Class 12 - Cost-Volume-Profit Analysis and Sensitivity Analysis

Cost-Volume-Profit (CVP) Analysis — Overview

• CVP analysis is used to answer questions such as:
  • How much must I sell to earn my desired income?
  • How will income be affected if I reduce selling prices to increase sales volume?
  • What will happen to profitability if I expand capacity?

Think of CVP as the "what if" tool for business — like adjusting sliders in a game to see how profit changes when you tweak price, cost, or volume.

Fixed Costs (and Fixed Expenses)

• Total fixed costs (ต้นทุนคงที่/ถาวร) remain constant as activity increases
  • e.g., monthly salary of a manager stays the same regardless of how many units are sold
• Cost per unit (fixed cost per unit) decreases as activity increases
  • Because the same total cost is spread over more units

Like a Netflix subscription — you pay the same $15/month whether you watch 1 show or 100. The more you watch, the cheaper each show becomes "per watch."

Variable Costs (and Variable Expenses)

ค่าใช้จ่ายแปรผัน/ผันแปร

• Total variable costs increase as activity increases
  • e.g., total direct labor cost rises as more units are produced
• Cost per unit (variable cost per unit) remains constant as activity increases

Like buying boba — each cup costs ฿60 no matter how many you buy. But the more cups you buy, the higher your total spend.

Cost Behavior Summary

CVP Relationships: A Graphical Analysis

• Step 1: Starting at the origin, draw the total revenue line with a slope equal to the unit sales price
• Step 2: Total fixed cost extends horizontally from the vertical axis
• Step 3: Draw the total cost line with a slope equal to the unit variable cost
• The point where the revenue line crosses the total cost line = Break-even Point
  • Above that point → Profit
  • Below that point → Loss

The graph is like two roads diverging — revenue zooms up faster than cost, and where they meet is break-even. Past that point, every extra sale adds pure profit.

Computing Break-Even Point

Company ต้องรู้ break-even point ของตัวเอง

• The break-even point is the unique sales level at which a company neither earns a profit nor incurs a loss

Example

• Contribution Margin = Revenue − Variable Costs
  • ==It is the amount by which revenue exceeds the variable costs of producing that revenue==
• Break-even = $30,000 ÷$20/unit = 1,500 units
  • How many units must this company sell to cover its fixed costs (break even)?

Contribution margin is like the "leftover" after paying for ingredients. You need enough leftovers to also cover rent (fixed costs). Once rent is covered — you've broken even.

How Many Units Must We Sell? (Break-Even in Units)

$\boxed{\text{Break-even point (units)} = \frac{\text{Fixed Costs}}{\text{Contribution Margin per Unit}}}$

• Contribution Margin per Unit = Unit Sales Price − Unit Variable Cost

Example (ABC Co.)

• Selling price: $5.00/unit
• Variable cost: $3.00/unit
• Fixed costs: $200,000

\text{Unit Contribution} = $5.00 - $3.00 = $2.00
\text{Break-even} = \frac{$200{,}000}{$2.00} = \boxed{100{,}000 \text{ units}}

How Many Dollars in Sales Must We Generate? (Break-Even in Dollars)

$\boxed{\text{Break-even point (dollars)} = \frac{\text{Fixed Costs}}{\text{Contribution Margin Ratio}}}$

• Contribution Margin Ratio (CM Ratio) = $\dfrac{\text{Unit Contribution Margin}}{\text{Unit Sales Price}}$

Example (ABC Co. continued)

\text{CM Ratio} = \frac{$2.00}{$5.00} = 0.40 = 40\%
\text{Break-even revenue} = \frac{$200{,}000}{0.40} = \boxed{$500{,}000}

CM Ratio tells you: for every $1 of sales, how many cents go toward covering fixed costs. A 40$1 in sales goes to cover fixed costs and eventually profit.

Computing Sales Needed to Achieve Target Operating Income

• Break-even formulas can be extended to find the sales needed to earn any target income

$\boxed{\text{Unit sales} = \frac{\text{Fixed Costs} + \text{Target Income}}{\text{Contribution Margin per Unit}}}$
$\boxed{\text{Dollar sales} = \frac{\text{Fixed Costs} + \text{Target Income}}{\text{Contribution Margin Ratio}}}$

Example (ABC Co.)

• Target income: $40,000
• Fixed costs: $200,000, Unit contribution:$2.00

\text{Units needed} = \frac{$200{,}000 + $40{,}000}{$2.00} = \frac{$240{,}000}{$2.00} = \boxed{120{,}000 \text{ units}}

Break-even is just "target income = $0". The formula generalizes so you can also aim for$40K, $100K, etc.

