Break-even Analysis and Profit Planning: CVP, BEP, Margin of Safety and Operating Leverage Questions

Question 1

Define break-even point (BEP).

Accepted Answer

**Break-even point (BEP)** is the level of sales where **Total Revenue = Total Cost** and profit is **zero**.

Question 2

What is contribution?

Accepted Answer

**Contribution** is **Sales − Variable Cost**; it first covers **Fixed Cost** and then becomes profit.

Question 3

Write the formula for BEP in units.

Accepted Answer

**BEP (units)** = **Fixed Cost / (Selling Price − Variable Cost)**.

Question 4

What is P/V ratio?

Accepted Answer

**P/V ratio** = **Contribution / Sales** (contribution margin ratio).

Question 5

What is margin of safety (MOS)?

Accepted Answer

**Margin of Safety (MOS)** = **Actual Sales − Break-even Sales** (sales buffer above BEP).

Question 6

What is CVP analysis?

Accepted Answer

**CVP analysis** studies the relationship among **Cost, Volume and Profit** to support planning decisions.

Question 7

Explain CVP analysis (meaning + use).

Accepted Answer

**CVP (Cost–Volume–Profit) analysis** studies how **costs** and **sales volume** affect **profit**. It is used for **short-run planning**.

**Uses (any three):**
- **Break-even analysis**: find sales needed for **no profit no loss**.
- **Target profit planning**: decide required sales to earn a desired profit.
- **Pricing and cost control**: see impact of changing **price**, **variable cost** or **fixed cost**.

A manager uses CVP to reduce uncertainty and set realistic sales targets.

Question 8

Explain contribution and P/V ratio with formulas.

Accepted Answer

**Contribution (C)** is the amount left after covering **variable cost** and is used to cover **fixed cost** and profit.

**Formulas:**
- **Contribution** = **Sales − Variable Cost**
- **Contribution per unit** = **SP − VC**
- **P/V ratio** = **Contribution / Sales**

| Term | Meaning | Formula |
|---|---|---|
| Contribution | surplus over VC | S − VC |
| P/V ratio | contribution margin | C / S |

Higher **P/V ratio** means higher contribution per rupee of sales.

Question 9

Explain break-even point and write BEP formulas (units and value).

Accepted Answer

**Break-even point (BEP)** is the sales level where **Total Revenue = Total Cost** and **Profit = 0**.

**Formulas:**
- **BEP (units)** = **FC / (SP − VC)**
- **BEP (sales value)** = **FC / (P/V ratio)**

At BEP, total contribution exactly equals fixed cost.

Question 10

Explain margin of safety (MOS) and its importance.

Accepted Answer

**Margin of Safety (MOS)** shows how much sales can fall before reaching **break-even**.

**Formulas:**
- **MOS** = **Actual Sales − BE Sales**
- **MOS%** = (MOS / Actual Sales) × 100

**Importance:** Higher **MOS** indicates lower risk of loss and a more stable profit position.

Question 11

State any five assumptions of break-even/CVP analysis.

Accepted Answer

Assumptions of **BEP/CVP** (any five):
- **Selling price per unit** is constant.
- **Variable cost per unit** is constant.
- **Total fixed cost** is constant within relevant range.
- **Production = sales** (or inventory changes ignored).
- **Product mix** is constant (multi-product case).
- Costs can be clearly split into **fixed** and **variable**.

These assumptions simplify analysis but may not always hold in real life.

Question 12

Explain operating leverage (meaning) and why it matters.

Accepted Answer

**Operating leverage** shows how sensitive **profit** is to changes in **sales** due to the presence of **fixed costs**.

**Basic formula:** **DOL = Contribution / Profit** (at a given sales level).

If fixed costs are high, a small change in sales causes a bigger change in profit, so operating leverage indicates **risk and profit volatility**.

Question 13

Explain break-even analysis in detail. Derive BEP formulas and mention managerial uses and limitations.

Accepted Answer

**Break-even analysis** is a technique to find the sales/output level where a firm has **no profit no loss** (i.e., **TR = TC**). It is part of **CVP analysis**.

