Chapter 2

Profit’s Sensitivity to Price

Conducting a Profit Sensitivity Analysis to Identify volume Hurdles and the Challenges Inherent in Economic Price Optimization

Agenda

• How do price changes influence the ability to capture customers?

• How sensitive are profits to price changes when we include the influence of price changes to sales volumes?

• When considering a price cut, what is the necessary increase in sale volumes to improve the firm’s profits?

• When considering a price increase, what is the allowable decrease in sale volumes that will leave the firm more profitable?

• How does elasticity of demand enable executives to optimize prices?

Profit Sensitivity Analysis

• If we know that the best price lies within a range, what is the effect of a small change in price?

• Profit Equation

p = Q (P – V) – F

p – ProfitQ – Quantity Sold (Volume)P – PriceV – Variable CostsF – Fixed Costs

Profit Sensitivity Analysis

• Price Sensitivity Analysis analyzes the sensitivity of profits to price changes

• Volume Hurdles are identified through the profit sensitivity analysis. They define the required changes in volume to justify a price change.

Volume Hurdle• Consider a Price Change

– How would volume need to change in order to improve profitability?– Call this the Volume Hurdle

• Let the initial price and quantity be denoted by the subscript i, and the final price and quantity be denoted by the subscript f

pi = Qi(Pi-V)-Fpf = Qf(Pf-V)-F

• Condition: any price change must improve profitability

pf > pi • Use algebra to rearrange the equations and simplify to identify the volume

hurdle.

Volume Hurdle

Where

%DQ ≥ – %DP

%CMi + %DP

%DQ ≡ Qf – Qi

Qi

%DP ≡Pf – Pi

Pi

%CMi ≡Pi – Vi

Pi

Percent Change in Volume

Percent Change in Price

Initial Contribution Margin as a percentage of the original price

The change in volume must be greater than this ratio for the price change to yield higher profits

Example

• A retailer is selling T-shirt for $40 to his customers which he purchase from the wholesaler at a price of $30. Normally the demand is 50 units per month. If the retailer plans to increase the price by $50 per unit, how much should be the allowable volume drop?

Ans: -50%

Fixed Costs Don’t Matter, Variable Costs Do.

• Notice Fixed Costs have no effect on a marginal price change decision

– Your overhead is your problem, not the customers. From a value perspective, customers never care about your cost structure. Only you do. They only care about value – how much value do they get for how high a price.

– Fixed costs are key in the decision to enter or stay in the industry. Once in the industry, they make no difference to marginal profitability decisions.

– Fixed costs more of an investment or strategy issue than a pricing issue.

%DQ ≥ – %DP

%CMi + %DP

Volume Hurdle for a Price Cut• Price cut, where %DP is negative, requires a

positive increase in volume to improve profitability– The amount of the required volume increase is

dependent on the size of the size of the contribution margin.

– Large CM implies a small DQ is required. – Small CM implies a larger DQ is required

• Strong implications with respect to tactical price cuts– Discounts– Short term sales– Creates a volume hurdle for the tactical price cut

to make sense to the firm

%DQ ≥ – %DP

%CMi + %DP

Volume Hurdle for a Price Hike• Price Rise, where %DP is positive,

will allow for a reduction in volume, up to a point.– The amount of forfeited volume is

dependent on the contribution margin.

– Small CM can handle a large DQ decrease

– Large CM needs a smaller DQ decrease

%DQ ≥ – %DP

%CMi + %DP

Profit Sensitivity towards Price Cuts

Manufacturer• 25% Contribution

Margin

• 5% Price Cut

• 25% Volume Growth Required to Break Even on the Decision

Broker• 1% Contribution

Margin

• 0.1% Price Cut (10 bp)

• 11.1% Volume Growth Required to Break Even on the Decision

Retailer• 50% Contribution

Margin

• 15% Price Cut

• 43% Volume Growth Required to Break Even on the Decision

Profit Sensitivity towards Price Increases

Manufacturer• 25% Contribution

Margin

• 5% Price Rise

• 14% Volume Loss or Less Decrease Would Leave the Firm More Profitable

Broker• 1% Contribution

Margin

• 0.1% Price Rise (10 bp)

• 9.1% Volume Loss or Less Decrease Would Leave the Firm More Profitable

Retailer• 50% Contribution

Margin

• 15% Price Rise

• 23% Volume Loss or Less Decrease Would Leave the Firm More Profitable

Price Increases and Decreases have Non-Symmetrical Effects on Profit

• Price Cuts require Larger Changes in Volume than Price Rises to leave the firm equally well off.

