The Role of the Basic Profit Equation in Selecting a Selling Price Ted Mitchell

Transcription

1 The Role of the Basic Profit Equation in Selecting a Selling Price Ted Mitchell Consider the following three exam questions: #1 A person bought a wagon at $4 and sold it at a price that provides the desired markup (on price) of 60%. What price did the person sell the wagon for? The answer is Price = V /(1-M p ) = $4 / 0.4 = $10 #2 You are a retailer with sales of 20,000 units per period. Your total overhead and advertising costs are $50,000 a period. The product you sell costs you $4 each. You have a desired target profit that can be earned with a markup (on price) of 60%. What should your selling price per unit be? The answer is Price = V / (1 BEM p *) = $4 / 0.4 = $10 #3 You are a manufacturer with sales of 20,000 units per period. Your total overhead and advertising costs are $50,000 a period. The product you sell has a variable cost of $4 each. You have a desired target profit that produces a return on sales of 35%. What should your selling price per unit be? The answer is Price = BEP / (1 ROS) = $6.5 / 0.65 = $10 A student can NOT memorize all the formulae involved. There are so many combinations and permutations of pricing formulae that there is no book that can list them all. A student must learn to derive the cost based pricing equations that he or she will use as a marketing manager from the Basic Profit Equation. Identifying the Basic Profit Equation The Basic Profit Equation is at the heart of all equations dealing with breakeven analysis, markup and cost based pricing equations. The Basic Profit Equation is (Equation 1) Z= PQ -VQ - F where Z = target profit P = selling price per unit 1

2 V = variable cost per unit Q = quantity sold F = total period or fixed costs We also know Revenue = PQ Total Variable Cost = VQ Gross Profit Contribution = PQ-VQ There are situations in which marketing analysts assume that there are no fixed costs (F = 0) in order to do an analysis of their gross profit margin or markup. It can be thought of as the gross profit return on sales and is interpreted as a measure of the firm s efficiency at converting sales revenue into gross profit. A firm with a declining markup is considered a poor investment. The most important markup is markup on price (Equation 2) Markup on price = (PQ-VQ) / PQ = (P-V)/P = M p Markup on cost, although intuitive to students, is not used very often. (Equation 3) Markup on cost = (PQ-VQ) / VQ = (P-V)/V = M v Another crucial ratio is the net profit margin or the ratio of net profit to revenue. It is often called the return on sales (ROS). (Equation 4) Return on Sales = ROS = Z / PQ = Z / R There are situations in which marketing analysts assume that the net profit is zero and calculate various values at which the firm breaks even. There are four important breakeven values that are important; Breakeven Quantity, Breakeven Revenue, Breakeven Price and Breakeven Markup. Breakeven Quantity is the most intuitive and allows managers to calculate the extra sales volume needed to cover an increase in period costs such as advertising, dealer promotions, etc. (Equation 5) Breakeven Quantity = BEQ= (F)/(P-V) Multiply the Breakeven Quantity (BEQ) by the price (P), simplify, and you have the Breakeven Revenue (BER) (Equation 6) Breakeven Revenue = BER = F / M p In practice Breakeven Revenue is more common than Breakeven Quantity because it is easier for managers to work with a general ratio such as a markup on price than specific dollar markups on specific products. 2

