Exam Question on Advertising Elasticity

Advertising Profit Z 0 Return on Advertising Expense is always falling Z = ROAE x Advertising Z = (Z/A) x A

Elasticity of Return on Advertising Is a metric that indicates if an increase in advertising will result in an increase or decrease in the profit after advertising. Aka, Elasticity of Advertising Productivity

Point Elasticity of ROAE Defined Elasticity of Return on Advertising Effort Ratio of (Percentage Change in ROAE) ÷ (Percentage Change in Advertising Expense) %∆ROAE / %∆A

How to use Elasticity of ROAE If the Elasticity of ROAE is equal to -1, then the optimal level of advertising expense has been reached for maximizing profit after advertising If the Elasticity of ROAE is between 0 and -1, then a small increase in advertising should increase profits If Elasticity is more negative than -1.0 then a decrease in advertising will increase profits

Advertising A* Profit Z Elasticity of Return on Advertising

Elasticity of Promotion Productivity How to estimate the arc elasticity of return on ANY or total promotional expenditure

Period 1 Revenue, R$1,000 Cost of Goods Sold, COGS$400 Gross profit, G = R-COGS$600 Total Promotion, TP$200 Profit after Promotion, NMC = G-TP$400 Return on Marketing Effort, NMC/TP$400/$200 = 200%

ROME Promotion Expenditure The Relationship between total promotion expenditure and the return on promotion expenditure

ROME = NMC/TP Promotion Expenditure Net Marketing Contribution= Total Promotion Expenditure x the Return on Total Promotion Expenditure NMC = ROME x TP = 200% x $200 = $ % $200

What We Know so far 1) That there is an optimal level of promotion, A* 2) That maximizes Profit after Promotion, NMC 3) Therefore there is an optimal Return on Promotion Expenditure, ROME*

ROME = NMC/TP Promotion Expenditure Maximum NMC* = ROME* x TP* ROME* A*

ROME = NMC/TP Promotion Expenditure ROME* A* ROME A ROME x A = the non- maximum NMC

ROME = NMC/TP Promotion Expenditure ROME* A* ROME A Increase in NMC due to change in Promotion, ∆A Decrease in NMC due to change in ROME

When the decrease in NMC due to the impact of the change in ROME is greater than the positive Impact of the change in Promotion, ∆A, then the profit, NMC, must decrease

How do we estimate the Elasticity of the Return on Promotion? PROMOTION, A Quantity Q = kA a

An Example Constant Price = $80 Constant Variable Cost = $20 Quantity sold, Q = 1600A 0.29 Total Promotion, A is changing What is the Gross profit, G ? What is the Profit after Promotion, NMC? What is the ROME?

Promotion Profit NMC 0 $1,700,000 $1,500,000 ?????

Period 1Period 2∆I∆ on NMC $Markup, P-V $60 Quantity, Q Q = 1600A ,898102,5533,656 Gross Profit, G = (P-V)Q $5,933,866$6,153,206$219,340 Promotion, A $1,500,000$1,700,000$200,000I∆A = 2.62($200,000) =$523,906 Profit after Promotion, G-A= NMC $4,433,866$4,453,206$19,340 ROME = NMC/A I∆ROME = $1,500,000(- 0.34)= -$504,566 Elasticity of ROME = I∆ROME/I∆A = -$504,566/$523,906 = -0.96

Period 1Period 2∆I∆ on NMC $Markup, P-V $60 Quantity, Q Q = 1600A ,898102,5533,656 Gross Profit, G = (P-V)Q $5,933,866$6,153,206$219,340 Promotion, A $1,500,000$1,700,000$200,000I∆A = 2.62($200,000) =$523,906 Net Profit, G-A= NMC $4,433,866$4,453,206$19,340 ROME = NMC/A I∆ROME = $1,500,000(- 0.34)= -$504,566 Elasticity of ROME = I∆ROME/I∆A = -$504,566/$523,906 = -0.96

An Example What is the ∆A? What is the ∆ROME? These will help explain the change in Profit after Promotion, NMC

