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MAC2601 Formulae
STUDY UNIT 2 – Estimation techniques and the linear equation:
The linear equation:
𝑦 = 𝑎 + 𝑏𝑥
The high-low method:
𝑇ℎ𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑐𝑜𝑠𝑡𝑠 𝑎𝑡 𝑡ℎ𝑒 ℎ𝑖𝑔ℎ𝑒𝑠𝑡 𝑎𝑛𝑑 𝑙𝑜𝑤𝑒𝑠𝑡 𝑎𝑐𝑡𝑖𝑣𝑖𝑡𝑦 (𝑅𝑎𝑛𝑑 𝑣𝑎𝑙𝑢𝑒)
𝑇ℎ𝑒 𝑑𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 ℎ𝑖𝑔ℎ𝑒𝑠𝑡 𝑎𝑛𝑑 𝑙𝑜𝑤𝑒𝑠𝑡 𝑎𝑐𝑡𝑖𝑣𝑖𝑡𝑦 (𝑢𝑛𝑖𝑡𝑠)
Simple regression analysis (least squares method): *given in the exam
2
∑ 𝑥𝑦 = 𝑎Σ𝑥 + 𝑏Σ𝑥 … … … … ①
∑ 𝑦 = 𝑎𝑛 𝑏Σ𝑥 … … … … … … . ②
STUDY UNIT 3 – Cost-volume-profit analysis:
Contribution:
Sales – total variable costs
Contribution ratio:
𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛
𝒔𝒂𝒍𝒆𝒔
× 100%
Profit can be calculated as:
Y = bx – a
Y = net profit (0 at breakeven)
B = contribution per unit
X = number of units sold
A = total fixed costs
Breakeven point in units:
𝑡𝑜𝑡𝑎𝑙 𝑓𝑖𝑥𝑒𝑑 𝑐𝑜𝑠𝑡
𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡
Breakeven value:
breakeven value × selling price per unit
OR
𝑡𝑜𝑡𝑎𝑙 𝑓𝑖𝑥𝑒𝑑 𝑐𝑜𝑠𝑡
𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜
Margin of safety in units:
total sales(units) – breakeven sales(units)
Margin of safety in value:
total sales – breakeven sales
Margin of safety ratio in units (%):
𝑇𝑜𝑡𝑎𝑙 𝑠𝑎𝑙𝑒𝑠(𝑢𝑛𝑖𝑡𝑠)−𝑏𝑟𝑒𝑎𝑘𝑒𝑣𝑒𝑛 𝑠𝑎𝑙𝑒𝑠(𝑢𝑛𝑖𝑡𝑠)
𝑇𝑜𝑡𝑎𝑙 𝑠𝑎𝑙𝑒𝑠(𝑢𝑛𝑖𝑡𝑠)
× 100
Margin of safety ratio in value (%):
𝑚𝑎𝑟𝑔𝑖𝑛 𝑜𝑓 𝑠𝑎𝑓𝑒𝑡𝑦 𝑖𝑛 𝑣𝑎𝑙𝑢𝑒
𝑡𝑜𝑡𝑎𝑙 𝑠𝑎𝑙𝑒𝑠(𝑣𝑎𝑙𝑢𝑒)
× 100
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Target sales in units:
𝑓𝑖𝑥𝑒𝑑 𝑐𝑜𝑠𝑡𝑠+𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑝𝑟𝑜𝑓𝑖𝑡
sales units = 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡
Target sales in value:
𝑓𝑖𝑥𝑒𝑑 𝑐𝑜𝑠𝑡𝑠+𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑝𝑟𝑜𝑓𝑖𝑡
Sales value = 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜
STUDY UNIT 4 – Material:
Average inventory:
1
× order size
2
Economic Ordering Quantity(EOQ):
2 × 𝑈 ×𝐶
√
𝐻 + (𝑃 × 𝑖)
U = annual usage(demand)
C = variable cost of placing order
H = other variable inventory holding cost (excluding interest) per annum per unit
i = interest rate or required return (used when provided)
P = purchase price per unit (used when provided)
STUDY UNIT 5 – Labour:
Overtime premium: 0,5 (normal rate is 1)
Budgeted labour recovery rate:
𝑇𝑜𝑡𝑎𝑙 𝑏𝑢𝑑𝑔𝑒𝑡𝑒𝑑 𝑎𝑛𝑛𝑢𝑎𝑙 𝑙𝑎𝑏𝑜𝑢𝑟 𝑐𝑜𝑠𝑡
𝑇𝑜𝑡𝑎𝑙 𝑏𝑢𝑑𝑔𝑒𝑡𝑒𝑑 𝑎𝑛𝑛𝑢𝑎𝑙 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑣𝑒 ℎ𝑜𝑢𝑟𝑠
Total budgeted annual labour cost:
Gross remuneration + employer contributions
Total budgeted annual productive hours:
Clock hours – idle time – public holidays – paid leave
STUDY UNIT 6 – Overheads:
Overhead recovery rate:
𝐵𝑢𝑑𝑔𝑒𝑡𝑒𝑑 𝑚𝑎𝑛𝑢𝑓𝑎𝑐𝑡𝑢𝑟𝑖𝑛𝑔 𝑜𝑣𝑒𝑟ℎ𝑒𝑎𝑑 𝑐𝑜𝑠𝑡𝑠
𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 (𝑢𝑛𝑖𝑡𝑠)
STUDY UNIT 9 – The direct costing method versus the absorption costing method:
Opening inventory (FIFO – Absorption costing):
𝑈𝑛𝑖𝑡𝑠 𝑜𝑓 𝑐𝑙𝑜𝑠𝑖𝑛𝑔 𝑖𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦
𝑢𝑛𝑖𝑡𝑠 𝑚𝑎𝑛𝑢𝑓𝑎𝑐𝑡𝑢𝑟𝑒𝑑
× 𝑚𝑎𝑛𝑢𝑓𝑎𝑐𝑡𝑢𝑟𝑖𝑛𝑔 𝑐𝑜𝑠𝑡
OR
Opening stock units × (variable cost per unit + fixed cost per unit)
Closing inventory (FIFO – Absorption costing):
𝑈𝑛𝑖𝑡𝑠 𝑜𝑓 𝑐𝑙𝑜𝑠𝑖𝑛𝑔 𝑖𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦
𝑟𝑎𝑛𝑑 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑐𝑜𝑠𝑡𝑠
𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑢𝑛𝑖𝑡𝑠
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MAC2601 Formulae
STUDY UNIT 2 – Estimation techniques and the linear equation:
The linear equation:
𝑦 = 𝑎 + 𝑏𝑥
The high-low method:
𝑇ℎ𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑐𝑜𝑠𝑡𝑠 𝑎𝑡 𝑡ℎ𝑒 ℎ𝑖𝑔ℎ𝑒𝑠𝑡 𝑎𝑛𝑑 𝑙𝑜𝑤𝑒𝑠𝑡 𝑎𝑐𝑡𝑖𝑣𝑖𝑡𝑦 (𝑅𝑎𝑛𝑑 𝑣𝑎𝑙𝑢𝑒)
𝑇ℎ𝑒 𝑑𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 ℎ𝑖𝑔ℎ𝑒𝑠𝑡 𝑎𝑛𝑑 𝑙𝑜𝑤𝑒𝑠𝑡 𝑎𝑐𝑡𝑖𝑣𝑖𝑡𝑦 (𝑢𝑛𝑖𝑡𝑠)
Simple regression analysis (least squares method): *given in the exam
2
∑ 𝑥𝑦 = 𝑎Σ𝑥 + 𝑏Σ𝑥 … … … … ①
∑ 𝑦 = 𝑎𝑛 𝑏Σ𝑥 … … … … … … . ②
STUDY UNIT 3 – Cost-volume-profit analysis:
Contribution:
Sales – total variable costs
Contribution ratio:
𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛
𝒔𝒂𝒍𝒆𝒔
× 100%
Profit can be calculated as:
Y = bx – a
Y = net profit (0 at breakeven)
B = contribution per unit
X = number of units sold
A = total fixed costs
Breakeven point in units:
𝑡𝑜𝑡𝑎𝑙 𝑓𝑖𝑥𝑒𝑑 𝑐𝑜𝑠𝑡
𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡
Breakeven value:
breakeven value × selling price per unit
OR
𝑡𝑜𝑡𝑎𝑙 𝑓𝑖𝑥𝑒𝑑 𝑐𝑜𝑠𝑡
𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜
Margin of safety in units:
total sales(units) – breakeven sales(units)
Margin of safety in value:
total sales – breakeven sales
Margin of safety ratio in units (%):
𝑇𝑜𝑡𝑎𝑙 𝑠𝑎𝑙𝑒𝑠(𝑢𝑛𝑖𝑡𝑠)−𝑏𝑟𝑒𝑎𝑘𝑒𝑣𝑒𝑛 𝑠𝑎𝑙𝑒𝑠(𝑢𝑛𝑖𝑡𝑠)
𝑇𝑜𝑡𝑎𝑙 𝑠𝑎𝑙𝑒𝑠(𝑢𝑛𝑖𝑡𝑠)
× 100
Margin of safety ratio in value (%):
𝑚𝑎𝑟𝑔𝑖𝑛 𝑜𝑓 𝑠𝑎𝑓𝑒𝑡𝑦 𝑖𝑛 𝑣𝑎𝑙𝑢𝑒
𝑡𝑜𝑡𝑎𝑙 𝑠𝑎𝑙𝑒𝑠(𝑣𝑎𝑙𝑢𝑒)
× 100
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Target sales in units:
𝑓𝑖𝑥𝑒𝑑 𝑐𝑜𝑠𝑡𝑠+𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑝𝑟𝑜𝑓𝑖𝑡
sales units = 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡
Target sales in value:
𝑓𝑖𝑥𝑒𝑑 𝑐𝑜𝑠𝑡𝑠+𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑝𝑟𝑜𝑓𝑖𝑡
Sales value = 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜
STUDY UNIT 4 – Material:
Average inventory:
1
× order size
2
Economic Ordering Quantity(EOQ):
2 × 𝑈 ×𝐶
√
𝐻 + (𝑃 × 𝑖)
U = annual usage(demand)
C = variable cost of placing order
H = other variable inventory holding cost (excluding interest) per annum per unit
i = interest rate or required return (used when provided)
P = purchase price per unit (used when provided)
STUDY UNIT 5 – Labour:
Overtime premium: 0,5 (normal rate is 1)
Budgeted labour recovery rate:
𝑇𝑜𝑡𝑎𝑙 𝑏𝑢𝑑𝑔𝑒𝑡𝑒𝑑 𝑎𝑛𝑛𝑢𝑎𝑙 𝑙𝑎𝑏𝑜𝑢𝑟 𝑐𝑜𝑠𝑡
𝑇𝑜𝑡𝑎𝑙 𝑏𝑢𝑑𝑔𝑒𝑡𝑒𝑑 𝑎𝑛𝑛𝑢𝑎𝑙 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑣𝑒 ℎ𝑜𝑢𝑟𝑠
Total budgeted annual labour cost:
Gross remuneration + employer contributions
Total budgeted annual productive hours:
Clock hours – idle time – public holidays – paid leave
STUDY UNIT 6 – Overheads:
Overhead recovery rate:
𝐵𝑢𝑑𝑔𝑒𝑡𝑒𝑑 𝑚𝑎𝑛𝑢𝑓𝑎𝑐𝑡𝑢𝑟𝑖𝑛𝑔 𝑜𝑣𝑒𝑟ℎ𝑒𝑎𝑑 𝑐𝑜𝑠𝑡𝑠
𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 (𝑢𝑛𝑖𝑡𝑠)
STUDY UNIT 9 – The direct costing method versus the absorption costing method:
Opening inventory (FIFO – Absorption costing):
𝑈𝑛𝑖𝑡𝑠 𝑜𝑓 𝑐𝑙𝑜𝑠𝑖𝑛𝑔 𝑖𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦
𝑢𝑛𝑖𝑡𝑠 𝑚𝑎𝑛𝑢𝑓𝑎𝑐𝑡𝑢𝑟𝑒𝑑
× 𝑚𝑎𝑛𝑢𝑓𝑎𝑐𝑡𝑢𝑟𝑖𝑛𝑔 𝑐𝑜𝑠𝑡
OR
Opening stock units × (variable cost per unit + fixed cost per unit)
Closing inventory (FIFO – Absorption costing):
𝑈𝑛𝑖𝑡𝑠 𝑜𝑓 𝑐𝑙𝑜𝑠𝑖𝑛𝑔 𝑖𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦
𝑟𝑎𝑛𝑑 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑐𝑜𝑠𝑡𝑠
𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑢𝑛𝑖𝑡𝑠
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