actual data for 20X6 was:
      Opening stock                                  2 000 units
      Sales                                         24 000 units
      Production                                    26 000 units
      Selling price per unit                           R90
      Variable costs per unit:         R
               Direct materials        20
               Direct labour           10
               Direct overheads         6
               Selling costs            4
      Fixed costs for the year:
               Production overhead – Actual R324 000 (Budgeted R300 000)
               Selling costs                          110 000
               Administration costs                    80 000

The fixed production overhead rate is based on a budgeted production volume of 25 000 units for the next year.

You are required to:
a)     Prepare UKZN Ltd’s profit statement for the 20X6 year based on absorption costing as well as
       variable costing principles.
b)     Explain the difference in net profit reported in the two profit statements in (a) and reconcile any
       such difference.
c)     Comment on a claim by UKZN Ltd’s operations manager that, when production fluctuates but sales
       remain constant, variable costing net profit will likewise fluctuate.

Suggested solution

a) Workings
FOAR: Budgeted cost/Budgeted prod units = R300 000/25000 = R12 per unit
Abs. product cost pu: Materials 20, Labour 10, Direct cost 6, Fixed prod.12 = R48
Variable product cost per unit: Materials 20, Labour 10, Direct expenses 6 = R36
Under recovery: 26000UxR12 =R312000–R324000 Actual= R12000
                                                          Absorption      Variable      Difference
                                                      R                            R                 R
Sales (24 000 @ R90)                              2 160 000                     2 160 000
Cost of sales                                     1 152 000                       864 000
         Opening stock (2000 @ R48) & R36VC          96 000                        72 000         -24 000
         Cost of production (26000 @ R48) & R36   1 248 000                       936 000
         Closing stock (4 000 @ R48) & R36         (192 000)                     (144 000)         48 000
Gross profit                                      1 008 000                     1 296 000
Under-absorbed overheads                             12 000                            -
Selling overhead: Variable 24000@4+110000 Fixed     206 000                        96 000
Contribution                                                                    1 200 000
Admin. R80000+Other FC(Prod. 324+Sell110+Admin80)    80 000                       514 000               .
Net profit                                          710 000                       686 000          24 000

b) Stock increased by 2 000 units and the fixed production overheads in absorption stock values increased by
R24000 (increase in absorption profit).
c) The Operations Manager’s claim is incorrect. Marginal costing profits fluctuate with sales volume only.
Absorption costing profits fluctuate with changes in both sales and production volumes, assuming that there
is no difference between budgeted and actual production volumes (no over/under recoveries of fixed production

The format of the above income statements is important and should be used at all times.

High-Low method: Variable costing requires all costs to be divided into fixed and variable cost elements. Divide
the change in cost by the change in activity between the highest and lowest levels of activity for the variable cost
per unit. The fixed cost element is the total cost less the total variable cost.

Example: Two products with different variable overhead costs per unit, but same FO cost per unit.
Products A and B have the same fixed cost per unit within a relevant range (combined 200 units). Total overhead costs:
        100 units of A and 50 units of B is R45 000
        150 units of A and 50 units of B is R50 000
         75 units of A is R5 750.
Required: The total fixed cost and variable cost per unit for both products A and B.

           Total overhead cost for 100 units of product A and 50 units of B       R45 000 or R300pu
           Total overhead cost for 150 units of product A and 50 units of B       R50 000 or R250pu
           Total overhead cost of 50 units of A                 0 units of B      R 5 000 or R100pu TFO
           Total overhead cost of 75 units of A                                   R 5 750
            Total variable cost of 25 units of A                                  R 750 or R30pu VC
                    FOH pu =R100-R30 = R70pu
                    FOH for 100 A and 50 B: R70 pu x 150 (100A+50B) = R10 500
                    Total OH for 100 A & 50B given as                       R45 000
                    Variable cost for 100 A & 50 B                           34 500
                    Less Variable cost for 100 A        100xR30pu             3 000
                    Variable cost for 50 B                                   31 500       /50 = R630 pu

External and internal financial reporting/Inventory valuation

            Financial accounting                                   Managerial accounting

 IAS 2 (AC108) regulates inventory                         Relevant variable cost principles apply

 Cost is added until inventory is in a                     Same criteria as for absorption costing apply,
 condition and location, ready for sale or                 but only variable production cost is included
 intended use
 Values inventory consistently on an                    Values inventory on Variable production cost
 absorption cost basis (including fixed                 basis and views fixed cost as a period cost
 production cost)

 Cost is actual FIFO or Weighted-average                LIFO can be used to charge current cost to
 cost                                                   sales for internal purposes.

 Direct production costs include a                      Same criteria as absorption costing apply, but
 systematic allocation of fixed and variable            only direct variable production cost is
 conversion cost at normal capacity                     included

Both external reports (absorption costing) and internal reports (variable costing):
• exclude abnormal waste from inventory (as discussed in process costing),
• deduct trade (not cash) discounts from the cost of materials,
• value inventory at the lower of cost or net realisable value (i.e. after cost essential for realisation/sale e.g.
   commission, trade discount and delivery cost),
• can value inventory at standard product cost if it approximates actual cost.

Absorption/Full costing                                     Variable/Direct/Marginal costing

Includes a systematic allocation of both fixed and          Includes only variable production costs in inventory
variable production costs in inventory values               values

Fixed production overheads are assigned to                  Fixed production overheads are excluded from
products by means of an FOAR                                inventory values and treated as a period cost

Matches sales and COS (FC & VC) and treats fixed            FC creates production capacity and is a period cost
costs as a necessary product costs                          (not linked to specific products sold or produced)

Profits changes with sales volumes                   and    Total contribution changes with sales and the impact
production/inventory levels (FC in stock)                   of decisions on profit is consistent and clear

Production cost per unit and profits changes with           Reflects a consistent contribution per unit or gross
increased/decreased production output                       profit percentage at all levels of production output

Arbitrary allocation of fixed overheads may over-           Variable overheads are more easily linked with and
/understate costs/selling prices/inventory                  allocated to production volumes

Is IAS reporting standard, valuing inventory at full        Is useful for internal (management) decision-making
cost to its condition and location for use or sale          as it clearly identifies the impact of decisions on profits

Is less costly to implement as fixed and variable           Controls variable cost per unit and total fixed cost per
production costs need not be split                          period. Resulting benefits may justify the extra costs

Presumed     to improve financial statement                 Losses may occur when sales volumes are low during
comparability by matching FC and revenues.                  out-of season periods but production/inventory levels
                                                            need to be high to meet impending seasonal demand.

Mathematical model of profit functions: Ignore (including Appendix 7.1)

Arguments in support of variable costing (p 237)
• More useful incremental/relevant information for decision-making (e.g. buy or make).
• Separates fixed and variable costs facilitating cost estimation at different activity levels.
•   Eliminates profit manipulation by means of increased inventory/production levels (deferring fixed costs). This
    strategy can also be discouraged by fixed inventory or stock turnover level requirements.
•   Excludes capitalising fixed overheads in unsaleable/obsolete/surplus inventory.

Arguments in support of absorption costing (p 238)
• Considers fixed production costs as essential for production and inclusion in products/inventory costs.
• Emphasises the recovery of fixed costs in sales revenue in the long run.
• Consistent with IAS 2 used by financial markets to appraise an entity’s performance and share price. The same
   reporting standards should be used to evaluate/reward managerial performance internally.

Alternative denominator (i.s.o. budgeted volume) level measures:
Problem: FOAR used budgeted production output determined at a specific time (discrete). FOAR is applied
constantly during the budget period when production volume fluctuates and actual fixed cost may increase
permanently in the short term (e.g. acquisition of new machinery) or unused capacity exists. Variable costs is
continually adjusted.

Alternative production activity levels include:
• Budgeted activity for the next budgeted period (most realistic and most widely used in practice). Fluctuates
    over time giving varying cost rates.
• Theoretical maximum capacity, which is most unlikely.
• Practical capacity allowing for unavoidable machine maintenance and plant holiday closures. It does not
    allow for bottle necks and unplanned delays resulting from machinery breakdowns and unavailability of
    materials, labour, energy (i.e. electricity) or other resource requirements. Does not fluctuate annually,
    providing more consistent cost rates.
• Normal activity required for average customer demand over the medium term (say 3 years) to factor in seasonal
    and cyclical fluctuations.
        IAS 2 (AC108) requires a systematic allocation of fixed and variable conversion cost at normal
        capacity per department (not firm-wide) over periods of normal circumstances, including planned
        maintenance but excluding periods with abnormally low production or high idle periods. Unallocated
        overheads, during periods with low production, are expensed as a period cost (excluded from inventory
        values) whilst lower fixed overheads per unit during abnormally high production periods should not
        increase inventory cost to normal capacity allocations. Thus, as a rule simply use the higher of actual or
        normal capacity. AC 108.11 states: “inventory is not measured above cost.” Inventory value should be
        conservative (prudently lowest cost).
        Example: Assume fixed overheads of R120 000 pa in years 1 and 2 and production levels pa of:
        Year 1: Normal production units 12 000 and Actual production units 15 000
        Year 2: Normal production units 12 000 and Actual production units 10 000
        Required: Calculate the fixed overheads per unit to be included in closing inventory in years 1 and 2.
        Solution: Year 1 - Fixed OH/Higher of normal & actual production= 120000/15000 =R8pu (lowest cost)
        Year 2 - Fixed OH/Higher of normal & actual production= 120000/12000 normal =R10pu (lowest cost)

                 Volume-Profit (assessed at level 3)
Chapter 8 – Cost-Volume

Economist’s CVP graph: Total revenue and total cost functions are curvilinear. To increase sales volume one
needs to reduce the selling price per unit. At low volume levels the total cost function rises quite steeply
because it is not efficient to operate a plant at a low volume. As the production volume rises total cost function
rises less steeply as economies of scale begin to filter through. At very high volume levels, total costs begin to
rise quite steeply again as bottlenecks develop. The model applies to all expected ranges of activity (long term).



Marginal revenue per unit is constantly declining. Profit maximising output is at the point at which marginal
revenue equals marginal cost. The economist’s model applies to all ranges of activity expected in the long

Economic theory (From pricing decisions): Economic theory assumes rational enterprises prefer selling prices
that maximise profits (most return with least risk/soonest) and that prices/profits can be estimated at each
potential demand level enabling profit maximisation decisions (where marginal revenue equals marginal cost
[see economist’s revenue/cost graph]) when the optimum output is sold at the optimum price.
Some difficulties include:
    • enterprises have multiple products and different demand curves,
    • various factors, apart from pricing, affect demand e.g. quality, packaging, advertising and credit terms,
    • marginal cost curves for individual products are complicated by joint/indirect costs.

Accountant’s cost- volume- profit model/ Break-even chart: Linear revenue and cost functions are assumed,
including a constant variable cost and selling price per unit within a relevant range.


