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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 – Profit Q – Quantity Sold (Volume) P – Price V – Variable Costs F – 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)-F pf = 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 %DQ ≥ – %DP %CMi + %DP Where %DQ ≡ Qf – Qi The change in volume must be greater than this ratio for the price change to yield higher profits Percent Change in Volume Qi %DP ≡ P f – Pi Percent Change in Price Pi %CMi ≡ Pi – V i Pi Initial Contribution Margin as a percentage of the original price 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 Retailer Manufacturer Broker • 50% Contribution Margin • 25% Contribution Margin • 1% Contribution Margin • 15% Price Cut • 5% Price Cut • 0.1% Price Cut (10 bp) • 43% Volume Growth Required to Break Even on the Decision • 25% Volume Growth Required to Break Even on the Decision • 11.1% Volume Growth Required to Break Even on the Decision Profit Sensitivity towards Price Increases Retailer Manufacturer Broker • 50% Contribution Margin • 25% Contribution Margin • 1% Contribution Margin • 15% Price Rise • 5% Price Rise • 0.1% Price Rise (10 bp) • 23% Volume Loss or Less Decrease Would Leave the Firm More Profitable • 14% Volume Loss or Less Decrease Would Leave the Firm More Profitable • 9.1% Volume Loss or Less Decrease Would Leave the Firm More Profitable Price Increases and Decreases have NonSymmetrical Effects on Profit • Price Cuts require Larger Changes in Volume than Price Rises to leave the firm equally well off. • 50% Contribution Margin • 50% Contribution Margin • 15% Price Rise • 15% Price Cut • 23% Volume Loss or Less Decrease Would Leave the Firm More Profitable • 43% Volume Growth Required to Break Even on the Decision Price Elasticity of Demand 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 Ed Ed ΔQ ΔP Q1, P1 (Q 1 Q 2) / Q 1 ( P 1 P 2) / P 1 D Q / Q1 D P / P1 %DQ %DP = price elasticity of demand = quantity change in demand = quantity change in demand = original quantity demanded and price, respectively Measured Elasticities Category Brand Choice Category Bacon -1.25 -0.32 Margarine -2.22 -0.12 Butter -1.24 -0.74 Ice Cream -1.89 -0.68 Paper Towels -4.00 -0.74 Sugar -4.03 -0.57 Liquid Detergents -3.95 -1.70 Coffee -1.65 -1.42 Soft Drinks -2.66 -0.42 Bath Tissue -3.85 -0.80 Potato Chips -2.50 -0.88 Dryer Softeners -4.08 -1.19 Yogurt -1.57 -0.35 Highly Elastic Markets Favor Price Cuts Elastic Demand Curve (e = -10) and Volume Hurdle for Firm with a 25% Contribution Margin 15% Percent Change in Price Decreasing Profits 10% 5% 0% Increasing Profits -5% -10% -15% -40% -20% 0% 20% 40% 60% 80% 100% 120% Percent Change in Volum e • Elastic markets mean a small price change induces a large volume change – |e| > 1 – Most brands face elastic markets © 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. Inelastic Markets Favor Price Increase Inelastic Demand Curve (e = -0.5) and Volume Hurdle for Firm with a 25% Contribution Margin Percent Change in Price Increasing Profits 15% 10% 5% 0% -5% -10% -15% -40% Decreasing Profits -20% 0% 20% 40% 60% 80% 100% 120% Percent Change in Volum e • Inelastic markets mean that a large price change is required to induce a noticeable volume change – |e| < 1 – Many industries face inelastic markets © 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 EI (D Q) DI (I) Q • 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 Ec DQA D PB PB QA • 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: Ve P 1 e – At the optimal price, the quantity sold is e P Q Q i Pi – Where Qi and Pi the current demand and price Optimal Price Measure Variable Cost V $5 Fixed Cost F $750,000 Elasticity of Demand e -1.8 Demand at $1 Qo 10,000,000 P* $11.25 Under the conditions, find Optimal Price 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”