Review of Key Quantitative Problems for Final Exam Ted Mitchell

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1 Review of Key Quantitative Problems for Final Exam Ted Mitchell One very important goal of this course is to ensure that all marketing students have mastered basic quantitative skills and have solved basic problems found in marketing management cases. Students must feel comfortable using a cost-based, a competitivebased and a customer-based approach to marketing management and planning. All the quantitative questions from the previous exams are potential candidates for the final exam. Some are more likely than others depending on how many students had problems with them on previous exams. The more students who find a question difficult, then the more likely the question will be on the final. For example, the first three questions have been poorly done in the first midterm and they will probably show up again. 1. Your boss is reviewing last year s sales performance. The quantity sold was 2,000 units and the revenue was $6,000 in period 4. The quantity sold was 2,500 units and the revenue was $5,000 in period 3. The $1,000 increase in performance must be explained. You had authorized a price increase from $2.00 to a higher price of $3.00 per unit. What is the dollar impact on the total revenue due to the change in selling price? a) $1,000 b) $2,000 * c) $1,500 d) $2,500 e) $1,000 Revenue change R4 R3 = 6,000-5,000 = 1,000 Price Variance = Impact on revenue change due to price change Qmin(P4 P3) = 2,000 ($3 $2) = $2,000 Quantity Variance = Impact on total revenue due to quantity change= Pmin(Q4 Q3) = $2 (2,000 2,500) = $1,000 Remember to use the minimum value of the two Prices (Pmin) and the minimum value of the two Quantities (Qmin). 2. You are reviewing your market share using the four component method of analysis. Your customer penetration is 30%. Your level of customer loyalty is 50%. When your customers buy from you their average order size is 150% of the average order size for the industry. Your prices are 110% of the average industry price. What market share do you believe you should be getting? a) 33% b) 10% c) 24.75% * d) 22.4% e) 21.87% 0

2 Market Share = share of customers (penetration) X share of purchases customers make (loyalty) x share of order size (share of size) x relative price ratio (share of average price) Market Share =.3 x.5 x 1.5 x 1.1 = = 24% 3. The audience response model implies that customers move through stages from Awareness to Purchase. Currently 60% of the target audience is aware of a product and 10% of the target audience is buying it. What percentage of the target audience would buy the product if your plan to increase customer awareness to 90% works? a) 15% * b) 32% c) 29.8% d) 25% e) 48% : The simple audience response chain is Purchases = (total audience) x (number aware of product) / (total audience) x (number who purchase) / (number aware of product) Purchase percentage = 100% x awareness transition x purchase transition We must first calculate the purchase transition rate Awareness transition = (number aware of product) / (total audience) Purchase transition = total audience) x (number who purchase) / (number aware of product) 10% = 100% x (60/100) x (Purchase Transition rate) Current Purchase transition = 10% / (100% x 0.6) = 10/60 = If the awareness transition is increased to 90% or 0.9 New Purchase percentage = 100% x 0.9 x = 15% Remember this simple audience response chain can be easily expanded into the classic chain Awareness-Knowledge-Liking-Preference-Conviction-Purchase See page 374 of the text 4. A boy buys a wagon for $60. He sells it with a 40% markup on the selling price. What is his selling price? a $4.20 b $100 * c $5.00 d $5.20 e $7.50 Best answer is P - V = Mp(P) P-60 =.4P P-.4P = 60.6P = 60 P = 60/.6 = 100 1