Mathematical approach to CVP analysis: NP = Px – (a + bx) or NP = SPpuX – (FC + VCpuX) (X=units sold)
Breakeven: 0 = Px – (a + bx) or FC/(P-b) or FC/Contribution pu BE at fixed profit (+FC)/Variable profit pu (-Cont.pu)
Breakeven sales value = FC/profit-volume ratio
Total sales = Breakeven sales + Safety sales
Breakeven sales x PV% = FC and Safety sales x PV% = NP
Sales units at fixed profit: (FC + NP)/(P-b) or NP = Px – (a + bx)
Sales units at variable profit: FC/(P-b-variable profit)
Selling price to achieve profit: P = [NP + (a + bx)]/x
Margin of safety: Safety Sales = Sales units – BE units; MOS% = (Sales units– BE units)/Sales units
Contribution margin/Profit-volume ratio: contribution/sales.
Contribution = sales x profit-volume ratio
NP = sales x profit-volume ratio (contribution margin ratio) – fixed costs.
NP = Margin of safety sales x profit-volume ratio
Min sales value = (fixed costs + required contribution)/ P/V ratio

i.   Calculate the total sales value when breakeven sales value is R1 million and the safety margin is 40%.
ii.  Calculate total fixed costs when the total sales value is R1,667 million, the safety margin is 40% and PV
     ratio 30%.
iii. Calculate total fixed costs when the total contribution is R0,5 million and the safety margin is 20%.
iv.  Calculate the total profit when total sales is R1,429 million, the breakeven sales value is 70% and the PV
     ratio is 20%.
v.   Calculate the contribution when breakeven sales are R420 000, the margin of safety is 30% and the
     profit margin is 10%.

i.    Safety sales = 40%. Breakeven sales = 60%. Thus BE sales of R1m/0,6 = R1,667m total sales.
ii.   FC = BE sales x PV% Thus R1,667m x 0,6 = R1m BE sales x 0,3 PV% = R0,3m FC
iii.  Total fixed costs = Total contribution x (1-Safety margin) thus R0,5m x (1-0,2) = R0,4 mil or NP = Cont. x
      Safety margin = R0,5m x 20% = R0,1m FC = Cont. – NP = 0,5m-0,1m = 0,4m
iv.   NP = Safety sales x PV% = (1,429x0,3)0,2 = R85 740.
v.    Total sales = BE sales/BE% = 0,42m/0,7 = 0,6 m and NP at 10% = R0,06m NP=Safety sales x PV%
      Thus 0,06m= (0,6mx0,3)PV% and 0,06/0,18 = PV% of 33,3% Contribution is R0,6m/3 = R0,2m

Profit-volume graph:

                                               Profit-Volume Graph                           Breakeven = Total
                                                                                             cost/Contribution per
                                       1000    Profit + Dep =                                unit
             Rands (Sales &

                                               Cash breakeven


                                        -500   1        3       5        7    9
                                                     Volume (Units)
This graph measures profits/losses on the vertical axis. The lower cash breakeven may enable the enterprise to
survive in the short term in spite of operating losses (below normal breakeven but above the cash breakeven
point). Short term survival becomes a valid business strategy only if long term recovery of profitable operations and
adequate funding are feasible.

Multi-product CVP analysis: A fixed sales mix (basket of products) is assumed with a weighted average
contribution (multiply each product’s unit contribution by the number of units of that product in the sales mix).

Example: Assume two products (A and B) are sold in fixed proportions of 2A:3B, contribution per product is R15 (A)
and R25 (B) and total fixed costs R787 500. The multi-product breakeven can be calculated as follows:

Total contribution per sales mix
Total contribution for A (2x15 =R30) and B (3x25=R75) is R105 (R30+R75) and
Breakeven is 787500/105 = 7500 sales mixes or 15 000 A (7500x2) and 22 500 B (7500x3)
Note that the total contribution is R787 500 [(15 000A x R15)+(22500 x R25)

Weighted average contribution per sales mix
Weighted average contribution: A R6 (2/5 x R15) plus B R15 (3/5 x R25) = WA R21 (R6+R15)
Breakeven is 787500/21 = 37500 units with 2/5ths or 15 000 of A and 3/5ths or 22 500 of B
Again, total contribution is R787 500 [(15 000A x R15)+(22500 x R25)

Note the CVP analysis assumptions.
(a) All variables other than volume remain constant so that volume is the only factor that influences costs and
(b) The entity sells a single product or if a range of products is sold the sales mix is constant.
(c) Selling price and variable cost per unit are constant resulting in linear total costs and revenue functions.
(d) A variable costing system is used for reporting purposes.
(e) The analysis applies to the accountant’s relevant range only.
(f) Costs can be accurately classified as fixed or variable. Semi-variable costs can be separated into their fixed and
variable elements.
(g) The analysis applies to the short term only, typically one year.
(h) Complexity related fixed costs do not change as a result of increasing the range of products.

Sensitivity analysis (BE) and profit elements:
     Actual Sales 100 000 units at R20                 2 000
     Variable cost                                     1 200 /100000 = R12 pu
     Contribution 40%                                     800 /100 000 = R 8 pu
     Fixed cost                                           500
     Profit 15%                                           300 /100 000= R 3 pu
     Breakeven FC/Contr. pu = 500 000/8 = 62 500 units
     Breakeven sales value = 62 500 units x R20 = R1,25m
A change in which profit element (i.e. SP, Sales volume, VC and FC) will have the greatest impact on profit?

Sensitivity analyses: Using changes to breakeven or an arbitrary % change:
a) Breakeven units-based sensitive test                 Total          Breakeven                Safety %
        Revenue/cost element
        Actual Sales Volume 100 000 units                  100         62,5        (100-62,5/100) 37,5%
        Actual sales value                               2 000         1 250       (2-1,25)/2m    37,5%
        S/Price (BE SP R20-R3 Profit pu =R17)            R20           R17         ( 20-17)/20     15%
        VC to BE (R12 + R3 Profit pu)                    R12           R15         (15-12)/12      25%
        FC to BE (R500 + 300 profit = R800)              R500          R800        (800-500)/500 60%
The profit is most sensitive (lowest safety margin) to changes in selling price, then variable cost, sales volume and
lastly fixed cost.

b) Arbitrary percentage (10%) change sensitive test
                                        Total       Vol-10%         SP-10%         VC+10% FC+10%
      Actual Sales                       2 000      1 800           1 800          2 000       2 000
      Variable cost                     -1 200      1 080           1 200          1 320       1 200
      Contribution                         800        720              600           680         800
      Fixed cost                          -500        500              500           500         550
      Profit                               300        220              100           180         250
      Effect on profit - Sensitivity                 -27%             -67%         -40%          -17%
                                                    80/300         200/300 120/300 50/300
The profit is most sensitive (largest decrease in profit) to changes in selling price, then variable cost, sales volume
and lastly fixed cost.

The above sensitivity test calculations could be shortened as follows:
                                                      Vol-10%          SP-10%     VC+10%       FC+10%
     Profit before changes in elements      300         300             300        300
     10% change in contribution/element                  80             200        120            50
      Profit                                         220             100         180          250
      Effect on profit – Sensitivity (80/300)       -27%            -67%         -40%       -17%

Main limitation of the sensitivity analysis: Only one variable is changed at a time when, in reality, management
requires the implications of simultaneous changes in a number of variables (spreadsheet model/analysis). See
scenario analysis in later weeks.

CVP analysis applied to absorption costing: The results of decisions made using variable costing based CVP
analysis are not reflected in the absorption costing reporting system if there are changes in inventory levels.

Absorption costing breakeven point formula: Assume either a:
    • production level (see below) and determine breakeven units or
    • level of sales (less appropriate) and determine breakeven units
BE = [All FC – Prod. FC recovered] / [Contr. pu – Production FC per unit]
Example: Assume a selling price of R10 pu, variable cost of R6 pu, total fixed cost of R400 000 and 150 000 units
produced (as budgeted). Budgeted production FC were R300 000. What is the breakeven point?
Solution: FOAR R300 000/150 000 = R2 and budgeted prod. FC of R300 000 were absorbed as actual production
was 150 000 units. Thus:
 BE = [All FC – Prod. FC recovered] / [Contr. pu – Production FC per unit]
    = (400 000 – 300 000)/(10-6 -2) = 50 000 units

A target profit can be added to the fixed costs in the above formula and a variable profit factor per unit
deducted from the contribution per unit.

Financial performance evaluation (QE : PV%, FC% of revenue/total cost, Operating profit % before/after
HO costs, Breakeven, Margin of safety, other ratios/component percentages.

Chapter 9 - Relevant costing (Level 3)
Introduction: Relevant costs and revenues are changes (incremental/ marginal) resulting from non-routine
decisions such as:
• Special pricing – Consider (all) costs and revenues for all alternatives under consideration or exclude the
    irrelevant costs and revenues because they are identical for both alternatives or consider
    differential/incremental relevant costs/revenues. Also consider:
         o effects of short term low priced sales on future selling prices,
         o spare capacity in short term and long term (if special prices will continue). Must meet orders at
             normal selling prices and avoid decline in demand/costly reduction in capacity,
         o the opportunity cost of resources used for the special order and
         o unavoidable/committed fixed costs are irrelevant.
• Labour or capital intensive production,
• Product mix when short term capacity constraints exist – Rank products to maximise contribution per unit
    of the limiting factor,
• Equipment replacement - long term decision (capital budgeting in week 17). Book value and depreciation of
    old equipment are not relevant to the replace decision. Fair value of old equipment is relevant to its own
    continuation. Separate considerations - Keep, replace or discontinue operation).
• Make or buy/outsource: Compare cost to buy to own production cost. Consider incremental revenue of
    alternative uses if capacity is released.
• Discontinuation options for product or part of operations: Consider relevant cost savings less present
    contribution to committed fixed cost.

Relevant costs/revenues ultimately result in cash out- or inflows (not allocations) .
• Past/sunk costs (e.g. depreciation and allocated committed FC and VC without an alternative use/NRV (e.g.
   raw material, temporary spare labour/machine capacity) are not incremental cash flows and irrelevant.
• Future costs/revenues are relevant if they represent a present obligation/ commitment which will result in
   future cash out or inflows.
• Opportunity (sacrifices or saving of) costs/revenues have alternative use/NRV.

Qualitative factors: Important considerations are not always expressed in monetary terms (quantified) and should
not be ignored e.g. accuracy of data or a decline in product quality/customer satisfaction/support, local or
export market, entity reputation, supplier support and quality of supplies, staff morale/health and capacity

Remember: When fixed costs will change in the long term as a result of a decision, they will become relevant
costs/savings. Variable costs which are identical for all alternatives are not relevant (can be ignored).


TOC is used to maximise operating profit by removing bottlenecks (limiting capacity/throughput) or maximise
(i.e. ranking) throughput contribution per bottleneck hour/usage (TC pbh):
      TC pbh = (SP pu – RM pu)/Bottleneck hour pu     (other costs are considered fixed in ST)

Throughput accounting (TA): Ranks products according to a Throughput Accounting Ratio (TAR) :
   TAR = TC pbh/Factory OH cost ph
               Factory OH cost ph = Factory OH cost / Total key resource hours
Note: TAC pu rankings = TAR ranking (both share a common denominator i.e cost per factory hour).

