Lecture 5

Cost-Volume-Profit Analysis

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CVP relation• CVP analysis is the study of effect of output volume on revenue (sales),

expenses (costs), and net income (net profit).• Let P and V be the price and variable cost per unit respectively. Let N be

the number of units sold and F be the fixed costs.• Profit before taxes = N × P – (F+NV) = N × (P-V) – F• Realize that P-V is the UCM (Discussed before)• Profit before taxes = N × UCM – F.• Define Contribution Margin Ratio (CMR) as (P-V)/P.• Profit equation can also be written following CMR approach.• N × (P-V) is the same as (N × P) × (P-V)/P. Notice that (N × P) is the

revenue and (P-V)/P is CMR. So, the profit equation can also be written as • Profit = Revenue × CMR - F

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Breakeven volume• BEV is the volume of sales at which profit equals zero

(alternatively, it is the volume at which all costs equal revenues).• 0 = NBEV × (P-V) – F NBEV = • BEV can also be expressed in sales dollars(SBEV)• SBEV = NBEV × P = = =

where CMR is the contribution margin ratio.We could have derived SBEV from the profit function that we had

developed using CMR approach.0 = Breakeven revenue × CMR – F SBEV = F/CMR

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VPF

PVPF

PVPF CMR

F

Bed-and-breakfast inn• Assume that you are starting a bed-and-breakfast inn. You are charging

$100 per person for a night’s stay and full breakfast next morning. You are “outsourcing” all essentials such as food, maid service for $70 per guest per night. Your utility company has an agreement with you whereby you pay the company $10 per guest per night. You have a manager with an annual salary of $ 10,000 and the building is leased from the city at an annual lease payment of $20,000.

• Here P =$100; V = $80 F = $30,000• UCM = $20; CMR = 0.2• Let us characterize the breakeven volume for this firm!• Using UCM approach, breakeven volume in number of units as

$30,000/$20 = 1,500 guest nights. Alternatively, we can use the CMR approach and calculate breakeven revenue as $30,000/0.2 = $150,000.

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Cost-Volume-Profit Graph

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0

$50000

$100000

$150000

$180000

$210000

$240000

0 3 6 9 12 15 18 21 24 27

Sales revenue line

Fixed cost line

Break-even sales point1,500 guests or $150,000

Total cost line

Guest-nights (hundreds)

Dol

lars

Target Profit

• Can use the profit equation to determine the number of units to be sold or revenue to be generated in order to achieve a target profit (TP).

• Number of units to be sold =

• Sales dollars required =

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UCMTPFNTP

CMRTPFSTP

CVP analysis and taxes

• BEV is not affected by taxes. Why?• Volume required for target profit is affected by

taxes. Convert target profit (which is after taxes) to equivalent profit before taxes and apply the same framework.

• TPbefore taxes = TPafter taxes/(1-tax rate)

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Using CVP model for pricing

• What is the impact of reducing selling prices on profit?– Reduction in UCM profits will decrease– Increase in sales volume profits will increase

• Total Contribution margin will be maximized for a particular price.

• Keep in mind the short term nature of this analysis.

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Evaluate operating risk using CVP

• Margin of safety (MOS) is the excess of expected (or current sales) over the breakeven sales, expressed as a percentage of expected (or current) sales.

• % change in profit before taxes = % change in revenues × (1/MOS)

• Operating leverage is measured as the ratio of fixed costs to total costs.– Higher the amount of fixed costs in the cost

structure, higher is the operating leverage. 9

Multiproduct CVP analysis• Characterize an average product with CM = weighted Unit

Contribution Margin (WUCM).• WUCM = CM of individual products weighted by the weights

in the product mix.• Find the BEV in terms of the average product.• Express BEV in terms of individual products to be sold in order

to breakeven.• Same for volume required to earn TP. • Alternatively, we could have characterized the average

product with Weighted Contribution Margin Ratio (WCMR).

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Key assumptions behind CVP model and model limitations

• Expenses can be classified into variable and fixed categories.

• The behavior of revenues and expenses is linear over the relevant range

• Expect no changes in efficiency and productivity.

• The difference in inventory level at the beginning and at the end of a period is insignificant.

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Key assumptions behind CVP model and model limitations

• Selling prices, unit variable costs and fixed costs are known with certainty.

• Assumption of “single period” horizon.• Assumption of product mix to handle multiple

products.• Does not address whether the existing

product mix or capacity is optimal.

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