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**Profit’s Sensitivity to Price**

Chapter 2 Profit’s Sensitivity to Price Conducting a Profit Sensitivity Analysis to Identify volume Hurdles and the Challenges Inherent in Economic Price Optimization

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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? 2

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**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

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**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.

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**Volume Hurdle pf > pi pi = Qi(Pi-V)-F pf = Qf(Pf-V)-F**

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.

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Volume Hurdle The change in volume must be greater than this ratio for the price change to yield higher profits – %DP %DQ ≥ %CMi + %DP Where Qf – Qi %DQ ≡ Percent Change in Volume Qi Pf – Pi %DP ≡ Percent Change in Price Pi Pi – Vi %CMi ≡ Initial Contribution Margin as a percentage of the original price Pi

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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%

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**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. – %DP %DQ ≥ %CMi + %DP

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**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 – %DP %DQ ≥ %CMi + %DP

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**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 – %DP %DQ ≥ %CMi + %DP

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**Profit Sensitivity towards Price Cuts**

Retailer 50% Contribution Margin 15% Price Cut 43% Volume Growth Required to Break Even on the Decision 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

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**Profit Sensitivity towards Price Increases**

Retailer 50% Contribution Margin 15% Price Rise 23% Volume Loss or Less Decrease Would Leave the Firm More Profitable 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

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**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

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**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 = price elasticity of demand ΔQ = quantity change in demand ΔP = quantity change in demand Q1, P1 = original quantity demanded and price, respectively

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**Measured Elasticities**

Category Brand Choice 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 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

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**Highly Elastic Markets Favor Price Cuts**

Decreasing Profits Volume Hurdle Increasing Profits Market Demand 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.

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**Inelastic Markets Favor Price Increase**

Increasing Profits Market Demand Volume Hurdle Decreasing Profits 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.

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**Other elasticities in Pricing**

Income elasticity of demand Cross price elasticity of demand

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**Income Elasticity of Demand**

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

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**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 If EC is negative, the two products are complementary If EC is positive, the two products are substitutes

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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

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**Optimal Price Measure Under the conditions, find Optimal Price P***

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

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**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

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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” 24

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