Example (9.34): Products                           A                              B
       Selling price                             R60                            R70
       Product cost: Raw material                   2                             40
                     Variable prod. OH             28                              4
       Contribution                              R30                            R26
       Fixed production OH pu                    R10                            R 6
       Total production hrs pu                   0,25hrs                        0,15hrs
       Bottleneck dept. hrs pu (Avail. 3075 hrs) 0,02hrs                        0,015hrs
       Budgeted production units                 120 000                        45 000
Required: Maximising profit

Traditional ranking:
Contr. per constraint i.e. bottleneck hr pu          R30/0,02                   R26/0,015
                                                     = R1500                    = R1733 maximise B
Theory of Constraint (TOC):
 TC bph = (SPpu - Direct mat cost pu)/Hrs pu         R58/0,2                    R30/0,15
                                                     =R2900 maximise A          R2000
Throughput Accounting (TAR):
 Total factory cost per bottleneck hour: [(R38x120000)+(R10x45000)]/3075 hrs = R1629,27 ph
 TARatio = TC pbh/Factory OH ph              R2900/1629,27        R2000/1629,27
                                             =1,78 maximise A     =1,225

Example: Relevant Costing - Intermediate S08

The following cost estimate had been prepared for a once-off furniture order, in excess of normal budgeted production:

                                                                                  Note                R
Direct materials:
Wood                              10m2 at R50 m2                                    1               500
Metal fittings                                                                      2               200
Direct labour
Skilled                           25 hours @ R80.00 per hour                        3             2 000
Unskilled                         10 hours @ R50.00 per hour                        4               500
Overheads                         35 hours @ R100.00 per hour                       5             3 500
Design                                                                              6             1 000
                                                                                                  7 700
Administration overhead           15% of production cost                            7             1 155

                                                                                                      8 855
Profit @ 20% of total cost                                                             8              1 771
Selling price                                                                                        10 26

1   The wood used for this order is in stock, cost R20per m2 (Market price is R50 per m2 and sale value is R40 per m2) and is
    not regularly used.
2   Metal fittings are in stock at R200 and are regularly used in products. The replacement cost is R250.
3   Skilled labour is paid R80 per hour and must work overtime at time and a half for the above order, unless the production of
    another product, that requires 2 hours of skilled labour, sells at R800 and has variable costs of R500 per unit, is reduced.
4   No further unskilled labour needs to be hired to complete the above order.
5   Overheads include electricity for machines at R8 per hour. The above order requires 35 hours of machining. Other overheads
    are not directly identifiable with this job.
6   Design time represents the normal working hours spent by full time employees to design the furniture for this order.
7   20% is normally added to the production cost to cover normal administration costs.
8   Products are normally priced at cost plus 20%.

• Define ‘relevant cost’, ‘opportunity cost’ and ‘discretionary cost’, and state the usefulness of these cost classifications to
• Prepare the lowest cost estimate for the above order. Give reasons for including/excluding all the given costs.
• Should the order be accepted at a total sales value of R5000? (discuss quantitative and qualitative factors).


        Cost estimate:                                                                                            R

         Wood                10 m2 @ R40m2 - Relevant as it is the opportunity cost.                            400
                              - R20m2 not relevant as it is a sunk cost.
                             - R50m2 not relevant wood will not be replaced.
        Metal fittings       R250 relevant as it is the replacement cost and fittings are regularly used.       250
                              - R200 not relevant as stock will be replaced.
         Skilled labour      25 hours @ R120 p\h relevant as work will be done in overtime.                     3 00
                              - R80 is not relevant/normal time rate. Will work has overtime
                              - R150 opportunity cost is not relevant. It is cheaper to work overtime.
         Unskilled           10 hours @ R0 relevant as there is spare capacity in this labour category.            0
                              - R50 p\h is not relevant and not an incremental cost.
        Overhead             35 hours @ R8 is relevant/overhead directly identified with the job.               280
                              - R92 of the overhead rate of R100 p/h is not incremental cost.
        Design               The design cost is a sunk cost and is not relevant.                                   0
        Admin costs          Not relevant as these costs are already incurred/sunk.                                0
        Profit               A lowest cost estimate excludes profit.                                               0
        Lowest estimate                                                                                       3 930

Chapter 10 – Activity Based Costing (Assessed at level 3)
ABC is an absorption costing system that provides more accurate product costs by allocating indirect costs (e.g.
overheads) to products by means of a variety of cause-effect cost drivers.

Need for ABC: The % indirect cost is significant and increasing. Relevant costs are required to identify
potentially unprofitable products in highly complex environments and numerous product lines on a continuous
basis. Resources are shared by many products.

Benefits of ABC
• ABC requires a better understanding of costs and cost drivers and can be expected to enhance cost
   awareness and promote control over costs. The extent of cost savings and other benefits from improved
   product costing resulting from ABC may not be measurable, but their existence cannot logically be denied.
• Enterprises require more sophisticated and accurate full product/contract costs when selling prices/contract
   tenders are prepared on a cost plus basis or a high proportion of overheads are independent of
   production volumes and a variety of products are produced.
• ABC is flexible and can be extended to determine cost per customer and for management and produces
   reliable product costs which are not ideal for short term decisions, but, in the long term, is useful for strategic
• An enterprise’s product range can be improved when new product costs are determined more accurately
   and less viable products (i.e. demand and profitability) are discontinued. Low-volume products are
   correctly allocated a higher proportion of costs (e.g. machine set-up and packing) while high volume
   products are justifiably allocated a lower proportion of costs.

Traditionally indirect costs were assigned to production and service departments based on a few volume
based cost drivers (e.g. machine and/or direct labour hours) resulting in the under-costing of low volume
ABC allocates costs to a variety of cost pools (e.g. production scheduling, machine set-up, materials handling and
materials purchases) and, using a wider variety of volume (e.g. hours, %, runs, batches and no. of orders) and
non-production volume (e.g. m2, %, kilowatts, no. of employees and value of PPE) based cost drivers, to
individual products.

Designing ABC systems:
• Identify major activities (cost pools) at unit/batch/product/facility level (e.g. material ordering cost),
• Assign costs to each activity/pool on cause-effect relationships (e.g. telephone, wages, office, etc)
• Identify measurable activity/resource based cost driver (e.g. no. of orders) for each activity and
• Assign costs to individual products based on cost driver usage (e.g. ordering cost/no. of orders).

Sample activities and cost drivers:
       Activity cost pool                                         Cost driver
   Production set-up cost                                  number of production runs
   Goods received cost                                     number of goods received transactions
   Quality control cost                                    number of quality inspections
   Raw material sourcing cost                              number of requests for raw material
   Sales salary cost                                       number of salesmen
   Sales delivery cost                                     number of sales orders
   Factory depreciation                                    number of machine hours/value of assets
   Product design                                          number of design hours
   Rates, Insurance, Electricity and Overheads             number of machine hours/floor space

Cost driver/denominator: Budgeted (problem: hides unused capacity and low demand will increase cost and SP
when a lower SP would stimulate higher sales volume) or preferred Practical capacity (does not fluctuate annually
- more consistent costing/SP). (Also unlikely theoretical capacity and IAS’s normal production level under AC/VC)

Cost driver/denominator: Budgeted capacity focuses on resource usage, hiding unused capacity. Also note that
low demand will increase cost and SP when a lower SP would stimulate higher sales volume. Practical capacity is
preferred (does not fluctuate annually - more consistent costing/SP). (Theoretical capacity is unlikely)(IAS’s
requires higher of normal or actual production level)

Resource consumption cost-models:
ABC focuses on resources consumed/ used, excluding unused/available resources.
ABC can be used to measure the cost of unused capacity (practical capacity [supplied] minus actual capacity
x recovery rate[FC]). The recovery rate = expected fixed costs/ practical capacity for the year. This indicates the
potential saving of excess resources/capacity.

Unused capacity arises with committed/inflexible resources acquired in discrete (constant) amounts in advance.

•   Resource supply cannot be adjusted continually/in ST to match resource usage.
•   Management decisions can change activity usage (e.g. discontinuation decisions reduce resource
    usage/increase unused capacity).

Resource consumption models – Example 10.2
Resources supplied: 10 staff at R30 000 per year          = R300 000 annual activity cost
Quantity of cost driver supplied pa: 1 500 orders per employee x 10= 15 000 orders
Cost driver = Number of orders processed Cost per order (R300 000/15000) = R20
Resources used: Actual annual number of orders (used) = 13 000
Cost of resources used to parts/materials = R260 000 (13 000*R20)
Cost of unused capacity = Resources supplied (15000) - Resources used (13000) orders = 2 000 orders
Cost of unused orders at R20 per order         = R40 000 (2 000*R20)

ABC profitability analysis: ABC product costs are not directly suitable for decision making, but more readily
reveal potential unprofitable products. For product mix and discontinuation decisions three contribution levels
should be analysed:
   • unit level contribution for each product (i.e. sales minus cost of unit level activities),
   • batch level contribution (i.e. unit level contribution minus batch related costs),
   • product sustaining contribution (i.e. batch level contribution minus product sustaining costs).
Two more contribution levels (after Brand sustaining expenses and product-line sustaining expenses) may be

See review problem 10.26 on page 400 to compare traditional and ABC cost allocations.

Chapter 11 – Pricing Decisions (Assessed at level 3, except target based pricing [level 2]) and Profitability
Analysis [level 3])

Price setters/takers: Price setters produce highly customised products and need accurate product cost
information to set selling prices. Price takers produce standard/commoditised products (i.e. not unique or
different e.g. maize meal. milk, gold, oil and petrol) and accept/take prices set by the market and need accurate
product cost information for product profitability and product mix decisions.

The decision time horizon (short and long-term) determines the cost information that is relevant for product
pricing or output mix decisions.

For short term decisions many costs are likely to be fixed and irrelevant and only incremental costs of accepting
an order must be recovered in the selling price provided:
     • spare capacity is available for all the resources used to fulfil the order – Opportunity costs,
     • the order is once-off (not likely to be repeated/minimised effect on normal operations) and
     • spare capacity will be released by the time that more profitable opportunities become available.
In the long-run virtually all costs are variable in nature and pricing decisions must be based on accurate full cost
information (i.e. ABC).

A price taker firm facing short- and long-run product–mix decisions: Periodic and ABC hierarchical profitability
analysis should be carried out to determine which products to sell.

Economic theory: Economic theory assumes rational enterprises prefer selling prices that maximise profits
(most return with least risk/soonest) and that prices/profits can be estimated at each potential demand level
enabling profit maximisation decisions (where marginal revenue equals marginal cost [see economist’s
revenue/cost graph]) when the optimum output is sold at the optimum price. Some difficulties include:
    • enterprises have multiple products and different demand curves,
    • various factors, apart from pricing, affect demand e.g. quality, packaging, advertising and credit terms,
    • marginal cost curves for individual products are complicated by joint/indirect costs.