3 The Breakeven Markup BEM p is simply a rewritten version of the Breakeven Revenue (BER). It is not a very popular metric until it is combined with a target profit. (Equation 7) Breakeven Markup = BEM p = F/BER The Breakeven Price (BEP) is also known as the average cost per unit or unit cost. The breakeven price becomes an important element inside most cost based pricing equations. (Equation 8) Breakeven Price = BEP = V + F/Q Most managers don t want to breakeven with a zero profit. They want a profit and the more general forms of the breakeven analysis involve a target profit. The four general breakeven equations with target profits are as follows: (Equation 9) Breakeven Quantity with target profit = BEQ*= (F + Z)/(P-V) (Equation 10) Breakeven Revenue with target profit = BER* = (F+Z) /M p Retailers rewrite the Breakeven Revenue with target profit (BER*) to get their Breakeven Markup with a target profit.. Retailers often use the Breakeven Markup with a target profit (BEM p *) in the pricing calculations. (Equation 11) Breakeven Markup with target profit = BEM p * = F / BER* The Breakeven Price with a target profit, is extremely important. (Equation 12) Breakeven Price with a target profit = BEP* = V + F/Q + Z/Q Equation 12 is nothing more than a rewritten form of the Basic Profit Equation that we started with in Equation 1. This rewritten form of the Basic Profit Equation is the fundamental formula for calculating cost based prices and is often called the Basic Cost Based Pricing Equation. The Basic Cost Based Pricing Equation is (Equation 13) P = V + F/Q + Z/Q and it includes the Breakeven Price (aka. the average cost per unit) and a target profit per unit (Z/Q). It is sometimes written as Selling Price per Unit = BEP + Target Profit per Unit or 3

4 Selling Price per Unit = Average Cost per Unit + Target Profit per Unit Firms use many derivations of the Basic Cost Based Pricing Equation. However, all practical cost based pricing equations are derived from the Basic Cost Based Pricing Equation. Answering The Questions The three exam questions at the top of this note are easily answer if a student knows how to derive the thirteen equations that are the classic variations of the Basic Profit Equation. In all three of the exam questions, the student is being asked to find the selling price using a cost based pricing formula. Answering Question 1 The first question is very popular in introductory marketing courses. In the first question we are given the markup, but no information on why the person desired this level of markup. We can assume the markup is a target markup which will cover the person s fixed costs and profits. We are told in the question that the desired markup on price is 60% and students know that the markup on price equation is (Equation 2) M p = (P-V)/P We must assume that the desired markup, M p, is the target markup. We simply substitute the BEM p * as the desired markup, M p, in equation 2. BEM p * = (P V)/P Reorganize to solve for the price, P. P(BEM p *) = P V P (1 BEM p * = V P = V / (1 BEM p *) This pricing formula is extremely popular among retailers and is often called the markup pricing equation because it involves the invoice cost of the goods being sold and the retailer s target markup on price. The Markup Pricing Equation is written (Equation 14) P = V / (1 BEM p *) In order to answer question #1, we substitute the values for the variable cost (V = $4) and the target markup (BEM p * = 60%) into equation 14 and solve for the person s selling price, P, P = $4/(1-0.6) = $4/0.4 = $10 4

5 Answering Question 2 Retailers often use a target markup that covers their fixed costs and provides a target markup. The second question is more realistic than the first because it gives us the retailer s costs, profit, and desired markup. The question gives the student enough information to calculate the average cost per unit, however, there is no need to calculate it because we are told the target markup that is needed. Most of the information, a student will find in the firm s data base and operating statement, is not needed to solve question 2. The second question is the same as the first question but it is more confusing to students because they are given more information than they need. Question #2 is solved in the same way as question #1 substituting the target markup BEM p * for the markup in equation 2. (Equation 2) M p = (P-V)/P BEM p * = (P V)/P The student solves for the price, P, using the same retailer s markup pricing equation used in solving question #1. (Equation 14) P = V / (1 BEM p *) The student substitutes the values given in the question and solves for the retailer s price using equation 14. P = $4/(1 0.6) = $4/0.4 = $10 Answering Question #3 Before we start question #3 we must remember that manufacturers tend to think in terms of their average costs of production and net profit margins. The third question provides information on the costs of production. The desired level of profit is given by providing information on the desired return on sales (a.k.a., the net profit margin). We know that the Basic Pricing Equation with a target profit is equation 13. (Equation 13) P = V + F/Q + Z/Q but there is a need to calculate the target profit. Calculating the Target Profit The target profit, Z, is the return on sales times the sales revenue or Z = ROS(R) = ROS(PQ). This value for Z is substituted into equation 13. P = V + F/Q + ROS(PQ)/Q and this is simplified to be P = V + F/Q + ROS(P) The equation is reorganized to solve for the selling price, P. 5