3 5. The company is losing 25% of its old customer accounts each year to its competitors. What is the average number of years for the company to keep an old account before it is lost to a competitor? a 20 years b 2 years c 4 years * d 5 years e 50 years Best answer is defection rate = 1 / life of customer 0.25 = 1 / life life = 1 / 0.25 = 4 years 6. The variable costs to make and sell a single product are 60% of the sales revenue. Fixed costs are $240,000 per period. What is the before tax profit if sales reach $900,000? What sales revenue must be achieved to breakeven? a Profit = $80,000, Breakeven revenue = $600,000 b Profit = $240,000, Breakeven revenue = $400,000 c Profit = $80,000, Breakeven revenue = $400,000 d Profit = $120,000, Breakeven revenue = $600,000 * e Profit = $480,000, Breakeven revenue = $320,000 Best answer is Contribution = R - 0.6R = 0.4R Z = 0.4R - F Z = 0.4(900,000) - 240,000 Z = 360, ,000 = 120,000 Breakeven Revenue = F / Markup Breakeven Revenue = $240,000 /.4 = $600, You are working for a boss using a cost based markup pricing formula. The variable cost per unit is $80 and the fixed costs are $400,000 per period. You expect to make a normal profit of $3,333,333 by selling 20,000 units next period. What is your average cost per unit or unit cost? What price per unit do you charge? a Unit Cost = $60, Price per Unit = $ b Unit Cost = $80, Price per Unit = $ c Unit Cost = $100, Price per Unit = $ d Unit Cost = $100, Price per Unit = $ * e Unit Cost = $80, Price per Unit = $ Best answer is Unit cost = Variable Cost + (Fixed Costs / Quantity) Unit cost = V + (F / Q) = $80 + ($400,000 / 20,000) = $80 + $20 = $100 Basic Profit Equation Z = PQ VQ F P = V + F/Q + Z/Q 2

4 P = 80 + (400,000/20,000) + (3,333,333/20,000) P = = $ Life is simple when the boss tells you the target profit in dollars. 8. You are a retailer using a cost based markup pricing formula. The variable cost per unit is $80 and the fixed costs are $400,000 per period. You expect to make a normal profit by selling 20,000 units next period with a normal markup of 70%. What is your average cost per unit? What price per unit do you charge? a average cost per unit = $60, Price per Unit = $ b average cost per unit = $80, Price per Unit = $ c average cost per unit = $100, Price per Unit = $ d average cost per unit = $100, Price per Unit = $ * e average cost per unit = $80, Price per Unit = $ Best answer is Unit cost = Variable Cost + (Fixed Costs / Quantity) Unit cost = V + (F / Q) = $80 + ($400,000 / 20,000) = $80 + $20 = $100 Markup Pricing Formula P* = Variable cost / (1 - Markup) P* = 80/ ( 1-0.7) = 80 /.30 = $ Remember the retailer is using markup based on the cost of his inventory because he has a target or normal markup = F+Z / R with a normal profit and fixed costs built in. The average cost per unit is not used in the formula because that would double count the fixed costs. However, manufacturers tend to use an expected or normal return on sales (ROS) in their cost based pricing calculations, not the simple markup on price. 9. You are a manufacturer using a cost based markup pricing formula. The variable cost per unit is $80 and the fixed costs are $400,000 per period. You expect to make a normal profit by selling 20,000 units next period and earn a normal profit of 62.5% RETURN ON SALES (ROS). What is your average cost per unit or Breakeven price? What price per unit do you charge? a BEP = $60, Price per Unit = $ b BEP = $80, Price per Unit = $ c BEP = $100, Price per Unit = $ d BEP = $100, Price per Unit = $266.67* e BEP = $80, Price per Unit = $ Best answer is Unit cost = Variable Cost + (Fixed Costs / Quantity) Unit cost = V + (F / Q) = $80 + ($400,000 / 20,000) = $80 + $20 = $100 Markup Pricing Formula P* = BEP / (1 - ROS) P* = 100/ ( ) = 100 / = $ Note that the prices in questions 7, 8 and 9 are the same because the information in the operating statement is the same. Revenue = PQ = x 20,000 = $5,333,333 COGS = VQ = 80 x 20,000 = $1,600,000 Gross = 3,733,333 markup = 3733,333 / 5,333,333 = 70% Fixed, F = $400,000 3