Selling prices should be maximised when demand is inelastic (vary little at varying prices).

Facility sustaining costs are incurred to support the organisation as a whole and may either:
   • be excluded from individual products costs or
   • included in product costs to be recovered in revenue/SP in the long term (cost-plus pricing), but not
        reported as production costs.

Pricing non-customized products: Market leaders use estimated sales volume/ demand to set production
volumes/costs and add a profit (cost plus) to determine selling prices. As selling prices affect demand it is
necessary to set selling prices for a range of potential demands.

Cost-plus pricing: Cost normally includes direct variable costs, total direct and indirect costs (overheads) and
apportioned organisational costs. A higher CV% is required to cover costs excluded from the cost base.
   • price-demand relationship is ignored,
   • production volume/budget is dependent on sales demand (problem: When demand/volume is low
        costs/prices increase when lower selling prices would stimulate demand/volumes),
   • if actual demand falls below estimated demand a loss may result even though selling prices were set on
        full costs.
 Cost plus pricing is useful:
    • when a wide variety of products is sold and demand curves are costly/ time consuming for unimportant
    • to predict the prices when industry/competitor cost structures are similar and may encourage price
 Cost plus selling prices are not ideal, and ignores market prices.

QE 2009 P2Q3: Identify and discuss any areas for improvement in the company’s existing pricing procedure of
generally marking up the estimated absorption manufacturing cost by 30% to determine the selling price.
Pricing procedure
• Relevant cost (hedged replacement cost of imports) should be considered for engines rather than the irrelevant
    historic cost per unit of R16 500. A standard cost could be developed from budgeted cost of R15 375 or actual
    cost of R17 000. Could also use the disposal value or opportunity cost if no information is available.
• Detailed supplier quotes for material components appear adequate.
• Variable costs appear to be an estimate based on the 2009 annual budget [R580 per unit]. No supporting
    calculation/proper allocation was given.
• Recovery of direct labour & other fixed overheads: The recovery of 27% of material cost is conservative
    compared to budget (21,9%), while the actual costs for 2009 was 20,4% of material cost. Increasing recoveries
    due to increases in material costs may not be appropriate as fixed costs do not increase with changes in
    production volume and material price increases. Recoveries should be based on normal production volumes and
    capacity and an appropriate cost driver (activity based costing) used.
Pricing policy
• Cost plus mark up policy appears to work in the company’s case, due to its actual GP% in 2009 of 24,5%, higher
    than theoretical GP% of 23,1%.
• The company should investigate the use of target costing.
• Competitors selling prices for similar products should be considered as well as the impact of increasing prices on
    customer orders. Is the company strategy differentiator (price setter) or a price taker. Elasticity of demand should
    be considered (price sensitivity).

Target costing is the inverse of the cost plus pricing and may be used to price non-customized products. The
required profit is deducted from the maximum market selling price to arrive at a target cost (limit). Unlike cost-
plus pricing it fully considers marketing factors.

Pricing policies: Management may choose a:
• price-skimming - highest SP in inelastic market or high demand earlier in product life cycle/few substitutes)
• price penetration policy - low initial prices to gain market share when close substitutes exist or when market
    is easy to enter.

Business goals: Short term: Breakeven and earn some NP;
Medium term : Maximise NP (↑SP&Units; ↓VC&FC&Tax)                 Long term: Maximise ROI (↑NP; ↓Investment)
Customer profitability analysis: ABC uses a hierarchical structure similar to product profitability analysis to identify
important customers and the price to charge for customer services based on the resources they consumed.

See Tutorial 11.21 – AC versus VC pricing
   Price elasticity of demand (reaction to price changes) is a major consideration
   •    Cost structures at varying output levels help to maximise profits with optimum price (i.e. Marginal
       revenue=marginal cost),
   •    AC results in SP being a function of overhead apportionment/ recovery appropriate at one level of output
       (i.e. ignoring the effects of changes in output on total costs/SP),
   •    See disadvantages of cost-plus pricing above,
   •    Advantage of AC: All production costs are included and recovered in SP
   •    Relevant (incremental) costing is preferred to AC e.g. The use of production facilities entails an
       opportunity cost from the alternative use of those facilities

Chapter 12 - Risk and Uncertainty (assessed at level 1)

Ignore maximin, maximax and regret criteria (pages 463 to 464) and Appendix 12.1 CVP analysis and uncertainty
(pages 470 to 474).

A decision- making model (p 452)
A structured approach to problem solving under conditions of uncertainty (see figure 2.1 on p453):
    1. identify the objective, for example, maximise profits.
    2. search for alternative courses of action which will enable the objective to be achieved.
    3. identify uncontrollable factors that may occur for each alternative, also known as events or states of nature.
    4. list and measure possible different outcomes for the various combinations of actions and events.
    5. select a course of action.
A decision tree (see below) is an illustrative diagram of the elements of the decision making model.

Buying perfect and imperfect information (p 463)
When faced with uncertain information one considers the costs/benefits of acquiring further information to
eliminate the uncertainty, i.e. perfect information. The maximum amount worth paying for perfect information
equals the expected value with perfect information less the expected value without that information. (See Q12.19

A probability (objective=statistical with decimal >0<1) expresses the likelihood of a particular outcome. E.g. 0,3 =
30%. The probability of a 6 with one throw of a dice: 1/6

Joint probability (all occurring/together): Assume two probable results ‘A’ and ‘B’ with probabilities of 40% and
30% respectively. Joint probability: PA x PB = 12%;
Getting two sixes in a row: 1/6 x 1/6 = 1/36 (1/6 ). Getting a six followed by any of 1 to 5: 1/6 x 5/6 = 5/36

Probability of either outcome occurring: PA + PB = 70%. Dice:1 or 6 in one throw = 1/6+1/6 = 2/6

Probability that neither A or B occur: 1 - PA + PB = 1=0,4-0,3 = 30%. Neither a 6 or 1: 6/6-1/6-1/6 = 4/6
Probability distribution (∑n=1) lists all possible outcomes (favourable or unfavourable [+ & -]) for an event. E.g.
0,3 + 0,5 + 0,2 = 1 Dice: 1 = 1/6; 2 = 1/6; etc to get 6/6 or 1

Continuous distribution: A mean/average outcome/value is available
Discrete distribution: No mean/average outcome (colour of cars) is available

                               Continuous distribution


                          30                        Mean
                          20               σ   σ                    10
                               1   3   5   7   9 11 13 15 17

        1 Std Deviation = 68% of deviations (2 Std Dev = 95%)

Expected value/mean ( ) of a distribution = ∑(Rn x Pn) if action is repeated many times.

Measure of uncertainty = Variance (σ2) = ∑[R-              ]2P) is the dispersion of possible outcomes on both sides of the

Example: Calculate the Variance (σ2) and Standard Deviation (σ) of the following sales unit distribution:
20% prob. salesR 25; 60%sales R30 and 2o% sales will be R35
Sales Probability Probable Mean Variation             Variation²        Probability     Variance
 25       0,2           5       30        -5           25                 0,2              5
 30       0,6          18       30         0             0                0,6              -
 35       0,2           7       30         5           25                 0,2              5
Expected sales/Mean 30 ( )                                              Variance σ2 = 10
                                                              Standard deviation(σ) √10 = 3,1623

Risk takers prefer maximum Risk and Return. Risk neutral/indifferent investors are not as aggressive as risk
takers and will accept reasonable degrees of risk. Risk averse investors prefer the lower return of lower risk

Example: Choose between alternative investments (A and B) with the following possible outcomes (Each
economic state has a 1/3rd chance of occurring):    A             B
                      Recession                   240              0
                      Normal                      300            300
                      Boom                        360            600

Solution: Expected return( )       A                B
  Recession (,333)                80                 0
  Normal      (,333)             100              100
  Boom        (,334)             120              200
       Expected value ( )        300              300
Note: A & B have the same mean outcome but different levels of risk.
       - A risk-seeker/taker will prefer B (higher risk and possible return)
       - A risk-averter will prefer A.
       - A risk-neutral/indifferent individual will be indifferent between A and B.

Do not use a single expected/mean sales value/volume to calculate a probable overall profit. Use all probable
sales or Si x to fist calculate a separate probable net profit (Q12.17 [c]) then apply each profit/loss’ own probability or
Pi to determine the overall/mean outcome (profit/loss) (∑[Sn x Pn])(see decision tree example below).
                                                        .                                                    .
Measurement of risk: Risk is expressed as σ or √σ2 (i.e. dispersion of possible outcomes = √∑[R- ] P and the
coefficient of variation(CV) (σ/R, risk per rand of return) allows the comparison of the relative risk of different
Z-value [z = (X-ẍ)/σ]: Z-value calculates the number of standard deviations of a value (X) from the mean (ẍ)
and indicates the chance (% probability) that a variable (i.e. sales or profit) will statistically occur or that the
variable will fall within a specified range (between two different points). According to the table a z-value of 1 (one
σ from the mean) covers 0,3413 or 34,13% of the area on one side of the mean, thus 68,26% of the total area
(both sides). Two σ’s from the mean covers some 98% of the total area.

Interrelationship between risk and return:
Progressively determine the best investment proposition below, reviewing your opinion as new information is
                                                                    Project A         Project B
        Risk (σ)(Deviation of returns)                              R1 000            R2 000
Opinion: In isolation, B seems more risky than B.
        Expected/mean return ( )                                    R10 000           R100 000
Opinion: In isolation B earns the most.
        Coefficient of Variation (CV)                               10% (R1/10)       2% (R2/100)
Opinion: B has a better CV (Risk per R1 return) and seems the best option.
        Investment made                                             R50 000            R1million
        ROI                                                         20% (R10/50) 10% (R100/1000)
Correct decision: A is 5 times (10%/2%) more risky than B, yet it offers a return twice (20%/10%) that of B.
Investors’ risk attitudes will select the preferred investment. A risk taker will invest in A while a risk averse investor
would probably prefer to invest in B.

Decision tree: The most beneficial outcome of different distributions (∑ each = 1) are chosen by backward
induction (rolled back). Study the comprehensive decision tree example on pages 466 to 468.

Decision trees/diagrams use cumulative probabilities and
   • ensures that all outcomes are considered in proportion of it’s probability,
   • the time value of money can be incorporated in the form of NPV outcomes,
   • risk attitudes can be compared with the cumulative probability of each alternative.

Tip: When unstructured/chaotic data is presented in the question, first structure/ organise the data per
category/logical sequence/patterns to highlight different options and outcomes as in Q12.22.

Note the weaknesses of decision trees.

Example: Management can develop and market a new product or continue as is. Development costs will be about
R180 000 and the chance of success is 75%. If successful the outcome, after development cost, may be a profit as
high as R540 000 (40% chance) or as low as R100 000 (30% chance) and, if a failure, a loss of R400 000 (30%
chance). Draw a decision tree for the above.

