Costs are classified by behaviour based on how they respond to changes in activity levels such as production volume or sales quantity.

Fixed Costs

Fixed costs are costs that remain constant in total regardless of changes in activity level. They do not vary with the number of units produced or sold.

Characteristics:

• Total fixed costs remain unchanged at all activity levels
• Fixed cost per unit decreases as activity increases (economies of scale)
• Examples: factory building rent, depreciation of machinery, management salaries, legal fees

Example: If a factory pays TZS 10,000,000 monthly rent for machinery, this cost remains TZS 10,000,000 whether the company produces 1,000 units or 50,000 units.

Variable Costs

Variable costs are costs whose total amount changes in direct proportion to changes in activity level. The variable cost per unit remains constant.

Characteristics:

• Total variable costs change proportionally with activity
• Variable cost per unit stays constant at all levels
• Examples: raw materials, direct labour, packaging materials, sales commissions

Example: If producing one brick requires TZS 820 in materials and labour, producing 5,000 bricks costs TZS 4,100,000, while 10,000 bricks costs TZS 8,200,000.

Semi-Variable (Mixed) Costs

Semi-variable costs contain both fixed and variable elements. The fixed portion is incurred regardless of activity, while the variable portion changes with activity.

Example: A mobile internet package charges TZS 10,000 per month for 5 GB (fixed portion), then TZS 500 per additional MB used (variable portion).

CVP analysis examines the relationships between costs, volume, and profit. It helps managers understand how changes in activity levels affect profit.

Key Assumptions

• All costs can be classified as fixed or variable
• Total fixed costs remain constant
• Total costs and revenue are linear functions of output
• Sales price per unit remains constant
• All output is sold (no inventory changes)

Contribution Margin

Contribution margin is the amount remaining from sales after deducting variable costs. It contributes to covering fixed costs.

$\text{Contribution Margin per Unit} = \text{Selling Price per Unit} - \text{Variable Cost per Unit}$

$\text{Total Contribution Margin} = \text{Total Sales} - \text{Total Variable Costs}$

Contribution Margin Ratio

The contribution margin ratio shows what percentage of each shilling of sales contributes to covering fixed costs.

$\text{Contribution Margin Ratio} = \frac{\text{Contribution Margin per Unit}}{\text{Selling Price per Unit}} \times 100$

The break-even point (BEP) is the activity level where total revenue equals total costs (no profit, no loss).

Formulas

Break-even point in units:

$\text{BEP (units)} = \frac{\text{Total Fixed Cost}}{\text{Contribution Margin per Unit}}$

Or equivalently:

$\text{BEP (units)} = \frac{\text{Total Fixed Cost}}{\text{Selling Price per Unit} - \text{Variable Cost per Unit}}$

Break-even point in revenue (TZS):

$\text{BEP (revenue)} = \text{BEP (units)} \times \text{Selling Price per Unit}$

Or using contribution margin ratio:

$\text{BEP (revenue)} = \frac{\text{Total Fixed Cost}}{\text{Contribution Margin Ratio}}$

Worked Example

DQP Ltd. produces bottled water with the following information:

• Selling price per unit: TZS 500
• Variable cost per unit: TZS 300
• Total fixed costs: TZS 150,000,000

Required: Calculate break-even point in units and revenue.

Solution:

Step 1: Calculate contribution margin per unit

$\text{Contribution Margin} = 500 - 300 = \text{TZS 200}$

Step 2: Calculate BEP in units

$\text{BEP (units)} = \frac{150,000,000}{200} = 750,000 \text{ units}$

Step 3: Calculate BEP in revenue

$\text{BEP (revenue)} = 750,000 \times 500 = \text{TZS 375,000,000}$

Interpretation: DQP Ltd. must produce and sell at least 750,000 bottles to cover all costs. Below this level, the company incurs a loss; above this level, it earns profit.

To determine sales needed to achieve a specific profit target:

$\text{Target Sales (units)} = \frac{\text{Total Fixed Cost} + \text{Target Profit}}{\text{Contribution Margin per Unit}}$

$\text{Target Sales (revenue)} = \frac{\text{Total Fixed Cost} + \text{Target Profit}}{\text{Contribution Margin Ratio}}$

Worked Example

Using the data from DQP Ltd. above, if the company targets a profit of TZS 50,000,000:

$\text{Target Sales (units)} = \frac{150,000,000 + 50,000,000}{200} = \frac{200,000,000}{200} = 1,000,000 \text{ units}$

$\text{Target Sales (revenue)} = 1,000,000 \times 500 = \text{TZS 500,000,000}$

The margin of safety shows how much sales can decline before the company incurs a loss. It indicates the risk of making a loss.

$\text{Margin of Safety (units)} = \text{Budgeted Sales} - \text{Break-Even Sales}$

$\text{Margin of Safety (\%)} = \frac{\text{Budgeted Sales} - \text{BEP (units)}}{\text{Budgeted Sales}} \times 100$

Worked Example

ARORA Company Ltd. has the following data:

• Budgeted sales: 40,000 units
• Selling price: TZS 2,000 per unit
• Variable cost: TZS 1,500 per unit
• Fixed costs: TZS 12,500,000

Solution:

Step 1: Calculate BEP

$\text{BEP} = \frac{12,500,000}{2,000 - 1,500} = \frac{12,500,000}{500} = 25,000 \text{ units}$

Step 2: Calculate margin of safety

$\text{Margin of Safety (units)} = 40,000 - 25,000 = 15,000 \text{ units}$

$\text{Margin of Safety (\%)} = \frac{15,000}{40,000} \times 100 = 37.5\%$

Interpretation: The company can experience up to a 37.5% drop in sales (from 40,000 to 25,000 units) before incurring a loss.

A small restaurant owner in Dar es Salaam can use CVP analysis to decide whether to expand seating capacity. By classifying costs into fixed (rent, salaries) and variable (food ingredients, packaging), the owner can calculate how many meals must be served monthly to cover costs and achieve target profit. For instance, if monthly fixed costs are TZS 3,000,000, variable cost per meal is TZS 8,000, and selling price is TZS 15,000, the owner can determine the minimum number of meals needed to break even and plan accordingly.