5 Profit, Z = 3,333,333 return on sales 3,333,333 / 5,333,333, = 62.5% All three questions tell you what the normal sales and costs are. The only difference is the manner in which the target or normal profit is discussed. The great weakness of all costbased systems is that it is Bass Ackwards. That is to say, sales volume is determining the price to charge, whereas the proper model is that the price we charge will determine the sales volume we get. 9. Market research has estimated the demand for your product to be Q = P The variable costs of producing and selling the product are $80 per unit and the fixed costs are 125,000. What price per unit will maximize revenues? What price per unit will maximize profit? a Price to Max Revenue = $500, Price to Max Profit = $530 b Price to Max Revenue = $500, Price to Max Profit = $470 c Price to Max Revenue = $250, Price to Max Profit = $220 d Price to Max Revenue = $300, Price to Max Profit = $340 * e Price to Max Revenue = $500, Price to Max Profit = $560 Demand is Q = a bp Revenue is R = PQ = P(a-bP) = ap bp 2 Take the first derivative dr/dp and set it equal to zero P to max revenue = a / 2b = 6000 / 2(10) = $300 Net Profit is Z = PQ VQ F Z = P(a-bP) V(a-bP) F Take the derivative dz/dp and set equal to zero P to max profit = (a / 2b) + (V/2) = (6000/2(10)) + (80 / 2) = = $ Your price elasticity is estimated at -2.5 and your marketing plan calls for a price decrease of 5%. What percentage increase in sales volume can you anticipate? a a quantity increase of 2.5% b a quantity decrease of 2.5% c a quantity increase of 12.5% * d a quantity decrease of 7.5% e a quantity increase of 6.5% Price elasticity = (% change in Q) / (% change in Price) -2.5 = (%change in Q) / -5% (%change in Q) =-2.5(-5%) = 12.5% 4

6 11. Your product has 150% markup on cost and your marketing plan requires $420,000 in new advertising budget. What is the markup on price? What sales revenue is required to breakeven on the new advertising budget? a Markup = 66.67%, Breakeven Revenue = $600,000 b Markup = 100%, Breakeven Revenue = $400,000 c Markup = 60%, Breakeven Revenue = $700,000 d Markup = 100%, Breakeven Revenue = $600,000 e Markup = 66.67%, Breakeven Revenue = $120,000 (1 / Mp) - (1 / Mc) = 1 or 150/250 = 3/5 = 60% Breakeven discussion chapter 16 pages BER = F / Markup = 420,000 /.60 = $700, The product manager has been studying the price elasticity of the demand in his target market and feels that a 6% reduction in price will generate 15% more sales volume without any new selling expenses. The marketing manager believes that any change in pricing strategy must maintain or increase the current gross contribution margin. Fixed costs are $170,000 per year and product has a 30% markup, Mp. What is the estimated price elasticity? What percentage increase in quantity is needed to maintain the current total contribution or gross profit margin? a Elasticity = -0.33, Minimum increase = 20% b Elasticity = -0.33, Minimum increase = 16.67% c Elasticity = -2.5, Minimum increase = 25% * d Elasticity = -3, Minimum increase = 16.67% e Elasticity = -0.3, Minimum increase = 20% Elasticity = ( % change in Q) / ( % change in P) = 15% / -6% = -2.5 The percentage increase needed to maintain the current gross profit contribution. % Increase in Q = -(%change in price) / Markup% + (% change in Price) % Increase in Q = - (-6) / (30 +(-6)) = 6 / 24 = 1/4 = 25% see pages You have marked down the original price of your inventory by 20% a month ago. You marked it down by an additional 25% two weeks ago. Yesterday you marked it up by 10%. What is the current price if the original price was $10 a) $6.60 b) c) Current price = $10 x (1-0.2) x (1-0.25) x (1+0.1) = $10 x 0.8 x 0.75 x 1.1 = $10x 0.66 The current price is 0.66 x10 = $6.60 5

7 14. The manufacturer's price is $100 and the retail list price is $500. The retailer gets a discount off list as his margin and the wholesaler gets an additional discount of 20%. What is the retailer's discount off list? The manufacturer's price is $100 and the retail list price is $500. The retailer gets a discount off list as his margin and the wholesaler gets an additional discount of 20%. What is the retailer's discount off list? a. 50% * b. 40% c. 80% d. 25% : The formula is Manufacturer s price = list price (1-retail discount) (1-wholesale discount) $200 = $500(1-retail discount) (1-20%) 200/500 = (1-retail discount) (.8).4/.8 = 1 -retail discount Retail discount = 1 -.4/.8 = 50% 15. Suppose a media planner has a budget of $5,000,000 and the cost per thousand exposures is $10. The planner wants a frequency of 20 exposures per household. The planner can attain a reach of households a. 50,000,000. b. 25,000,000. * c. 250,000,000. d. 2,500,000. e. 5,000,000. Reach x Frequency x cost/1000 = the budget The budget = R x F x cost per 1,000 exposures 5,000,000 = R x 20 x10/1000 5,000,000,000 = R x 200 R = 5,000,000,000/200 = 50,000,000/2 = 25,000,000 households 16. A manufacturer makes a product for a variable cost of $120 per unit. He sells the product with a 40% markup to the wholesaler. The wholesaler sells the product to a retailer. The retailer sells the product to consumers for $400 and has a 60% markup on his cost from the wholesaler. What is the wholesaler s markup in dollars? a. $250 b. $200 c. $72 d. $50 * e. $240 Manufacturer s price = P P 120 =.4P 6