Illustrative example – Decision tree Question 10 - 1

An investors wants to start either a small plant (if demand is low - 25% chance) or large plant (if demand is high –
75% chance).
                                                                    Small plant (1or 2)     Large plant
       If demand is low (m=million) and one plant only              R+3m profit             R-3m (loss)
       If demand is high and one plant only                         R+4m profit             R+7m profit
       Chance of competing plant if demand high                     60%                     0%
       High demand & 2 small plants–30% chance 2 plant result R+8m profit
       High demand 70% chance 2 small plant result                  R-2m loss
       No competition 55% chance two plants result                  R+8m profit
       No competition & one expanded/new plant – 55% result R+6,5m profit
       No competition & 2 or new plant fail – expected result R+2,5m profit

Required: Draw a decision tree and determine the highest expected profit. Also determine the course that a
risk averse investor would prefer.

Suggested solution       Q10 – 1 Part A

Conclusion: Choose Large plant as this choice has a value of R4,5 Million which is 0,3 Million higher than the
Small plant.

Buying perfect and imperfect information:
Costs of eliminating the uncertainty versus the benefits. Thus maximum cost = Increase in

Portfolio analysis: Diversification spreads/reduces risk if investments/projects are not perfectly positively
correlated (respond differently to same circumstances) and overall variability of cash flows is reduced. One must
consider the extent to which each investment/project affects the overall risk of the entity.

              A v era g e an n u al
              s ta n d a rd d ev ia tio n (% )

                                                 D iv er sifia b le ris k    /Unsystematic

                                                                   N o n d iv ers ifiab le     /Systematic

                                                                                                     N u m b e r o f sh a re s
                            1           10              20           30          40          10 00   in p o r tfo lio

Example: Negatively correlated products
Season               Coat         Ice-cream      Combined
                     Sales        Sales           activities
                       R               R            R
Summer             –40 000          +60 000        +20 000
Winter             +60 000          –40 000        +20 000
Each activity is risky/loss on its own, but combined risk is reduced/eliminated.

Chapter 15 - BUDGETING PROCESS – Intermediate only
Advanced - Activity-based budgeting (ABB)
Conventional budgeting: Unfit for activities that consume resources not per output volume of products,
• produce incremental budgets, merely authorizes spending levels and views non-unit level activity cost as fixed,

ABB aims to authorize only resources essential to meet budgeted production and sales volumes.
ABB reverses the ABC process: Essential cost driver/activity (e.g. Process 5000 sales orders) and resource
needs (e.g. 0,5 hr per order = 2500 labour hours /1500 hrs per person pa = 2 persons). Thus cost pool (i.e.
budget) includes salary of 2 persons.

Periodically actual results are compared with an adjusted (flexible) budget.
Budgeted activity for processing orders                  = 2,800 orders
Orders processed per person                              = 600
Resources required 2800/600                              = 4,67 persons
Resources supplied (practical capacity for 3000 orders)= 5 persons
Employment costs (R25,000 per person pa x 5)             = R125,000
Cost driver rate (R125,000/3,000 orders)                 = R41,67
Actual orders processed for the period                   = 2,500 orders
Performance report:
Flexed budget (2,500 ×R41,67 )                           = R104,175
Budgeted unused capacity (3,000 — 2,800)× R41,67         =    8,334
Unplanned unused capacity (2,800 –2,500)× R41,67         = 12,491

Chapters 18 & 19 - STANDARD COSTING
Chapters 18

Sales and cost variances: There are two basic variances for sales, materials, labour and variable/fixed overheads:
    • Price/rate/expenditure variance determined by one standard and two actuals, as follows:
        (Standard – Actual Price/ rate/expenditure) x Actual Volume sold/quantity purchased/hours used
    •   Volume/quantity/usage or efficiency variance determined by one actual and two standards as follows:
           (Standard cost for actual production volume – Actual Volume/quantity/usage) x Standard Price/rate/expenditure
Two exceptions (Budgeted replaces Standard) :
    • The Sales volume variance is: (Budgeted less Actual sales volume) x Budgeted contr. (VC) or Contr.pu – FOAR (AC)
    • Fixed overhead variances: Expenditure variance = Budgeted fixed cost less Actual fixed cost
                                : Volume variance(Rate per unit) = (Budgeted prod. units – Actual prod. units)FOAR per unit
                                : Volume variance(Rate per Hour) = (Budgeted hrs – Std hrs for actual prod)FOAR per hour
A variable standard costing system has only one fixed overhead variance, namely the fixed overhead expenditure variance.

Fixed overheads variances: FOAR per unit(only one product) produced: Budgeted FC R120000 (Actual R116000)
Budgeted production 10 000 units (Actual 9 000 units)         FOAR 120000/10000 = R12 pu
             Fixed production overhead control account (R’000)
Actual cost incurred                    116 Absorbed (or std) cost              108
                                                (actual Prod units x FOAR
                                                (9 000 units x R12)

                                                Under-absorbed cost                  8
                                         116                                       116

Expenditure variance: Budgeted cost – Actual cost = R120 000 – 116 000 =              R 4 000 F
Volume variance: (Budgeted production – actual production)FOAR = (10 000 – 9 000)12 = R12 000 A
                                           Total variance                             R 8 000 A

Fixed overheads variances: FOAR per std production hour: Budgeted hrs 30 000 for 10000 units
New FOAR: R120000/30000 = R4 per hour
             Fixed production overhead control account (R’000)
Actual cost incurred                    116 Absorbed (or std) cost                   108
                                                (Std hrs for Actual Prod. – Actual hrs)FOAR
                                                (9 000 units x 3 hours x R4)
                                                Under-absorbed cost                    8
                                         116                                         116

Expenditure variance as above                                                         R 4 000 F
Volume variance = (budgeted hrs – Std hrs for actual prod.)FOAR =[30000– (9 000x3)]4= R12 000 A

Fixed overhead capacity/efficiency variances: Fixed costs are sunk costs that do not change with production volumes or
efficiency of production. As a result separate fixed overhead capacity and efficiency variances are not considered
meaningful and are seldom calculated in practice. These variances are more meaningfully combined into a single volume
         Fixed overhead capacity variance: [Budgeted machine hours – Actual machine hours] x FOARph
         Fixed overhead efficiency variance: [Std machine hrs of actual output – Actual machine hours] x FOAR
         FOH volume variance: [Budgeted hrs – Std hrs for Act. Output) x FOAR

Detailed volume/quantity/usage variances: When more than one product is sold as substitutes or more than one raw material
is used and material is interchangeable, the volume/quantity/usage variance may be split into separate mix and yield variances
as follows (from example 19.2, p783):

Budgeted Sales/Mix               Standard       Mix     Actual Mix &
                                 (Actual sales)         Sales
X:     8 000 (40%)                  8 800 (40%)          6 000Dif@SM
Y:     7 000 (35%)                  7 700 (35%)          7 000 “
Z:    5 000 (25%)                   5 500 (25%)          9 000 “
     25 000                        22 000               22 000

                     Quantity                  Mix
                     Variance                Variance


Material Mix and Yield
Mix variance: (Standard mix for total actual sales/quantity/usage - Actual mix)Standard sale price per unit
           o Using the data from example 19.1 (page 779), the material mix variance is calculated as follows:
                       Standard Mix              Actual Mix         Variance      Std Pce     Variance
          X: 50% x 100 000 = 50 000                53 000           3 000 A       R7          21 000 A
          Y: 30% x 100 000 = 30 000                28 000           2 000 F       R5          10 000 F
          Z: 20% x 100 000 = 20 000                19 000           1 000 F       R2            2 000 F
          Total Actual usage 100 000             100 000            Nil                         9 000 A

Yield/Usage variance: Material: (Standard mix and usage for actual prod. - Standard mix for Actual usage) x Std price pu
           Budgeted usage (std mix)       Actual usage (std mix)                  Variance
        X: 50% x 103 000 = 51 500         50% x 100 000 = 50 000 1500F x R7= R10 500
        Y: 30% x 103 000 = 30 900         30% x 100 000 = 30 000 900F x R5= 4 500
        Z: 20% x 103 000 = 20 600         20% x 100 000 = 20 000 600F x R2= 1 200
              Total        103 000                         100 000 as before      R16 200F

Materials variances summary:
       Price variance (calculated as normal)          R12 200 A
       Mix variance               R 9 000 A
       Yield variance             R16 200 F           R 7 200 F Usage variance
       Total variance                                 R 5 000 A

         When more than one type of labour (skilled, semi-skilled and unskilled) is used, separate labour mix and efficiency
         variances can be calculated as demonstrated above.

Sales Mix and Qty variances
                      Budgeted Sales/Mix1                Standard       Mix2     Actual Mix &
                                                         (Actual sales)          Sales
                        X:     8 000 (40%)               8800 (40%)               6 000
                        Y:     7 000 (35%)                  7 700 (35%)           7 000
                        Z:    5 000 (25%)                   5 500 (25%)           9 000
                             25 000                        22 000                22 000

                                             Quantity                            Mix
                                             Variance                          Variance

                      Budgeted mix = standard mix for budgeted volume
                      Standard mix = standard mix for actual volume

Sales quantity variance split into two further variances (if industry sales volumes are available).
• Market size variance – Keep the firm’s market share constant (say 10%). If the total market grows by 75 000 units, the
    firm’s sales would increase by 10% (i.e. 7 500 units at a contribution of R14,45pu = R108 375).
• Market share variance – Keep the industry market size constant (say 275 000 units). If the firm’s market share falls by
    2%, its sales decrease by 2% of the market size of 275 000 units (i.e. 5 500 units at R14,45 = R79 475).

Thus, the sales quantity variance comprises:          Units           Contribution
                  Market size variance                7 500 F         108 375 F
                  Market share variance               5 500 A          79 475 A
                  Sales quantity variance             2 000 F          28 900 F

Criticisms of sales volume/margin variances
• Sales price and volume are mostly interdependent, so it serves no purpose to differentiate these effects, though one
    could use the variance information sensibly, aware of the interrelationships,
• Different sales weighting methods (i.e. by units or by revenue) result in different sales mixes resulting in different mix
    and quantity variances. It is better to use the firm’s target sales mix,
• Though firms sell a range of different products with different margins, the products themselves are independent of
    one another (i.e. no planned sales mix) and there is no point in calculating a mix and quantity variance (i.e. rather use a
    single volume variance by product).

Recording standard costs in the accounts
Standard values inventory standard cost (i.e. FIFO, LIFO or WA now irrelevant). IAS allows standard cost stock values if it
approximates actual cost. Drury suggests that all variances be eliminated before transactions are recorded in the work-in-
progress control account (i.e. all entries in WIP account at standard). Thus, individual cost control accounts (i.e. material,
labour, etc) are credited at standard costs and resulting variances from actual costs (debits) are either written off as period
variances in the income statement or allocated between stock values and cost of goods sold per p794):
                                                                        R                 R
         Debit raw material stock control account                      6 000}
         Debit work-in-progress stock control account                  3 000}R13 500, adjusting standard cost to actual
         Debit finished goods stock control account                    4 500}
         Debit Cost of goods sold                                     16 500
                  Credit material price variance account                                30 000

Drury suggests (p795) that, at the beginning of the new accounting period, the above stock entries of R13500 be reversed to
restore stock values to standard.

