Exam Question on Advertising Elasticity

Advertising

Profit

Z

0

Return on Advertising Expense is always falling

Z = ROAE x AdvertisingZ = (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

AdvertisingA*

Profit

Z

0

-0.5 -0.75 -1.0 -1.25 -1.5 -1.75 -2.0

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 = $400

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

QuantityQ = kAa

An Example

• Constant Price = $80• Constant Variable Cost = $20• Quantity sold, Q = 1600A0.29

• 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 1 Period 2 ∆ I∆ on NMC$Markup, P-V $60 $60

Quantity, QQ = 1600A0.29

98,898 102,553 3,656

Gross Profit, G = (P-V)Q

$5,933,866 $6,153,206 $219,340

Promotion, A $1,500,000 $1,700,000 $200,000 I∆A = 2.62($200,000) =$523,906

Profit after Promotion, G-A= NMC

$4,433,866 $4,453,206 $19,340

ROME = NMC/A

2.96 2.62 -0.34 I∆ROME = $1,500,000(-0.34)= -$504,566

Elasticity of ROME = I∆ROME/I∆A = -$504,566/$523,906 = -0.96

Period 1 Period 2 ∆ I∆ on NMC$Markup, P-V $60 $60

Quantity, QQ = 1600A0.29

98,898 102,553 3,656

Gross Profit, G = (P-V)Q

$5,933,866 $6,153,206 $219,340

Promotion, A $1,500,000 $1,700,000 $200,000 I∆A = 2.62($200,000) =$523,906

Net Profit, G-A= NMC

$4,433,866 $4,453,206 $19,340

ROME = NMC/A

2.96 2.62 -0.34 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 1 Period 2 ∆ I∆ on NMC$Markup, P-V $60 $60

Quantity, QQ = 1600A0.29

98,898 102,553 3,656

Gross Profit, G $5,933,866 $6,153,206 $219,340

Promotion, A $1,500,000 $1,700,000 $200,000 I∆A = 2.62($200,000) =$523,906

Net Profit, NMC

$4,433,866 $4,453,206 $19,340

ROME 2.96 2.62 -0.34 I∆ROME = $1,500,000(-0.34)= -$504,566

Elasticity of ROME = I∆ROME/I∆A = -$504,566/$523,906 = -0.96

Period 1 Period 2 ∆ I∆ on NMC$Markup, P-V $60 $60

Quantity, QQ = 1600A0.29

98,898 102,553 3,656

Gross Profit, G $5,933,866 $6,153,206 $219,340

Promotion, A $1,500,000 $1,700,000 $200,000 I∆A = 2.62($200,000) =$523,906

Net Profit, NMC

$4,433,866 $4,453,206 $19,340

ROME 2.96 2.62 -0.34 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 1 Period 2 ∆ I∆ on NMC$Markup, P-V $60 $60

Quantity, QQ = 1600A0.29

98,898 102,553 3,656

Gross Profit, G $5,933,866 $6,153,206 $219,340

Promotion, A $1,500,000 $1,700,000 $200,000 I∆A = 2.62($200,000) =$523,906

Net Profit, NMC

$4,433,866 $4,453,206 $19,340

ROME 2.96 2.62 -0.34 I∆ROME = $1,500,000(-0.34)= -$504,566

Elasticity of ROME = I∆ROME/I∆A = -$504,566/$523,906 = -0.96

Period 1 Period 2 ∆ I∆ on NMC$Markup, P-V $60 $60

Quantity, QQ = 1600A0.29

98,898 102,553 3,656

Gross Profit, G $5,933,866 $6,153,206 $219,340

Promotion, A $1,500,000 $1,700,000 $200,000 I∆A = 2.62($200,000) =$523,906

Net Profit, NMC

$4,433,866 $4,453,206 $19,340∆NMC = I∆A + I∆ROME

ROME 2.96 2.62 -0.34 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 1 Period 2 ∆ I∆ on NMC$Markup, P-V $60 $60

Quantity, QQ = 1600A0.29

98,898 102,553 3,656

Gross Profit, G $5,933,866 $6,153,206 $219,340

Promotion, A $1,500,000 $1,700,000 $200,000 I∆A = 2.62($200,000) =$523,906

Net Profit, NMC

$4,433,866 $4,453,206 $19,340∆NMC = I∆A + I∆ROME

ROME 2.96 2.62 -0.34 I∆ROME = $1,500,000(-0.34)= -$504,566

Elasticity of ROME = I∆ROME/I∆A = -$504,566/$523,906 = -0.96

Period 1 Period 2 ∆ I∆ on NMC$Markup, P-V $60 $60

Quantity, QQ = 1600A0.29

98,898 102,553 3,656

Gross Profit, G $5,933,866 $6,153,206 $219,340

Promotion, A $1,500,000 $1,700,000 $200,000 I∆A = 2.62($200,000) =$523,906

Net Profit, NMC

$4,433,866 $4,453,206 $19,340∆NMC = I∆A + I∆ROME

ROME 2.96 2.62 -0.34 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 -0.96

• If we spend more on promotion, then will we make more profit?

Promotion

Profit

NMC

0

Elasticity of Return on Promotion

$1,700,000

-0.96

PromotionA*

Profit

NMC

0

-0.5 -0.75 -1.0 -1.25 -1.5 -1.75 -2.0

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

AdvertisingA*

Profit

Z

0

Profit Function can be very flatThus Small Errors From Optimal can have little

Impact