### 1) Key idea (Contribution approach)
- **Contribution (C)** = **Sales − Variable Cost**
- Contribution first covers **Fixed Cost (FC)**; the balance becomes profit.

### 2) Derivation of BEP formulas
Let **SP** = selling price per unit, **VC** = variable cost per unit.
- **Contribution per unit** = **SP − VC**
At BEP, **Profit = 0**, so **Total Contribution = Fixed Cost**.
- **Q × (SP − VC) = FC**
So, **BEP (units)**:
- **Q = FC / (SP − VC)**
For BEP in sales value, use **P/V ratio**:
- **P/V ratio = Contribution / Sales**
- **BEP (sales)** = **FC / (P/V ratio)**

| Output | Formula |
|---|---|
| **BEP (units)** | FC / (SP − VC) |
| **BEP (sales value)** | FC / (C/Sales) |

### 3) Managerial uses
- **Minimum sales** required to avoid loss.
- **Target profit planning** (required sales for desired profit).
- Compare proposals using **contribution** and fixed cost changes.
- Assess **risk** using **MOS** and operating leverage.

### 4) Limitations
- Assumes constant **price**, **VC/unit**, and **FC**.
- Difficult with changing **sales mix** and inventory changes.
- Ignores competition and capacity constraints.

Thus, BEP is a useful planning tool but should be used with realistic assumptions.

Question 14

Solve a CVP-style problem: FC=₹50,000; SP=₹100; VC=₹60. Find BEP units, BEP sales, MOS for 2,000 units, and required units for ₹20,000 profit.

Accepted Answer

Given:
- **FC = ₹50,000**
- **SP = ₹100**
- **VC = ₹60**

### Step 1: Compute contribution
- **Contribution/unit (C)** = **SP − VC** = 100 − 60 = **₹40**

### Step 2: BEP (units)
- **BEP (units)** = **FC / C** = 50,000 / 40 = **1,250 units**

### Step 3: BEP (sales value)
- **BEP sales** = **BEP units × SP** = 1,250 × 100 = **₹1,25,000**

### Step 4: MOS at 2,000 units
- Actual sales (units) = **2,000**
- **MOS (units)** = 2,000 − 1,250 = **750 units**
- Actual sales (₹) = 2,000 × 100 = **₹2,00,000**
- BE sales (₹) = **₹1,25,000**
- **MOS (₹)** = 2,00,000 − 1,25,000 = **₹75,000**

### Step 5: Units for target profit ₹20,000
At target profit:
- Required units = (FC + Profit) / C
- = (50,000 + 20,000) / 40 = 70,000/40 = **1,750 units**

```text
Flow: FC, SP, VC → Contribution → BEP → MOS/Target profit
```

Final answers: **BEP=1,250 units**, **BEP sales=₹1,25,000**, **MOS=750 units (₹75,000)**, **Target profit units=1,750**.

Question 15

Explain operating leverage and margin of safety. Show how they indicate business risk using a simple flow/table.

Accepted Answer

### 1) **Margin of Safety (MOS)**
**MOS** shows the safety buffer above **break-even**.
- **MOS = Actual Sales − BE Sales**
- Higher MOS ⇒ lower risk of loss.

### 2) **Operating Leverage**
Operating leverage shows how sensitive **profit** is to **sales changes** due to **fixed costs**.
- **DOL = Contribution / Profit** (at a given sales level)
- Higher fixed costs ⇒ higher DOL ⇒ profit changes sharply with sales.

### Risk interpretation (simple table)
| Indicator | High value means | Risk impact |
|---|---|---|
| **MOS** | big buffer above BEP | **Lower risk** |
| **DOL** | profit very sensitive to sales | **Higher risk** |

```text
Sales drop
  ↓
MOS low? → quickly reaches BEP → loss risk rises
  ↓
DOL high? → profit falls sharply even with small sales drop
```

Thus, managers use **MOS** and **operating leverage** together to judge stability and risk while planning sales targets and cost structure.

Break-even Analysis and Profit Planning: CVP, BEP, Margin of Safety and Operating Leverage

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