Investigation (cost control) of variances
Reported variances need to be investigated (if material in R or %) if expected benefits will exceed the likely cost of
investigation and correction. Possible causes of variances are listed and discussed on pp802/3.

Out-of-date standards and recording errors must be identified and excluded from variance. It serves no purpose to
investigation variances resulting from random or uncontrollable factors, as opposed to variances caused by out-of-control
operations which need to be corrected.

Criticisms of standard costing
Usefulness is decreasing because:
    • Cost structure are changing
    • Inconsistent with modern management approaches - Ongoing attempts to reduce inventories/costs and improve
         product/service quality are impeded (i.e. price variances lessens focus on raw material quality)
    • Over-emphasis on direct labour i.s.o. overhead costs,
    •      Delayed (not online, real time) feedback reporting,
Despite criticisms, standard costing is widely used in practice.

 Exercise - 2009 QE P2 Q3                Labourers          Electricians    Total
 Available production hours
               Budget                    294400             62560           hrs
               Actual                    294400             62560           hrs

 Overtime      Budget                    0                  0               hrs
               Actual                    11600              0               hrs

 Idle time      Budget                     44160              0             hrs
                Actual                     0                  3060          hrs
 Production units                          7820 Bud           8500 Actual
 The electrician labour rate per hour is 3 times that of labourers
 Overtime is paid at time and a half the normal wage rate.

 Labour cost               Budget R      19 283 200
                           Actual R      21 977 120

 Required: Analyse and comment on the labour expense (e.g.
 rates, efficiency, capacity utilisation, idle time and ratios).

 Solution      Exercise - 2009 QE P2 Q3                     Budget          Actual
 Labourer hrs pd A        294400       11600 x1,5           294400          311800
 Electrician hrs pd B     (62560x3)                         187680          187680
 Total hrs paid A+B=C                                       482080          499480
 Wage expense D           +14%                              19283200        21977120
 Labourer rate ph E       = D/E                             R 40            R 44
 Labourer expense F = A x E                                 11776000        13719200
 Electrician wage rate ph             Ex3                   R 120           R 132
 Electrician expense BxE              10.00%                7507200         8257920
 Labourer hrs used A - 44160 Idle &11600OT                  250240          306000
 Lab. hrs used pu         7820        8500                  32              36
 Elec.Hrs used pu         B/3/7820 & B/3-3060/8500          8               7
 Capacity utilised:
 Labourers                (294400-44600)/294400             84.85%
                          (311800-11600/2)/294400                           103.94%
 Electricians             (62560-3060)/62560                100.00%         95.11%

QE 2009 P2Q3: Performance discussion
Wage rates
• Wage rates are 10% higher than budgeted Labour efficiency
• Production personnel worked far less effectively than budgeted. It took on average 36 hours of labour time per
   unit (budget of 32 hours is 12,5% more time). Reasons for deterioration should be investigated. Possible reasons
       o Attempt to earn extra cash by forcing overtime hours
       o Delays/inefficiencies in receiving material components
•  Electricians worked more efficiently than forecast (12,5% less time per unit than budgeted). Budgeted time per
   unit needs to be checked for reasonableness.
Capacity/idle time
• Company is operating at or near capacity at present.
• Production personnel worked overtime in FY2009 to complete 8,500 units.
• The availability of electrician hours was budgeted as a capacity constraint, but they operated more efficiently and
   ended up with idle hours. Reasons for this need to be determined. Current estimated capacity is 95%.
• Company must urgently address the capacity constraints to increase output.
• Production personnel were budgeted to have idle time, but were inefficient using more hours and incurring
   overtime. Investigate and revise future budgets.
Overall comments
• Total direct labour costs were 14% higher than budget.
• Over time costs added to cost overrun (increase of 4% over budgeted cost)
• Manufacturing output was 7,3% higher than forecast and due to budgeted excess production personnel hours no
   additional cost was expected due to higher output, though electrician over time hours would have been required
   per budget.
• On a flexed budget, direct labour costs increased by 15,4%. Flexed budget:
       o Std Lab. hrs (294400-44160)=250240hrs/7820x8500= 272000 hrs
       o Std Electr. hrs 62560/7820 Units x 8500 Units =               204000 hrs 476000 x R40 = 476000 x R40
            and 476000hrs x R40 =R1,904m/R21 977 120 or up by 15,5%
• Wage increases were partially offset by improved efficiency of electricians

NB: For comparison among divisions:
    • Adjust for different business risks (GOSEPTICS & CLAPS) of divisions? Higher risk demand higher target
         returns/costs of capital %.
    •    Value assets at RC (age of FA differ). Older asset base→lower depreciation and NAV→ ↑ROI & ↑RI.
    •    Ensure divisions use same accounting policies. (e.g. depreciation and stock value).
    •    Ensure divisions all lease or own fixed assets. Finance charges are not classifies as operating costs.

QE 2009 P2Q3: Identify and describe four key business risks faced by the company.
• Adverse movements in exchange rate may erode gross margins. The majority of COS comprises imported diesel engines.
   Volatile exchange rate movements will make it difficult to accurately cost orders. Management’s speculation in FEC
   contracts is a major potential risk in view of the Rand’s very volatile behaviour in recent times could cause material financial
• Current capacity constraints (direct labour hours) may cause the loss of key customers and/or market share if customer
   demand is not met or there are delays in filling orders.
• The current economic slowdown in SA may result in lower revenue/reduced profitability and cause liquidity or cash flow
• Lead time on the ordering of diesel engines may cause working capital problems. If demand suddenly declines, a heavy
   investment in engines cannot be immediately converted into cash.
• Electricity supply may normalize in SA and reduce demand for diesel generators.
• New market entrants may emerge with better competing technologies.

ROI: Say OPBIT =A, Sales =B, NAV EOY =C, OPBIT % (A/B) =D, NAV TO(B/C) =E ROI =A/C or DxE

Residual income (is an absolute value, unlike ROI %, does not adjust for relative size of divisions)
Divisional Manager                                            Division

Controllable contribution                                            Divisional contribution
Less: Capital charge on controllable investment (Wacc x NA EOY) Less: capital charge on divisional net assets
Controllable OPBIT exclude arbitrary group interest (finance not operating cost) and HO cost allocations.
Controllable OPBIT include depreciation (controlled operating cost), normal trading exchange gain and other

ROI(%) vs RI (Amount)
ROI is better understood (compare % to inflation rate) and used by mnt/external users,
ROI can be analysed further to pinpoint problem areas e.g. GP margins and working capital management,
RI encourages goal congruent capital expenditure decisions (assess (dis)investment separate from existing returns.
RI is consistent with NPV if LT performance is emphasised (PV of RI over assets’ life = NPV).
RI charges opportunity cost of capital against operating profits (encouraged focus on shareholder value creation).

Economic value added (EVA)
EVA = NOPAT (net operating profit after tax) – CAPITAL CHARGE (WACC X Invested Capital) at beginning of year
Estimated operating cash generated (NOPAT)
         NPAT (per income statement)
         + Non-cash items * (e.g. goodwill, R & D) * don’t add back depreciation (valid operating cost)
         + Interest expense after tax (Finance cost)
         ± Deferred tax for period
Invested Capital BOY: Equity + Liabilities (per Balance Sheet) + PV of non-capitalised leases + Cumulative arbitrary write-off
of intangibles e.g Goodwill, R & D

1.   Divisional profit and ROI, are unlikely to lead to goal congruent (NPV consistent) investment decisions.
2.   If long-term EVA is emphasised, goal congruent decisions will be made.
3.   If short-term EVA is emphasised, incorrect decisions are possible unless managers’ budgets include ST EVA losses.

Long-term Performance Measures               (not in textbook)
ROI, RI and EVA are short-term measures and focuses divisional managers similarly. Two commonly used longer term
measures are measures are Shareholder Value Analysis (SVA) and Market Value Added (MVA).
SVA - In essence, this method is the free cash flow (FCF) valuation technique with seven key value drivers.
MVA: A cumulative measure of wealth creation: MVA = MV of capital employed - BV of capital employed

Comparative analysis performance measures: NB - Advantages & Disadvantages of each performance measure

                   ROCE               ROI               RI                 EVA                 SVA           MVA
Earnings/          OPBIT              PAT               OPBIT –            Taxed               FCF           MVof
Value                                                   Notional           OPBI –              method        debt+Equity
added                                                   interest           interest at                       (Ord. &
                                                                           WACC                              Pref) –BV
                                                                                                             of CE
General            Generally          Generally         More               Discounts           Estimate      Not for
                   accepted           accepted          neutral            taxed RI            7 key         unlisted
                   and                and               and                                    drivers &     entities
                   understood         understood        useful                                 sensitivity
Nature             % return           % return          Income             PV of               PV of         Trend in
                                                        amount             future              FCF –         MV surplus
                                                        after cost         EVA                 long term     over BV-
                                                        of capital         flows               measure       LT
Encourages         No -               No -              Yes-               Yes- taxed          Yes           Yes Market
goal               division           division          wealth             &                   Measures      Assessed
congruency         /manager’s         /manager’s        creation           discounted          wealth        wealth
                   interest           Interest          after cost         wealth              created       created
                                                        of capital         created
Tax                Before tax         After tax         Before           Taxed             Taxed            Taxed
                                                        tax, but         OPBI &            FCF              increase in
                                                        taxed            taxed                              wealth
                                                        WACC             WACC
Time value         No                 No                Yes –            Discounts         Discount         Present MV
of money                                                WACC             EVA pa at         FCF at
considered                                                               WACC              WACC
Comparable         Yes                Yes               No-amount        No                No               No

Week 8 Transfer pricing (Drury Chap 21)(level 3)
Note the purposes (goal congruency, fairly reward managers, maintain managers’ autonomy, move profits).
Primary transfer prices:
• Perfect intermediate market (i.e TD has stable SP and demand): TP = MP- internal cost savings,
• Imperfect or no intermediate market and TD has unused prod. Capacity and operates above BE: TP of TD’s
    marginal cost (MC) will optimise group profit (RD’s NMR>TD’s MC)(NMR=SP-Incr. cost). TD not motivated at MC.
    What about FC and profit? If TP = TD’s AC (AC=LT MC) still no profit. If TP=AC + mark-up the RD is demotivated.
    Negotiated TP is unlikely to result in optimal group output.
• If TD at full prod. capicity: TP = TD’s MC + opportunity cost (Contribution) to free up capacity for RD (see above

Best policy: Optimum (two-part) TP for TD, RD and group? TD’s MC + lump sum (covering TD’s FC & profit). Motivates
TD and RD views lump sum as FC and optimises output/contribution based on VC, thus group goal congruent (RD’s

Use standard MC to prevent the passing on of cost inefficiencies to the RD.