Margin of Safety

• Margin of Safety = the amount by which sales may decline before reaching break-even

$\boxed{\text{Margin of Safety} = \text{Actual Sales} - \text{Break-even Sales}}$

• Also used to quickly estimate operating income at any sales level:

$\boxed{\text{Operating Income} = \text{Margin of Safety} \times \text{Contribution Margin Ratio}}$

Example

• Actual sales: $100,000 | Break-even sales:$80,000
• CM Ratio: 40%

\text{Margin of Safety} = $100{,}000 - $80{,}000 = $20{,}000

\text{Operating Income} = $20{,}000 \times 0.40 = \boxed{$8{,}000}

Margin of safety is your "buffer zone." If break-even is 80K and you're selling 100K, you can afford to lose 20K in sales before going into loss territory.

Change in Operating Income

• Once break-even is reached, every additional dollar of contribution margin becomes operating income

$\boxed{\Delta \text{Operating Income} = \Delta \text{Sales Volume} \times \text{Contribution Margin Ratio}}$

Example

• ADM expects sales to increase by $15,000
• CM Ratio: 40%

\Delta \text{Operating Income} = $15{,}000 \times 0.40 = \boxed{$6{,}000}

After break-even, the CM ratio is basically your profit rate on new sales. Sell $15K more → earn$6K more profit automatically.

Business Applications of CVP: Sensitivity Analysis

• Sensitivity Analysis = testing how changes in assumptions (price, cost, volume) affect operating income
• Used to evaluate business decisions such as advertising spend, price cuts, compensation changes

Base Case: Speedo Bicycle Retailer

Scenario 1: Spend $12,000 on Advertising to Increase Sales by 10%

• ❌ No — income decreased from $20,000 to$18,000

Advertising cost ($12K) exceeded the extra contribution margin gained ($10K). More sales ≠ more profit if fixed costs jump too.

Scenario 2: Advertising + 10% Price Reduction → Sales Increase by 25%

• New price: $500 × 0.90 =$450/unit
• New units: 500 × 1.25 = 625 bikes

• ❌ Income decreased even more — contribution margin shrank because of the price cut

Cutting price reduces contribution margin per unit. Even with more units sold, total CM can drop if the price cut is too aggressive.

Scenario 3: Advertising + Price Cut + Replace Salary with Commission

• Replace $50,000 in fixed sales salaries with$25/unit commission (variable)
• Variable cost per unit: $300 +$25 = $325
• Sales increase: 50% above original → 750 bikes
• Fixed expenses: $92K −$50K = $42K

• ✅ Income increased significantly — shifting fixed costs to variable reduced risk and the volume increase more than compensated

Converting salary (fixed) to commission (variable) is a classic risk-reduction strategy. Fixed costs are "always owed," but variable costs only happen when you sell — aligning cost with revenue.

Additional Considerations in CVP

Three key areas to watch out for:

1. Different products with different contribution margins → use Sales Mix analysis
2. Determining semi-variable cost elements → costs that have both fixed and variable components
3. Complying with the assumptions of CVP analysis

CVP Analysis When a Company Sells Many Products (Sales Mix)

• Sales Mix = the relative combination in which a company's different products are sold
• Different products have different selling prices, costs, and contribution margins
• For break-even with multiple products → use a weighted average CM ratio based on the sales mix

Example: Speedo sells Bikes and Carts

Overall CM Ratio

\text{Overall CM Ratio} = \frac{$265{,}000}{$550{,}000} = \boxed{48\%}

Break-Even in Sales Dollars

\text{Break-even} = \frac{$170{,}000}{0.48} = \boxed{$354{,}167 \text{ (rounded)}}

With multiple products, you blend their individual CM ratios based on how much of each you sell. The more you sell of the higher-margin product, the higher your overall CM ratio — and the sooner you break even.

Assumptions Underlying CVP Analysis

For CVP to be valid, the following must hold:

1. Relevant range — CVP relationships are assumed linear only within a limited range of activity
   • Unit selling price remains constant
   • Unit variable costs remain constant
   • Total fixed costs remain constant
2. Sales mix remains constant (for multi-product companies)
3. Production = Sales (no changes in inventory)

CVP is a model, not reality. It's like assuming a straight road — useful for planning, but in practice roads curve. Stay aware of the assumptions when applying CVP to real decisions.