Period 1Period 2∆I∆ on NMC $Markup, P-V $60 Quantity, Q Q = 1600A ,898102,5533,656 Gross Profit, G $5,933,866$6,153,206$219,340 Promotion, A $1,500,000$1,700,000$200,000I∆A = 2.62($200,000) =$523,906 Net Profit, NMC $4,433,866$4,453,206$19,340 ROME I∆ROME = $1,500,000(- 0.34)= -$504,566 Elasticity of ROME = I∆ROME/I∆A = -$504,566/$523,906 = -0.96

Period 1Period 2∆I∆ on NMC $Markup, P-V $60 Quantity, Q Q = 1600A ,898102,5533,656 Gross Profit, G $5,933,866$6,153,206$219,340 Promotion, A $1,500,000$1,700,000$200,000I∆A = 2.62($200,000) =$523,906 Net Profit, NMC $4,433,866$4,453,206$19,340 ROME I∆ROME = $1,500,000(- 0.34)= -$504,566 Elasticity of ROME = I∆ROME/I∆A = -$504,566/$523,906 = -0.96

An Example What is the impact of the change in Promotion, ∆A, on the increase in the Profit after Promotion, ∆NMC? What is the impact of the change in ROME, ∆ROME, on the increase in the Profit after Advertising, ∆NMC?

Period 1Period 2∆I∆ on NMC $Markup, P-V $60 Quantity, Q Q = 1600A ,898102,5533,656 Gross Profit, G $5,933,866$6,153,206$219,340 Promotion, A $1,500,000$1,700,000$200,000I∆A = 2.62($200,000) =$523,906 Net Profit, NMC $4,433,866$4,453,206$19,340 ROME I∆ROME = $1,500,000(- 0.34)= -$504,566 Elasticity of ROME = I∆ROME/I∆A = -$504,566/$523,906 = -0.96

Period 1Period 2∆I∆ on NMC $Markup, P-V $60 Quantity, Q Q = 1600A ,898102,5533,656 Gross Profit, G $5,933,866$6,153,206$219,340 Promotion, A $1,500,000$1,700,000$200,000I∆A = 2.62($200,000) =$523,906 Net Profit, NMC $4,433,866$4,453,206$19,340∆NMC = I∆A + I∆ROME ROME I∆ROME = $1,500,000(- 0.34)= -$504,566 Elasticity of ROME = I∆ROME/I∆A = -$504,566/$523,906 = -0.96

An Example What is the ARC Elasticity of ROME?

Period 1Period 2∆I∆ on NMC $Markup, P-V $60 Quantity, Q Q = 1600A ,898102,5533,656 Gross Profit, G $5,933,866$6,153,206$219,340 Promotion, A $1,500,000$1,700,000$200,000I∆A = 2.62($200,000) =$523,906 Net Profit, NMC $4,433,866$4,453,206$19,340∆NMC = I∆A + I∆ROME ROME I∆ROME = $1,500,000(- 0.34)= -$504,566 Elasticity of ROME = I∆ROME/I∆A = -$504,566/$523,906 = -0.96

Period 1Period 2∆I∆ on NMC $Markup, P-V $60 Quantity, Q Q = 1600A ,898102,5533,656 Gross Profit, G $5,933,866$6,153,206$219,340 Promotion, A $1,500,000$1,700,000$200,000I∆A = 2.62($200,000) =$523,906 Net Profit, NMC $4,433,866$4,453,206$19,340∆NMC = I∆A + I∆ROME ROME I∆ROME = $1,500,000(- 0.34)= -$504,566 Arc Elasticity of ROME = I∆ROME/I∆A = -$504,566/$523,906 = -0.96

Elasticity of our Promotional Productivity is equal to If we spend more on promotion, then will we make more profit?

Promotion Profit NMC 0 Elasticity of Return on Promotion $1,700,

Promotion A* Profit NMC Elasticity of Return on Promotion $1,700,000

What we learned! You can easily overspend your optimal advertising budget if you use the cost based average sales ratio as a straight line advertising rate. e.g. Q = Q/A x A Use estimates of the estimates of the elasticity of advertising and return on marketing effort

Advertising A* Profit Z 0 Profit Function can be very flat Thus Small Errors From Optimal can have little Impact