Dual rate transfer pricing system: TD =AC+mark-up; RD=TD’s MC; Overstates divisions’ profits - Seldom used in practice

Week 9 - Cost management and Strategic management accounting – Drury chap 21 (level 1)

Overriding objective is customer satisfaction (product usefulness) to maximise profits.

Traditional Man. Acc: Cost containment focus, now cost reduction – Eliminate activity, perform it more efficiently or
redesign it (do differently) using accounting and other techniques such as:
Cost reduction (profit improvement) techniques: Tear-down analysis and Value and functional analyses

Life Cycle Cost (LCC): Research & Development, Design, Pilot/Main production, After-sales service/Warranties

Example 2008 SQ2: Company has just completed the product planning and design of a new product at a total cost of
R1 000 000. Manufacturing and sales is about to commence and future demand is:
                          Months                  Monthly demand
                          1-10                       200
                          11-20                      500
                          21-30                      750
                          31-70                   1 000
                          71-80                      800
                          81-90                      600
                          Thereafter                 nil
Unit selling prices for the new product are expected to decline as the number of units sold increases as follows:
                                  Unit selling price      Unit variable cost
                                            R                       R

        First 2 000 units                100                      50
        Next 5 000 units                  80                      40
        Next 7 500 units                  70                      30
        Next 40 000 units                 60                      25
        Next 14 000 units                 40                      30
Fixed costs during months 1 to 90 will be R900 000. Post sales service and abandonment will be R300 000.
You are required to
a. calculate the expected total contribution from the new product during each of the product’s:
    i. introductory phase ii. growth phase iii. maturity phase           iv. decline phase
b. Also calculate the life cycle profit/loss of the new product.
c. Should manufacturing and sales commence?

Suggested Solution 2008 SQ2
a. Contribution per phase
Introductory phase: Sales (10 x 200 x 100)                           200 000                      1
                      Variable costs (2 000 x 50)                    100 000                      0.5
                      Contribution                                   100 000
Growth phase:            Sales (10 x 500 x 80)                       400 000                      1
                                 (10 x 750 x 70)                     525 000                      1
                         Total sales                                 925 000
                         Variable costs (12 500 x 40)                500 000                      0.5
                         Contribution                                425 000
Maturity phase: Sales (40 x 1 000 x 60)                              2 400 000                    1
                         Variable costs (20 000 x 30)       600 000
                                           (20 000 x 25)    500 000 1 100 000                     0.5
                         Contribution                               1 300 000
Decline phase:           Sales (10 x 800 x 40)                      320 000                       1
                                  (10 x 600 x 40)                   240 000                       1
                         Total sales                                560 000
                         Variable costs (14 000 x 30)               420 000                       0.5
                         Contribution                               140 000
        Total contribution                                          R1 965 000

b. Life cycle profit/loss
Total sales (200 000+400 000+525 000+2 400 000+320 000+240 000) 4 085 000             1m
Total costs: Planning and design                                 1 000 000            0.5
         Manufacturing and sales
              Variable (100 000+500 000+600 000+500 000+420 000) 2 120 000            0.5
               Fixed                                               900 000            0.5
               Post sales service and abandonment                  300 000            0.5
         Life cycle net loss                                      (235 000)

Life cycle profit/loss (alternative solution)
Contribution - part (a) 100 000 + 425 000 + 1 300 000 +140 000 =     1 965 000        1m
Costs: Planning and design                                           (1 000 000)      0.5
         Manufacturing and sales – fixed                               (900 000)      0.5
         Post sales service and abandonment                            (300 000)      0.5
         Life cycle net loss                                           (235 000)      0.5

c.   Should manufacturing and sales commence?
         Life cycle net loss                                          (235 000)
         Add back planning and design – sunk cost                    1 000 000        2
         Incremental profit                                            765 000
As the incremental profit is positive the company should commence with manufacturing and sales.   1

Continuing with Cost management and Strategic management accounting

Target costing: Find customer (target) price - target profit margin = target product cost

Kaizen costing focuses on the production process cost (not product cost). Seeks to empower employees.

Activity-based management (ABM): Analyses entity by business activities (e.g. ordering cost not just telephone cost) -
Knowing activity costs stimulates competitive actions and identifies non-value adding activities (adds cost not value).

Business process re-engineering (BPR): Group linked activities/ operations in a co-ordinated manner to reduce costs,
simplify activities/operations and improve product quality and customer satisfaction.

Tear-down analysis or Reverse Engineering: Identify product improvement or cost reduction opportunities by dismantling
competitor’s product’s functionality, design, processes and cost component.

Value engineering/analysis: Systematic interdisciplinary analysis (by survey or interview) of a product/service’s
functionality and related costs to achieve the target product/service cost.

Total quality management (TQM): Strives to promote continuous improvement (ultimately - zero-defects) in
products/service quality by performing tasks once (right first time) and so reduce waste, inspections, reworking, scrap and
warranty repairs. Uses non-financial measures and statistical quality control tools to improve quality (standards) and reduce
internal/external failure costs.

A cost-of-quality report is prepared to highlight:
    • quality compliance costs (i.e. prevent sub-standard products/service) by preventive maintenance, quality
         planning/training and better quality raw materials,
    • product and material appraisal costs, including inspections, quality audits and field tests,
    • internal (pre-delivery) failure or non-compliance costs, including the costs of scrap, repairs, stoppages and defects and
    • external (post delivery) failure or non-compliance costs, including costs of handling, warranty replacements, repairs
         to returned products and damaged reputation.

Example 2008 SQ3: The following data is available:
         Units requiring rework                       1 200 Units requiring warranty repair service           800
         Inspection hours                               900
Cost data: Inspection per hour                        R50     Rework per unit                               R250
            Warranty repairs per unit                 R300 Staff training costs                             R95 000
You are required to prepare a total cost of quality report clearly distinguishing between prevention costs, appraisal costs,
internal failure costs and external failure costs. Also prepare a total cost of quality report showing the costs of compliance
and the costs of non-compliance.

Prevention costs         Staff training               95 000
Appraisal costs          Inspection (900 x 50)        45 000
        Cost of compliance                           140 000
Internal failure costs   Rework (1 200 x 250)        300 000
External failure costs   Warranty (800 x 300)        240 000
        Cost of non-compliance                       540 000
        Total cost of quality                        680 000

The value chain: Linked set of value-creating activities from supplier to customer to be more efficiently/cost effective than
competitors by using customer focus on each link.

Week 9 (continued) Chapter 23 – Strategic Management Accounting (SMA)(level 1)

Strategic planning: Endeavours to analyse an enterprise’s historical and expected internal and external environments for 5 to
10 years and to establish financial and management objectives i.e.
    • L/term vision (size, reputation, financial strength and niche or uniqueness),

    •     medium and short term plans/mission (i.e. values, corporate culture, attitude towards risk and change, market segment and
It also determines and controls human, physical, operational and financial resource needs with the objective of developing
distinctive and innovative policies, plans and actions which are sustainable over a long period, to generate superior
performance or competitive advantage and create shareholder wealth.

SMA assesses external competition and own competitive status to gain competitive advantage by exploiting value chain links
and adopt performance measures aligned with entity strategy.

Benchmarking: Improve key activities/processes to world-class best practices. (Virgin/Richard Branson and Formula 1)

Environmental cost management: An environmental cost report (like quality cost report above) can be used.

Just-in-time systems: Goals:
• Eliminate non-value added activities (only add costs not value),
• Convert materials to products in lead time=process time,
• Zero inventory/defects/breakdown (Right 1st time and preventative maintenance)
• Batch sizes of one (reduce set-up/throughput time
• 100% on-time delivery service
• Change factory layout from batch production to
    • cellular flow lines of dissimilar machines producing similar/families of products/components)
    • Push to pull systems to minimise material movements
•Long-run low idle time to short-run more idle time, but lower inventory,
• JIT purchasing/supplies arriving when needed.
YE 2008: Q 4: Identify the potential benefits and pitfalls of implementing a just-in-time system.
Benefits of just in time
•    Favourable impact on cash flow from reduced inventory levels (handling/holding costs) and lower interest costs.
•    Lower number of dependable suppliers offer quantity discounts, less supplier negotiation and reduced order
Pitfalls of just in time
• Lost sales/goodwill/customers when demand is high
• Product quality/defect rate may deteriorate.
• Uneven demand may result in unused/lost capacity, unless safety stock is produced when demand is low.
• Conventional management accounting systems may conflict with JIT manufacturing philosophy.

The balanced scorecard (Porter): Incorporates both financial (typically ROI, RI, EVA, Revenue↑, Cost↓ and asset
utilization) and three new non-financial performance perspectives, namely:
• The customer perspective: Generic measures include Market share, Customer retention/ loyalty/ acquisition/satisfaction
• The internal business perspective: Critical processes the entity must excel at include: % sales from new products, New
products, Product development and break-even time, process cycle time, Quality, Post-sales service.
• The learning and growth perspective: Focuses on infrastructure needed to create long-term growth and improvement,
including Employee capabilities, Information system capabilities and Motivation, empowerment and alignment.

Week 10 COST ESTIMATION & BEHAVIOUR (Drury Chapters 24 & 26) (Quantitative methods)
Level 1: Scatter graphs & Linear regression, Level 3: High-low method, learning curve. IGNORE: Multiple regression analysis
& Simplex method

QE 2009 P2Q3: Discuss, with reasons, whether or not direct labour expense is a fixed manufacturing overhead
• Variable costs are defined as cost items that vary according to different levels of activity (production in the
    present scenario).
• Labour costs have traditionally being regarded as variable on the assumption that management can retrench
   workers in the event that production levels decline. In practice, downsizing and retrenching workers is not a
   unilateral decision and negotiations are required with unions and others before wide-scale retrenchments can be
   implemented. Retrenchments and downsizing are not an everyday occurrence. To assume that labour costs are
   variable because of the potential to reduce these may be inappropriate.
• Labour costs are incurred irrespective of production activity and, in the short term, labour costs are fixed in
   nature provided production is within normal capacity/relevant levels.
• Overtime costs are certainly variable in nature.
• The company forecast to have excess production personnel in 2008. If this transpired it would be inaccurate to
   assume production personnel was a variable cost and be misleading from a decision making perspective.
• Direct labour is a fixed cost as it can only be reduced through the drastic and unusual occurrence of retrenching
   labour. At worst, direct labour is a short term fixed cost.
• The wage rate would be variable, but the number of employees would be fixed.
• If there was an alternative use for employees, the labour costs would be variable.

