Sales Math Workshop

Power-Up Sales

with the

Math Workshop

Page 2 Improving Performance

Topics Everyday challenges for sales, marketing and finance: 1. GM, Cost, and Price Relationships 2. Income (Expense), Profit (Loss), and GM Relationship 3. Calculate Compound Annual Growth Rate (CAGR) 4. Creating and using a Price Model 5. The impact of price changes on Revenue and Profit 6. Pareto Analysis (the 80/20 Rule) 7. Calculate Monthly Quota for an Annual Forecast 8. Calculate Quarterly Prices for a Step Price Proposal


Scenario’s


Scenario 1

Cost, ASP, and GM

Problem 1: Distributor says the competition is selling the product for $3.25, and his cost is $1.50. What is his GM? Problem 2: Distributor says he can’t charge more than $4.00, and he needs to make 25% GM on this deal. What does his cost need to be? Problem 3: The distributor cost is $7.25, and you know he is getting 25% GM. What will his selling price be?


Scenario 2

Income, Expense, and Profit

Problem 4: Our GM is 50% and we want to buy a printer for $1,000, what amount of incremental income is required? Problem 5: Our GM is 5% and our ASP is $10, how many units do we need to sell to generate a profit of $2,000? Problem 6: Our income was $25M and COGS was $18M, what is our GM in percent?


Scenario 3

Compound Annual Growth Rate (CAGR)

Problem 7: CEO wants CAGR data in your report to the BOD (Note: each year referenced to 2000)

2000 2001 2002 2003 2004 2005 2006

Revenue $76,627 $111,389 $82,821 $136,111 $187,442 $256,620 $251,487

$0

$60,000

$120,000

$180,000

$240,000

$300,000

Rev

enu

e


Scenario 4

Price Model

Problem 8: Marketing provided this Price Model, and you need to determine the GM for the missing unit quantities for your Price Book.

40.0%

50.0%

60.0%

70.0%

80.0%

1 10 100 1,000 10,000 100,000 1,000,000

GM

Units

GM vs Units

Price Model 1 10 100 500 1k 5k 10k 20k 50k 100k 1,000k

82% 82% 80% 78% 70% 55% 45%


Scenario 5

Price Drop – Maintain Revenue

Problem 9: Our Super Widget had a subtle, but constant price erosion of 5% in the second and third year after it was introduced. How many more units must be sold to meet the same revenue as when the SuperWidget was introduced?


Scenario 6

Price Drop – Maintain Profit

Problem 10: Our GM was 15%, and we decreased our ASP by 5%. How many more units must be sold?


Scenario 7

Pareto Analysis, the 80/20 Rule

Problem 11: Determine the vital few for new Key Accounts Program

Cust Rev

1 P $350

2 F $25,180

3 K $7,885

4 L $5,285

5 M $4,327

6 D $105,118

7 C $116,038

8 A $225,767

9 N $3,840

10 I $10,809

11 J $8,770

12 E $57,021

13 H $11,456

14 B $169,793

15 Q $200

16 O $856

17 G $12,153

$764,848


Scenario 8

Forecast

Problem 12: CEO wants a $10M annual quota with 14% growth. Calculate the monthly quota amounts that total $10M, and reflect the required growth.


Scenario 9

Step Pricing

Problem 13: You agreed to sell the client 2MU @ $4.00 each, but he will not commit to taking all 2M units. Determine quarterly prices, so that if he buys all 2M units his average price will be $4.00, but if he buys fewer units his price will be higher.


Answers


GM, Cost, and Price Problem 1: Distributor says the competition is selling the product for $3.25, and his cost is $1.50. What is his GM? Solution: 53.85% Problem 2: Distributor says he can’t charge more than $4.00, and he needs to make 25% GM on this deal. What does his cost need to be? Solution: $3.00 Problem 3: The distributor cost is $7.25, and you know he is getting 25% GM. What will his selling price be? Solution: $9.67


Income, Expense, and Profit Problem 4: Our GM is 50% and we want to buy a printer for $1,000, what amount of incremental income is required? Solution: $2,000 Problem 5: Our GM is 5% and our ASP is $10, how many units do we need to sell to generate a profit of $2,000? Solution: 4,000 Problem 6: Our income was $25M and COGS was $18M, what is our GM in percent? Solution: 28%


Compound Annual Growth Rate

Problem 7: CEO wants CAGR data in your report to the BOD (Note: each year referenced to 2000)

Solution: See data table

2000 2001 2002 2003 2004 2005 2006

Revenue $76,627 $111,389 $82,821 $136,111 $187,442 $256,620 $251,487

CAGR 45.37% 3.96% 21.11% 25.06% 27.34% 21.91%

0%

10%

20%

30%

40%

50%

$0

$60,000

$120,000

$180,000

$240,000

$300,000

CA

GR

Rev

enu

e

1001Yr

YrCAGR

1

1

n xn


Price Model

Problem 8: Marketing provided this Price Model, and you need to determine the GM for the missing unit quantities for your Price Book. Solution: See equation y=mx+b (for logarithmic x axis)

y = -0.0362Ln(x) + 0.65


Price Drop – Maintain Revenue Problem 9: Our Super Widget had a subtle, but constant price erosion of 5% in the second and third year after it was introduced. How many more units must be sold to meet the same revenue as when the SuperWidget was introduced? Solution: 16.64%

Note: A small price erosion, compounded over time, can amount to a large difference for the sales team to overcome.