8 0.6P = 120 P = $200 = Vw Retailer s cost = V 400 V = 0.6V V+ 0.6V = V = 400 V= 400/1.6 = $250 = Pw Retailer s dollar markup = Pw-Vw = $250 $200 = $ You know that a customer based advertising model is superior to a cost based model for setting advertising budgets. You have estimated the audience s response to your advertising budget to Q = 20,000 A 0.4 where A is the size of the budget, and Q is the volume sold. Your selling price is $6 and your variable cost per unit is $5.90. Your current advertising budget is $300,000 and you are selling 3,103,370 units. Your boss is incompetent and he wants to increase the sales volume by increasing the advertising budget by $100,000. He uses the average response of sales to budget and believes the $100,000 increase in effort will increase the sales volume by 1,034,560 units. What is the sales volume you should predict to be the result of the $100,000 increase in budget and what is the new breakeven volume needed to cover the $400,000 budget? a) 3,482,202 units and BEQ = 4,000,000 units b) 4,137,930 units and BEQ = 4,000,000 units c) 3,482,202 units and BEQ = 3,000,000 units d) 4,137,930 units and BEQ = 3,000,000 units Q = 20,000 A 0.4 Q = 20,000 (400, ) = 3,482,202 units BEQ = F/(P-V) = $400,000 /(6-5.9) 4,000,000 units If the boss expects you to reach a breakeven volume in the next period then you might want to start looking for a new place to work and tell your boss to take marketing 316. Never use the average rates unless the changes in budget are very small and a 25% increase in budget is NOT small. 18) The target audience has the following transition rates in the audience response model awareness to knowledge = 40% knowledge to liking = 30% liking to preference = 60% preference to conviction = 20% conviction to purchase = 50% The current awareness level is 70%. What percentage of the target audience is purchasing the product? If your plan to use a new coupon increases the conviction to purchase rate to 60% then what is the new percentage of the audience purchasing the product? a) 0.5%, new purchase rate 0.6%* b) 0.7%, new purchase rate 0.5% c) 0.7%, new purchase rate 0.6% d) 0.5%, new purchase rate 0.86% e) 0.7%, new purchase rate 0.86% 7

9 Purchase Percentage =.7 x.4 x.3 x.6 x.2 x.5 =.005 = 0.5% New Purchase percentage =.7 x.4 x.3 x.6 x.2 x.6 =.006 = 0.6% If the increase is worth the cost depends on the size of the audience and the profit per purchase. The high involvement model of the audience response chain students learn in MKT210 is awareness-knowledge-liking-preference-conviction-purchase. The transition rates from one stage in the buyer response chain to the next allows advertising managers to predict the consequences of changing the transition rates by changing advertising strategy. 19. Your company is experiencing a 77% customer retention rate per year. What is the average number of years a customer stays loyal to your company? a. 5 years b years * c. 2 years d. 3 years Years = 1 / (1-.77) = 1 /.23 = 4.35 Remember the loss rate or defection rate is 1-(the retention rate) Other closely related questions dealing with retention. Your company is losing customers to your competition at a rate of 25% a year. You have proposed a new loyalty program that should improve the current retention rate by 105%. If your plan is adopted there will be a smaller rate of loss. The plan needs to have the life of the average customer account increase by 6 months to breakeven What is the average life of a customer s account with the current loss rate? What is the current retention rate? What is the new loss rate if your plan is accepted? What is the new retention rate? With the new loss rate, what is the average life of a customer? Is the improved life of an account greater than 6 months? s The current loss rate is 25% The average life of a current account is 1/.25 = 4 years The current retention rate is 1-25% = 75% The new retention rate will be 1.05(75%) =78.75% The new loss rate will be % = 21.25% The average life = 1/ = 4.71 years The average life increases by.71 years which is greater than 6 months 8