Engineering methods: Observe physical quantities required for activity→cost estimate - Expensive
Inspection of accounts method: Man. & accountant inspect & classify cost accounts as fixed, var, semi-variable
Graphical or scatter graph method: Plot past observations on graph and draw a line of best fit
High – low method: Reliance on two extreme observations to determine normal cost behaviour

Example: High-Low (multiple products same FOHpu) QE07
Two products A & B have different variable overhead costs per unit, but same FO cost per unit within a relevant range
(combined 200 units). Total overhead costs:
        100 units of A and 50 units of B is R45 000
        150 units of A and 50 units of B is R50 000
         75 units of A is R5 750.
Required: The total fixed cost and variable cost per unit for both products A and B.

Solution:Total overhead cost for 100 units of product A and 50 units of B      R45 000 or R300pu
         Total overhead cost for 150 units of product A and 50 units of B      R50 000 or R250pu
         Total overhead cost of 50 units of A                 0 units of B     R 5 000 or R100pu TFO }
         Total overhead cost of 75 units of A                                  R 5 750               }FOH R70pu
          Total variable cost of 25 units of A                                 R 750 or R30pu VOH }
                 FOH for 100 A and 50 B: R70 pu x 150 (100A+50B) =             R10 500
                 Total OH for 100 A & 50B given as                             R45 000
                 Variable cost for 100 A & 50 B                                 34 500
                 Less Variable cost for 100 A        100xR30pu                   3 000
                 Variable cost for 50 B                                         31 500/50 = R630 pu

Regression equation/cost function (Y=a+bx): Measures past cause-and-effect relationship or correlation between dependent
variable (total cost=Y) and independent variable (i.e. cost drivers/activity =b). Simple regression y = a + bx (Ignore Multiple
regression). Cost functions must be economically plausible/sensible e.g. Total labour cost is function of labour hrs not OT hrs
Regression analysis assumptions:
• circumstances underlying the cost/volume sample will remain the same in future,
• current (inflation adjusted) cost meaningfully predict future costs and
• unexplained errors (y-y1) (i.e. observed cost (y) - regression line (y1) are normally distributed above/below the line.

The total cost (y) formula (y = a + bx) is derived from the
opposite accountant’s Cost-Volume-Profit graph:

Least squares method (Linear regression) = Mathimatical calc
of best-fit-line: Y=a+bx using multiple observations                                BE

Use Y=a+bx and multiply by ∑ to get ∑Y=na+b∑x and multiply
by ∑x to get ∑xY = a∑x + b∑x2
Note: To calculate ∑xy and ∑x2 the x is first multiplied by y or x
for each observation before the results are added (∑ = sum of).

Linear regression steps (6): 1 Check for Economic plausibility;
2 Draw a Scatter diagram for visible evidence that observed data
and proposed variables have a linear relationship; 3 Use
Simultaneous equations to calculate fixed cost (a) and variable cost pu (b);

4 Coef. of Determination (r2) or Goodness of Fit expresses the explained [Σ(y1- )2/n] variations as a % of the total [Σ(y-
 )2/n] deviations from the mean. Thus:
         Coef. of Determination or r2 = [Σ(y1- )2/n] / [Σ(y- )2/n] (deviations above and below line -Minimum 0,3 0r 30%)
         Coef. of Correlation or r = √r2 (deviations on one side of regression line)
A r of 0,8 means 80% of the deviations in Y (cost) result from changes in volume (x). Thus a strong correlation exists
between total cost/activity. The remaining deviations (20%) are random variation of cost from other (omitted) variables.

Step 5: Standard error (Se) of the estimate (y) determines the extent (absolute value) of dispersion of unexplained deviations
around the regression line. If Se is R4 and estimate(y) is R100, possible estimates range from R96 to R104. ‘n-2’ equals the
number of observations less a statistical degree of freedom of 2 for the number of variables (a & b), thus:
         Se = √(∑[y-y1]2)/(n-2) Per p1060 Se = R201,25 and T-tables (p1063) at 10 (12 observations – 2) for a 90% (,05)
confident estimate require an estimate range of 1,812Se or ±R380,97 [R210,25Se x 1,812) (Assuming a normally distribution).

Step 6: A significant relationship between volume [x] and total cost [y]) exists when a deviation in variable cost [b] per unit
is greater than 2 standard errors from zero (i.e. b/Sb > 2), where Sb = Se/√(Σ[x2 - Σx]) or Sb = Se/√ [∑(x- )2]

Note: Simultaneous, Se and Sb equations will be given and questions will likely require an interpretation of given statistics.

A full learning effect (say 80%) occurs at each doubling point in production runs/lots/units (1, 2, 4, 8, 16, etc.) and effectively
reduces the previous cumulative average production time (previous average x learning %).
         1st Batch                 100      Average per batch 100 hours
         2nd Batch                  60      Learning percentage is 80% (Actual/Expected time = 160/200) or
         Cum. Average 160/2=80 160          New Cumulative average time/Previous cum. Avg time = 80/100 = 80% or
         3rd & 4th Batches          96
         Average 256/4=64          256      New Cum. Avg./Previous Cum. Avg = 64/80 = 80% Learning

Total estimated hours/cost (y) at natural doubling points (2, 4, 8, 16 etc): y= axbd where
         y = total cumulative hours (including the learning effect) or total cum. Cost (if ‘a’ is labour cost for 1st run)
         a = hours for 1st batch/run/product (or labour cost for 1st run)
         x = total number of runs/batches/units
         b = learning percentage (e.g. 90% displayed as 0,9)
         d = number of natural doubling points

Example: Calculate the cumulative hours (y) for the first 4 batches (x), thus 2 doubling points (d) when the first batch took 300
hours (a) at a learning percentage of 80% (0,8)(b).
Solution: y = axbd and y = 300 x 4 x 0,82 = 768 hours

Learning percentage at natural doubling points: Learning %= 100h/ax where:
         h = total actual hours to 1st doubling point,
         a = hours for 1st batch                                 Example above: %=(100x160)/(100x2) = 80%
         x = total number of runs/batches/units
Learning % at 2nd doubling point: 100√h/ax where h = total hours to 2nd doubling point.
         Example above: % = 100√256/(100x4) = 80%
At 3rd and 4th doubling points replace the above √ with the 3rd and 4th roots. ‘h’= cum. hours to 3rd and 4th doubling points.

Rate of learning and effect at non-doubling points
At non-doubling points the basic formula is applied using logarithms. (log of 10 is 1 and of 100 is 2, thus 10log x = x [anti-log])
                           Natural numbers              Logarithms
                           Multiplication               Addition of logs
                           Division                     Deduct logs
                           Powers (e.g. Squared)        Multiply logs
                           Roots (e.g Square root)      Divide logs
Formula for use at non-natural doubling points: y = axb
   where y = cumulative average time or cost (see below) per batch/run/product (not total cumulative hours)
            a = hours or cost for 1st batch/run/product
            x = total number of runs/batches/units
            b = log of learning percentage/log 2
Formula for use with logarithms: log y = log a + log x(b) where b = log learning %/log 2

Example: The first production run produced 700 units and required 100 labour hours at a cost of R40 per hour. The second batch
of 700 units required only 70 hours as a normal learning curve effect occurred. To date the company produced 5 600 units.
Calculate the labour costs for the 5 600 units produced.
Solution: Learning percentage: 100h/ax =(100 x 170)/(100x2) = 85%           Production runs 5 600/700 = 8
Production doubled at 2, 4 & 8 (3 times)        Total labour hours(y) = axbd = 100(8)(0,85)3 = 491,3 x R 40 = R19 652
Solution using logarithms: Log y = log a + Log x (b)
where b = log learning % / log 2       Thus b = log 0,85/log 2 = -0,070581/0,30103 = -0,234465
Thus log y = log100 + (log 8)(-0,2345) = 2 + 0,90309(-0,2345) = 1,788225 (log y) Anti-log is 61,41 avg time x 8 runs = 491,3 hours

Learning percentage at non-doubling point: Use simultaneous equations at different cumulative average times.
Example: It took 135 days to build 3 aircrafts and 231 days to build 7 aircrafts. Determine the learning percentage.
Solution: Cumulative average times: 135/3=45 days and 231/7=33 days
log y = log a{1st unit} + b.log x {#runs/units}       Thus log45 = log a + b.log 3 and log33 = log a + b.log7
         Thus       1,653212514 = log a + b.0,47712154       (1)
         And        1,51851394 = log a + b.0,84509804        (2)
         (1)-(2)    0,134698573 = 0 + b.-0,367976785            Thus b = 0,1347/-0,36798 = -0,366052 and b = log%/log2
Thus log % = b.log2         and log% = -0,366052 x 0,30103 = -0,110192259 and anti-log = 0,7759% (learning percentage)
Review the section on “estimating incremented hours and incremental cost” on page 1053 which is self explanatory.

Week 11 - Linear programming Chap 26 (Level 3: Linear programming, sensitivity and shadow prices).
LP assumptions: Linearity, Divisibility of products and resources, all alternatives are included in the model and FC stay constant.
1st test for limiting factors - use sales demand
Single constraint – maximise product with highest contr. pu (e.g. bottleneck hour)
Multiple constraints may favour same product/use (same strategy as above) – draw graph for visual & maximise contribution
Constraints favour diff. prod./uses – use LP (Note LP assumptions)
LP steps: Formulate the problem algebraically, specify the objective function (max. contribution) (e.g. 14Y+16Z),
Formulate input constraints (e.g.Mat: 8Y+4Z ≤3440; Lab: 6Y+8Z≤2880; Mach. capacity: 4Y+6Z≤2760; Min./Max. Sales : 0
≤Y≤420 and Z≤0). Zero sales prevents solutions with negative sales qty.
Solve Y and Z with simultaneous equations (P1114 solved mat (8Y+ 4Z ≤3440) and lab (6Y+8Z≤2880) to 400Y and 60Z
Labour constraint 6Y + 8Z ≤ 2,880 (When Z = 0, Y = 480; When Y = 0, Z =360)
Machine capacity constraint 4Y + 6Z ≤ 2,760 (When Z = 0, Y = 690; when y = 0, Z = 460)

Opportunity cost: Scarce resources have opportunity cost (i.e. shadow price) See Easy method and Drury p1110)
Easier method: Objective function: 14Y + 16Z Mat.: 8Y + 4Z ≤ 3440 Lab: 6Y + 8Z ≤ 2880
Contribution Y: 8M + 6L = 14        Contribution Z: 4M+8L=16 x2: 8M +16L = 32 Difference 0 +10L = 18
Thus L=R1,80 and M=R0,40 shadow prices
Entity can ↑labour rate by a max. of R1,80 and ↑mat price by a max. of 40c to ↑3440 lab hrs and ↑2880 mat units.

Shadow prices Drury: Mat.8Y+4Z ≤3441 & Lab. 6Y+8Z≤2880 →Y=400,2 & Z=59,85 MC is 40c [2,8 (,2Yx14)-2,4(,15Zx16)]
Similarly: 8Y+4Z ≤3440 & 6Y+8Z≤2881 →Y=399,9 & Z=60,2 MC is R1,80 [R3,2(,2Zx16)-1,4(,1Yx14)]

Simplex method: This non-graphical method for>two products is not part of the syllabus and may be ignored.


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