• 50% Contribution Margin

• 15% Price Rise

• 23% Volume Loss or Less Decrease Would Leave the Firm More Profitable

• 50% Contribution Margin

• 15% Price Cut

• 43% Volume Growth Required to Break Even on the Decision

Price elasticity of demand measures the responsiveness of the quantity demanded for a product or service to a change in the price of the product or service

Price Elasticity of Demand

EQ Q Q

P P P

Q Q

P PQ Pd

( ) /

( ) /

/

/% %

1 2 1

1 2 1

1

1

Ed = price elasticity of demand

ΔQ = quantity change in demand

ΔP = quantity change in demand Q1, P1 = original quantity demanded and price, respectively

Measured ElasticitiesCategory Brand Choice Category

Bacon -1.25 -0.32

Margarine -2.22 -0.12Butter -1.24 -0.74

Ice Cream -1.89 -0.68

Paper Towels -4.00 -0.74Sugar -4.03 -0.57

Liquid Detergents -3.95 -1.70Coffee -1.65 -1.42

Soft Drinks -2.66 -0.42

Bath Tissue -3.85 -0.80Potato Chips -2.50 -0.88

Dryer Softeners -4.08 -1.19Yogurt -1.57 -0.35

Highly Elastic Markets Favor Price CutsElastic Demand Curve (e = -10) and

Volume Hurdle for Firm with a 25% Contribution Margin

-15%

-10%

-5%

0%

5%

10%

15%

-40% -20% 0% 20% 40% 60% 80% 100% 120%

Percent Change in Volume

Per

cen

t C

han

ge

in P

rice

• Elastic markets mean a small price change induces a large volume change– |e| > 1– Most brands face elastic markets

Increasing Profits

Decreasing Profits

Market Demand

Volume Hurdle

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Inelastic Markets Favor Price IncreaseInelastic Demand Curve (e = -0.5) and

Volume Hurdle for Firm with a 25% Contribution Margin

-15%

-10%

-5%

0%

5%

10%

15%

-40% -20% 0% 20% 40% 60% 80% 100% 120%

Percent Change in Volume

Per

cen

t C

han

ge

in P

rice

• Inelastic markets mean that a large price change is required to induce a noticeable volume change– |e| < 1– Many industries face inelastic markets

Increasing Profits

Decreasing Profits

Market

Dem

and

Volume Hurdle

© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Other elasticities in Pricing

• Income elasticity of demand• Cross price elasticity of demand

Income Elasticity of Demand

• Income elasticity of demand: responsiveness of the quantity demanded of a product or service to a change in personal income

EQ

I

I

QI

( ) ( )

• If EI is negative, the product is an inferior good

Income goes up fewer units are demanded (switch to steak, less hamburger)

• If EI is positive, the product is a normal good

Demand increases as income increases

• If 0<EI<1, the product becomes less important in households’ consumption plan

• If EI >1, the product becomes more important as income increases.

Cross-Price Elasticity of Demand

• Cross price elasticity of demand: responsiveness of demand for a product to a change in the price of another product

E cQ A

P B

P B

Q A

• If EC is negative, the two products are complementary

• If EC is positive, the two products are substitutes

Price Optimization• The above analysis implies that optimal pricing can be found, one where in

increase or decrease in price leads to less profit than otherwise would be found.

– Assuming a constant elasticity of demand over a wide range of price, through integral calculus we find the Optimal Price for elastic markets at:

– At the optimal price, the quantity sold is

– Where Qi and Pi the current demand and price

e

ii P

PQQ

ee

1

VP

Optimal PriceMeasure

Variable Cost V $5

Fixed Cost F $750,000

Elasticity of Demand e -1.8

Demand at $1 Qo 10,000,000

Under the conditions, find

Optimal Price P* $11.25

Key Challenge of Price Optimization What is the relevant Elasticity of Demand?

• Always a “historic” number, not forward looking number.– Dependent upon the economic conditions, competing alternatives, tastes of the

market, and other market factors, all of which are constantly changing.– Can be influenced by the firm’s actions: Branding enables higher prices,

discounting can reset price expectations lower lowering the potential price capture

• Non-measurable for revolutionary products

• Small versus large price changes may exhibit different a elasticity

• Upward versus downward price changes may exhibit different a elasticity

Summary• A Profit Sensitivity Analysis should be used to identify Volume Hurdles

for tactical pricing actions (Discounts, Price Promotions, Specific Sales Opportunities)

• Profit is asymmetrically sensitive to price cuts vs. price hikes

• Inelastic markets favor price increases

• Elastic Markets favor price decreases

• Given the elasticity of demand, one could identify “optimal prices”