10 20. There are 4 companies competing in the Shoe industry. The average expenditure on all forms of promotion for each firm is $3 million. Your firm is spending $4 million. Your firm is charging an average price for an average quality shoe and you have an average customer satisfaction rating. According to the fundamental theorem of marketshare determination, what market share should you have given your share of voice? a) 25% b) 10% c) 13.3% d) 75% e) 33.3 %* : Assume that if all elements of marketing competition are equal in general Firm s Market Share = (Firm s effort)/ (total industry effort) Assume in this case all things are equal then Market Share = Share of Voice Market Share = $4/(4x$3) = $4/$12 = 33.33% 21. A customer will provide a positive net cash flow of $850 at the end of five years. If our cost of capital is 5%, then what is the best estimate of the present value of the $850? a. $410 b. $310 c. $666* d. $356 e. $518 Too many students get this wrong! It is basic finance to know that there is a time value to the money marketing pulls from customers over time. PV = 850 /( 1+.05) 5 PV = You have a current market share of 25% and the total size of the market is 9,000 units. Last period you had a market share of 20% and the total size of the market was 10,000 units sold. Your sales volume increased by 250 units from the last period to the current period. Your boss wants you to explain the change in our sales volume from the previous period to the current period. What impact, measured in number of units sold, did the shrinkage in the total market have on your sales volume? a) 200 units * b) 450 units c) 250 units d) 250 units e) 450 units The best answer is You have explain the change in your sales volume from period to period. It might be part of the problem in explaining the change in sales revenue. Remember Quantity sold = market share x market size or Q = S x M Current Volume = Q2 = 25% (9000) = 2,250 units Last Period Volume Q1 = 20% (10,000) = 2,000 units 9

11 Q2-Q1 = S2M2 S1M1 = 2,250-2,000 = 250 units Remember that Q2 Q1 = Smin(M2 M1) + Mmin(S2-S1) + joint impact Impact on Sales due to change in total market = 20% (9,000 10,000) = -200 units * Impact on Sales due to change in market share = 9,000 (25% 20%) = 450 units Net Change = 250 units joint impact = 0 Because quantity sold = market size x market share, students will see that basic revenue equation revenue = price x quantity is expanded to read revenue = price x market share x size of market (see pages 90-91) The change in revenue = change due to price + change due to share + share due to size + joint impacts It is the key to ensuring that marketing managers are rewarded for increasing their market share not the total market size. 23. You have forecasted the sales volume for the coming period to be 300,000 pairs of shoes, and your cumulative production up to the current period is 1,100,000 pairs. You know the learning curve for your business is V = 7500 Q where V = variable cost per pair, Q = cumulative quantity If you reach your forecasted volume, then the cost of making a pair of shoes will be close to $ a pair. a) $2 b) $21* c) $210 d) $26 e) $267 V = 7500( 1,400, ) = Many students seem to miss the negative sign The alternative way to write it is V = 7500/(1,400, ) But it is seldom written as a fraction 10

12 24. In the New Shoes simulation, you have the opportunity to bid on contracts to make private label or generic shoes. You estimate that if you do not win the bid for providing 40,000 pairs of shoes to Target that your cost per pair will be $24.27 for the period. If you win the bid then you estimate that your cost will be $23.88 per pair. You estimate your sales volume without winning the bid to be 260,000 pairs and if you win the bid, then your volume will be 300,000 pairs of shoes. Your average selling price per pair in your normal markets is $85 per pair. What is the lowest bid price you can offer that if it wins will maintain the same gross profit contribution as you would have earned if you didn t win the bid? a) bid $24.27 per shoe b) bid $23.88 per shoe c) bid $24.66 per shoe d) bid $21.35 per shoe * e) bid $ per shoe Situation 1: Without winning the bid Sales revenue without the winning bid is 260,000 x $85 = 22,100,000 Total cost of goods sold is 260,000 x $24.27 = $6,310,200 Gross profit contribution or gross profit margin is ($85-$24.27) 260,000 = $15,789,800 Situation 2 Winning the bid If I win the bid my total cost of goods sold is 300,000 x $23.88 = $7,164,000 I need to maintain the same gross profit contribution of $15,789,800 as in Situation 1 The revenues needed in situation 2 to maintain the same gross margin are calculated as Total Revenue needed = $7,164,000 + $15,789,800 = $22,953,800 Revenue from the 260,000 shoes in the regular market = $85(260,000) = $22,100,000 Revenue needed from winning the bid = total revenue regular revenue Revenue needed from winning the bid = $22,953,800 - $22,100,000 = $853,800 Revenue = price x quantity necessary Bid price per shoe = $853,800 40,000 = $21.35 per shoe 25. You are using a competitive based approach to setting your price. You want your price to be set to match your relative product quality. Your product has received a 4.5 star quality rating in the Industrial Digest Magazine compared to the average of 3.25 stars. There are 7 major brands in your industry and you have a market share of 15%. The average price in the industry is $90 per unit. What price should you charge if you want your price to reflect your relative quality? a) $65 b) $ c) $ * d) $ e) $ Relative quality is 4.5/3.25 = % of average quality 11

