18. Financial and Management Accounting 2

Cost Concepts

A technique for determining the cost of a project.

Manufacturing Costs

Raw materials, work-in-progress and finished goods. Inventory size determined by:

Demand
Lead time and production process
Nature of goods
Supply chain management (e.g. JiT)

Fixed Costs

Costs that do not vary with output e.g. rent, depreciation, lighting and supervisor salaries.

Usually they are only fixed over a certain range of production - the relevant range. Factors such as requiring bigger warehouses limit the range.

Variable Costs

Cost that vary with output:

Direct materials
Direct labour

Usually a linear function of quantity.

Total Cost

\begin{aligned} \mathrm{TC}(x) &= \mathrm{VC}(x) + \mathrm{FC} \\ &\approx mx + c \end{aligned}

Where $x$ is quantity.

Total costs can be calculated through several methods:

Job costing (for one-off jobs)
- Sum cost of raw materials materials, labour, overhead, etc.
Process costing (for mass production lines)
- Sum costs of individual processes per batch
- Does not include cost of raw materials, overhead, shipping etc.
Standard costing (for large manufacturers producing different products but with some sort of standard costing)
- Cost per unit output established in advance of production/service delivery
- Establish standards of work (e.g. worker can pack x products/minute) then calculate time and hence cost to pack some unit of product (e.g. container) The above are all CPV methods - cost-volume-profit. Activity based costing, which tracks hidden overhead costs to the activities that cause them, is not covered.

Costing Terminology

  ┌─            Direct  ───┐  ─────┐  ─────┐
  │            Material    │       │       │
  │                        │       │       │
  │                     Prime      │       │
  │        ┌──  Direct   Cost      │       │
  │        │    Labor      │     Cost      │
  │        │               │   of Goods    │
  │        │               │ Manufactured  │
  │        │   Indirect ───┤       │       │
  │        │   Material    │       │     Cost
  │Conversion              │       │   of Goods
  │  Costs │               │       │     Sold
  │        │   Indirect  Factory   │       │
  │        │    Labor   Overhead   │       │
Selling    │               │       │       │
 Price     │               │       │       │
  │        │    Fixed/     │       │       │
  │        └──  Misc    ───┤  ─────┘       │
  │                        │               │
  │             General/   │               │
  │              Admin    Non-Factory      │
  │                        Overhead        │
  │            Selling/    │               │
  │            Marketing  ─┘  ─────────────┘
  │
  │
  └─             Profit

Prime costs: AKA direct costs
Fixed/misc: electricity, rent etc.
Indirect material: cleaning supplies, glues etc. that aren’t allocated on a per-unit basis
Selling price (SP): price each unit is sold at
Total revenue (TR): selling price times units sold
- Not all units produced may be sold
Profit §: revenue after deducting relevant costs

Price-Demand Relationship

Law of Demand: inverse price-quantity relationship (price rising reduces quantity demanded). Not necessarily linear.

\text{SP} = a - b\text{D}

Where $\text{D}$ is the demand (units demanded) and $\text{SP}$ is the selling price.

Hence, total revenue, $\text{TR} = \text{SP} \cdot \text{D} = a\text{D} - b\text{D}^2$ where $a$ and $b$ are positive and $D < \frac{a}{b}$ .

Limitations of CPV Analysis

CPV analysis has a short-term decision-making model with no recognition of the time value of money.

It:

Assumes clear separation of fixed and variable costs
Assumes constant unit (variable) cost and revenue - not true in reality

Long-term analysis should consider the entire life-cycle of the product (activity-based costing). In the future the selling price may include externalities such as the cost of battery recycling for EVs, carbon costs for flight tickets etc.

Break-Even Analysis

Used to evaluate the minimum amount of sales required to cover costs at a given price.

At break even, $\text{TR} = \text{TC}. Hence:

\text{SP} \cdot x = \text{VC}(x) + \text{FC}

Where $x$ is the number of units.

This assumes that any quantity can be sold at a given price and that the total cost curve is a straight line.