16.64%

37.17%

62.83%

95.31%

0%

20%

40%

60%

80%

100%

-5% -10% -15% -20%

Unit

Incre

ase

Price Erosion in %

Price Erosion, Units to Maintain Revenue $

Yr 1 Yr 2 Yr 3


Price Drop – Maintain Profit

Problem 10: Our GM was 15%, and we decreased our ASP by 5%. How many more units must be sold? Solution: 50.0%

Note: A small price drop requires much higher volume to maintain profitability with low GM

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

50% 45% 40% 35% 30% 25% 20% 15% 10%

Unit

s

GP

Price Erosion, Units to Maintain Profit

5% PE 10% PE 20% PE


Pareto Analysis, the 80/20 Rule

Problem 11: Determine the vital few for new Key Accounts Program Solution: Customers A, B, C, and D should be Key Accounts

Cust Rev

1 P $350

2 F $25,180

3 K $7,885

4 L $5,285

5 M $4,327

6 D $105,118

7 C $116,038

8 A $225,767

9 N $3,840

10 I $10,809

11 J $8,770

12 E $57,021

13 H $11,456

14 B $169,793

15 Q $200

16 O $856

17 G $12,153

$764,848

Cust Rev Cum Rev % Rev % Cum Rev % Cust

1 A $225,767 $225,767 29.5% 29.5% 5.9%

2 B $169,793 $395,560 22.2% 51.7% 11.8%

3 C $116,038 $511,598 15.2% 66.9% 17.6%

4 D $105,118 $616,716 13.7% 80.6% 23.5%

5 E $57,021 $673,737 7.5% 88.1% 29.4%

6 F $25,180 $698,917 3.3% 91.4% 35.3%

7 G $12,153 $711,070 1.6% 93.0% 41.2%

8 H $11,456 $764,848 1.5% 94.5% 47.1%

9 I $10,809 $721,879 1.4% 95.9% 52.9%

10 J $8,770 $730,649 1.1% 97.0% 58.8%

11 K $7,885 $738,534 1.0% 98.1% 64.7%

12 L $5,285 $743,819 0.7% 98.7% 70.6%

13 M $4,327 $748,146 0.6% 99.3% 76.5%

14 N $3,840 $751,986 0.5% 99.8% 82.4%

15 O $856 $752,842 0.1% 99.9% 88.2%

16 P $350 $753,192 0.0% 100.0% 94.1%

17 Q $200 $753,392 0.0% 100.0% 100.0%

$764,848


Forecast

Problem 12: CEO wants a $10M annual quota with 14% growth. Calculate the monthly quota amounts that total $10M, and reflect the required growth. Solution: See table and graph above

Scenario 1

Given: Quota ($) Sn 10,000,000

Given: Growth Rate (%) y 14.00%

First Term a1 13

Number of Terms n 12

Difference d 9,912

Find: Term 1 a1 778,816

Find: Term 2 a2 788,728

Find: Term 3 a3 798,641

Find: Term 4 a4 808,553

Find: Term 5 a5 818,465

Find: Term 6 a6 828,377

Find: Term 7 a7 838,289

Find: Term 8 a8 848,202

Find: Term 9 a9 858,114

Find: Term 10 a10 868,026

Find: Term 11 a11 877,938

Find: Term 12 a12 887,850

Total 10,000,000

Q1 2,366,185

Q2 2,455,395

Q3 2,544,605

Q4 2,633,815

10,000,000

778,816

788,728

798,641

808,553

818,465

828,377

838,289

848,202

858,114

868,026

877,938

887,850

y = 9912.2x + 768904 R² = 1

720,000

740,000

760,000

780,000

800,000

820,000

840,000

860,000

880,000

900,000

a1

a2

a3

a4

a5

a6

a7

a8

a9

a1

0

a1

1

a12

Forecast


Step Pricing

Problem: 17 Problem 13: You agreed to sell the client 2MU @ $4.00 each, but he will not commit to taking all 2M units. Determine quarterly prices, so that if he buys all 2M units his average price will be $4.00, but if he buys fewer units his price will be higher. Solution: See table and graph above

$/Mo Units/Mo ASP

Find: Term 1 a1 720,721 166,667 4.32

Find: Term 2 a2 710,893 166,667 4.27

Find: Term 3 a3 701,065 166,667 4.21

Find: Term 4 a4 691,237 166,667 4.15

Find: Term 5 a5 681,409 166,667 4.09

Find: Term 6 a6 671,581 166,667 4.03

Find: Term 7 a7 661,753 166,667 3.97

Find: Term 8 a8 651,925 166,667 3.91

Find: Term 9 a9 642,097 166,667 3.85

Find: Term 10 a10 632,269 166,667 3.79

Find: Term 11 a11 622,441 166,667 3.73

Find: Term 12 a12 612,613 166,667 3.68

Total Price 8,000,000 2,000,000

Q1 $ 4.27 0 500,000

Q2 $ 4.09 500,001 1,000,000

Q3 $ 3.91 1,000,001 1,500,000

Q4 $ 3.73 1,500,001 2,000,000

Avg Price $ 4.00

$4.27

$4.09

$3.91

$3.73

$2.70

$3.20

$3.70

$4.20

$4.70

$5.20

Q1 Q2 Q3 Q4

Pri

ce

Ea

ch

Quarters

Step Pricing


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