13 26. Your boss is very proud of the firm s product quality. The product has received a 4.5 star quality rating in the Industrial Digest Magazine compared to the average of 3.25 stars. There are 7 major brands in the industry and your firm has a market share of 15%. Your quality rating suggests that your firm could have a market share of almost 20%. The average price in the industry is $90 per unit. You have average distribution and promote your product regularly. You are currently charging the average price per unit but the boss is concerned that the market share is not reflecting the superior quality of the product. He believes that your promotion efforts are the reason that firm s superior product is not being converted into market share. What is the efficiency of your firm s ability to convert its share of quality into actual market share? a) 65% b) % c) 75%* d) 38.46% e) 72.22% answer Market Share Theorem holds that Actual market share = Efficiency of quality conversion x share of quality 15% = Efficiency of conversion x 20% by definition the Efficiency of conversion (actual share) (share of quality) 15/20 =75% The fact that the firm is having difficulty converting its premium quality into market share may be due to the lack of promotion effectiveness. Maybe the customers are not hearing how great the product is. Some firms assume that the lack of conversion efficiency is due to a lack of promotional effectiveness. 27. You are charging $85 for your product. The average industry price is $90 and it is used by your customers as their reference price. The market size is 1,000,000 shoes and you are selling a product with quality rated at level 2. There is a total of 10 firms in the industry and the average quality is rated at level 1.5. You are spending $3,000,000 in total promotion and the industry is spending a total of $50,000,000 in total promotion. Assume the simple revenue chain of R = Price x Quantity is expanded into the following marketing variables. Revenue = relative price ratio x reference price x market size x share of quality x share of voice x promotional effectiveness index where relative price ratio = % reference price = $90 market size =1,000,000 pairs of shoes share of quality = % share of voice = 6% efficiency in converting share of product quality into market share= 90%, promotional effectiveness index = 15 If your plan to improve the effectiveness of promotion budget works and promotion effectiveness index increases from 15 to 16 then the new sales revenue will be increased by approximately $. 12

14 a) $500,000* b) $1,500,000 c) $5,500,000 d) $15,000,000 The answer starts with Revenue is the product of a chain of marketing ratios For example: Revenue = $85 x 120,000 = 10,200,000 Where Actual price = $85 relative price ratio = 85/90 = % reference price = $90 market size =1,000,000 pairs of shoes Quantity sold = 120,000 Market share = 119,970/1,000,000 = 12% However, Market share is explained by the ability of the firm to converts its share of product quality or customer value into market share. We believe that market share must follow the relative product quality. Market Share = (efficiency in converting share of product quality into market share) x (share of quality) where (share of quality) = 2/(1.5 x10) = 2/15 = % (efficiency in converting share of product quality into market share) = (market share/ share of quality) = 12% / % = 0.9 = 90% Thus by this definition Market share = share of quality x efficiency of conversion Market share = 13.33% x 0.9 = 12% The ability of the firm to convert its share of product quality into market share is directly linked to the effectiveness of its promotional efforts in telling customers about the product s relative value. The firm s ability to promote effectively is directly related to its share of voice and its promotional effectiveness index. Efficiency of share of Quality Conversion = promotional effectiveness index x share of voice where share of voice = $3 million/ $50 million = 6% promotional effectiveness index = 90%/6% = 15 by this definition Efficiency of Quality conversion = 15 x 6% = 90% Substituting the values into each part of the chain Revenue = Price x Quantity Revenue = $85 x 120,000 = $10,200,000 Price = relative price ratio x reference price 13