Significance:

If production/sales (assuming they are equal) is less than the break-even cost, a loss will occur
Lower break-even quantities are generally desireable. This can be done by:
- Reducing the fixed costs
- Reducing variable costs
- Increasing the revenue rate (essentially the selling price)

Average Cost and Economies of Scale

Average Cost (AC): total cost over units produced. This is the basis for normal pricing.

As production volume increases, average costs decreases - fixed costs spread over a larger number of units.

Marginal Costs

Marginal Cost (MC): incremental/variable cost of producing one more unit ( $\mathrm{TC}(x + 1) - \mathrm{TC}(x)$ ). Hence, marginal cost varies depending on current production quantity.

Marginal cost is the basis for last minute pricing.

Contribution Margins

Profitability when taking variable costs into account.

\begin{aligned} \text{Contribution Margin (CM)} &= \text{Total Revenue} - \text{Variable Costs} \\ \\ \text{Contribution Margin per Unit} &= \frac{\text{Total Revenue}}{\text{Units}} - \frac{\text{Variable Costs}}{\text{Units}} \\ &= \text{Selling Price} - \frac{\text{Variable Costs}}{\text{Units}} \\ \\ \text{Contribution Margin Ratio (CMR)} &= \frac{\text{Contribution Margin per Unit}}{\text{Selling Price}} \end{aligned}

Example: Break-Even Analysis with Contribution Margins

Variable costs: $100/unit
Fixed costs: $10,000/month
Production rate: 500 units/month
Selling price: $200/unit

Without Contribution Margins

\begin{aligned} \text{TC}(x) &= x \cdot \text{SP} \\ 10,\!000 + 100x &= 200x \\ 10,\!000 &= 100x \\ x &= 100 \end{aligned}

With Contribution Margins

\begin{aligned} \text{CM}(x) &= x\cdot \text{SP} - x \cdot \text{VC} \\ &= x(\text{SP} - \text{VC}) \\ &= x(200 - 100) \\ \\ \therefore \text{CM per Unit} &= 100 \\ \\ \therefore \text{CMR} &= 100/\text{SP} \\ &= 0.5 \\ \end{aligned}

Now for break-even units:

\begin{aligned} \text{TR} &= \text{TC} \\ \text{SP} \cdot x &= \text{FC} + \text{VC} \cdot x \\ \therefore x &= \frac{\text{FC}}{\text{SP} - \text{VC}} \\ &= \frac{\text{FC}}{\text{CM per Unit}} \\ &= \frac{10,\!000}{100} \\ &= 100 \end{aligned}

Break-even revenue ( $\text{BE}_{\text{\textdollar}}$ ):

\begin{aligned} \text{TR} &= \text{TC} \\ &= \text{TC} \cdot \text{SP} \\ &= \frac{\text{FC}}{\text{CM per Unit}} \cdot \text{SP} \\ &= \frac{\text{FC}}{\left(\frac{\text{CM per Unit}}{{\text{SP}}}\right)} \\ &= \frac{\text{FC}}{\text{CMR}} \\ &= \frac{10,\!000}{0.5} \\ &= 20,\!000 \end{aligned}

Aside: Service Costing

Calculate costs of:

Direct materials
Direct labour
Overhead

\text{price of service} = \text{materials cost} + \text{hourly charge-out rate}

Hourly charge-out rate includes labour, overhead (including procurement cost for materials) and margins.

Example: nominal 40 hours a week for 2080 hours per year (52 weeks a year) minus:

Days not worked: sick leave, state holidays, holidays
Time not worked: lunch, breaks, clean up/maintenance

So potential chargeable time is ~70% of the time, minus management, meetings, marketing etc that is not directly chargeable to the client.

Then there are costs for rent, power, stationary, depreciation, vehicle expenses, phones/internet, insurance, accountants, legal, advertising, cleaning etc.

So chargeable rate per hour could be something like direct labour (salary) plus annual expenses divided by ~25 hours/week * 48 week. Hence, chargeable rate can easily be more than double the hourly cost of labour.