6 P - ROS(P) = V + F/Q P (1-ROS) = V + F/Q P = (V+ F/Q) / (1 ROS) and is often written as (Equation 15) P = BEP / (1 ROS) where BEP is the Breakeven Price or average cost per unit. Equation 15 is one of the best known formulae for calculating cost based prices in the manufacturing environment. Equation 15 is found in most introductory textbooks on marketing as a version of markup pricing equations. The values given in question #3 are substituted into equation 15 to find the manufacturer s selling price, P. P = ($4 + ($50,000/20,000)) / (1 35%) P = ($4 + $2.5) / 0.65 = $6.5 / 0.65 = $10 The fundamental difference between equation 14 and equation 15 is that retailers use the variable cost per unit and have a target profit built into their markups and manufacturers use the average cost per unit and have a target profit built into their return on sales ratio. In all three questions, the answer is to set a selling price of $10. They have a common answer because all three problems are drawn from the same operating statement and have the same basic profit equation. Exploring The Proof The basic profit equation is (Equation 1) Z= PQ -VQ - F where Z = target profit P = price cost per unit = $10 (as calculated above) V = variable cost per unit = $4 (as given in the problem) Q = quantity sold = 20,0000 (as given in the problem) F = total period or fixed costs = $50,000 (as given in the problem) Substitute all the values into equation 1 to calculate the net profit, Z. Z = $10 (20,000) - $4 (20,000) - $50,000 = $70,000 The return on sales (ROS) is calculated as ROS = Z/PQ = $70,000/$200,000 = 35% 6

7 and this corresponds to the information in question #3 The markup on price (M p )is calculated as M p = (P-V)/P = ($10-$4)/$10 = 60% and this corresponds to the information in questions #1. Other calculations that can be tested are: Breakeven Quantity = BEQ = (F)/(P-V) BEQ = $50,000/$10-$4) = 8,334 units Breakeven Quantity with a target profit = BEQ*= (F + Z)/(P-V) = BEQ* = ($50,000 + $70,000) /$10-$4) = 20,000 units Breakeven Revenue = BER = F / M p BER= $50,000 / 0.6 = $83,334 Breakeven Revenue with a target profit = BER* = (F+Z) /M p BER* = ($50,000 + $70,000) / 0.6 = $200,000 The Breakeven Markup with a target profit re-writes Breakeven Revenue as Breakeven Markup with target profit = BEMp* = (F+Z) / BER* BEMp* = ($50,000 + $70,000) / $200,000 = 60% and this corresponds to the information in question #2. The retailer s markup pricing equation (14) and the manufacturer s ROS based pricing equation (15) are very popular. The equation that retailers tend to use relies on having a target markup (on price) that covers the fixed costs for the period and produces the desired profit level. Retailers like equation 14 because it allows them to mark up the invoice cost of the goods they have bought by their desired target Markup. They find the equation easy because they know the variable cost (a.k.a. CoGS) and the target markup they need to cover fixed costs and profit. That is to say, they use equation 14 where Retailer s price = (Variable Cost per unit) / (1- Desired Markup on Price) or Retailer s price = (Invoice Cost per unit) / (1-Target Discount Off List) 7

8 The equation that manufacturers tend to use relies on having a target profit measured as a return on sales (ROS) that covers the average cost per unit and the desired level of profit. That is to say, they use equation 15 where Price = (Average cost per unit) / (1- the desired return on sales) or Manufacturer s price = (Breakeven Price) / (1- target ROS) Conclusion The crucial point of this note is that all cost based pricing formulae are derived from the basic profit equation in equation 1. 1) Students must know the Basic Profit Equation. 2) Students should know how to derive the Basic Cost Based Pricing Equation from the Basic Profit Equation 3) Students should know how to derive the Retailer s Markup Pricing Equation from the Basic Cost Based Pricing Equation. 4) Students should know how to derive the Manufacturer s ROS Based Pricing Equation from the Basic Cost Based Pricing Equation. Students who can NOT derive basic equations such as breakeven, markup and pricing from the basic profit equation are doomed to memorize them again and again and again and... 8