15 $85 = x 90 Quantity = market size x market share 120,000 = 1,000,000 x 0.12 Market share = share of quality x conversion efficiency.12 = x.90 Conversion efficiency = share of voice x promotional effectiveness index.90 =.06 x 15 Through a series of substitutions we have the total chain as Revenue = relative price ratio x reference price x market size x efficiency of quality conversion x share of voice x promotional effectiveness index Revenue = (85/90 x 90) x 1,000,000 (.1333 x.06 x.90/0.06) Revenue = % x $90 x $1,000,000 x % x 6% x 15 = $10,199,999 Or approximately $10,200,000 with lots of potential for rounding errors. The new revenue is increased because the promotional effectiveness is increased and it is measured by the increase in the promotional effectiveness index from 15 to 16. This improvement increases the ability of the firm to increase its share by increasing the rate at which share of quality is converted into market share. Calculating the new revenue with the new promotional effectiveness. New Revenue = % x $90 x $1,000,000 x % x 6% x 16 = $10,879,999 Or approximately $10,880,000 and this represents an approximate increase in revenue of $680, The most important implication of using models of how the customers respond to advertising, quality, promotion and price, etc. is that there is an optimal level of marketing effort for maximizing the firm s profits Your market researchers have estimated the customer s response to advertising expenses to be Q = 40A 0.5 where Q = the quantity of units sold A = the size of the advertising budget Your firm is currently spending $45,000 on advertising. The selling price is $60 per unit and the variable cost is $50 per unit. General overheads and other fixed costs for the period are $25,000. How many units are being sold because of your advertising efforts? What is the firm s current net profit? a) the current volume is 8,485 units with a profit of $14,853 * b) c) Z = PQ VQ F A Where P = Price = $60 per unit 14

16 V = variable cost = $50 per unit Q = 40A 0.5 F = fixed period costs = $25,000 A = advertising = $45,000 First calculate the quantity sold Q = 40A 0.5 Q = 40 (45, ) = 8100 Then profit Z = $60(8485.3) - $50(8485.3) -25,000 45,000 =$14, Your market researchers have estimated the customer s response to advertising expenses to be Q = 40A 0.5 where Q = the quantity of units sold A = the size of the advertising budget Your firm is currently spending $41,000 on advertising. The selling price is $60 per unit and the variable cost is $50 per unit. General overheads and other fixed costs for the period are $25,000. What is the advertising budget that will maximize the profit in the period and how many units will be sold with the optimal advertising budget? a) optimal budget is $40,000 and sells 8,000 units* b) c) d) e) Z = PQ VQ F A Where P = Price = $60 per unit V = variable cost = $50 per unit Q = 40A 0.5 F = fixed period costs = $25,000 A = advertising = $45,000 First substitute the quantity sold into the profit equation Q = 40A 0.5 Z = P(40A 0.5 ) - V(40A 0.5 ) - F A Z = (P-V) (40A 0.5 ) F - A Take the first derivative w.r.t. advertising and set equal to zero dz/d A = (P-V)(40)(0.5) A dz/da = ((P-V)(20)/A 0.5 ) -1 set = 0 (P-V)(20)/A 0.5 = 1 A 0.5 = (P-V)(20) A = ((P-V)20) 2 A = 400(P-V) 2 15

17 Substitute P =$60, V = $50 A = 400 (60-50) 2 = $40,000 Proof At $40,000 in advertising Q = 40(40, ) = 8,000 Z = (P-V) 8,000 F -40,000 Z = (60-50) 8,000 25,000-40,000 = $15,000 Which is greater than the current profit of $14,853 with current advertising of $45,000. You are SELLING FEWER UNITS and making greater profits than with a smaller, optimal, advertising budget If $35,000 is spent in advertising Q = 40(35, ) = 7,483.3 Z = (60-50) (7,483.3) 25,000-35,000 = $14,833 Which is less than the maximum profit of $15,000 at Advertising = $40,000 16