Detailed Solution to Quantitative Analysis Exercise – Note on Marketing Arithmetic and

Related Marketing Terms (Horatio Alger)

1. Unit Contribution = Price (the price manufacturer to wholesaler) – Variable Cost

Wholesaler price to retailer = Retail Price * (1- Retail Margin) = $1 * (1-33%) = $0.67

Manufacturer price to wholesaler = Wholesaler to Retailer price * (1-Wholesaler margin) =

$0.67 * （1-12%）= $0.59

Variable cost: (1) manufacturer costs $0.09 per unit, (2) sales commission: 10% of the

manufacture to wholesaler price = $0.59 * 10% = $0.06, (3) shipping costs, breakage, insurance,

etc.: $0.02 per unit

Variable Cost: $0.09 + $0.06 + $0.02 = $0.17

Unit Contribution = Price (the price manufacturer to wholesaler) – Variable Cost = $0.59 - $0.17

= $0.42

2. Break-even volume = Fixed Cost / UC = ($900,000 Fixed manuf. costs + 35,000 Alger's salary

+ $500,000 advertising) /$0.42 = $1435000 / $0.42= 3416667

3. Break-even market share = 3416667/20000000 = 17.08%

4. Profit impact = UC x Units Sold – FC = 20000000 (total market) * 0.24 (market share)* 0.42 -

$1435000 = 581,000

5. Industry demand is expected to increase to 23 million units next year. Alger is considering

doubling his advertising budget to $1 million.

New FC = $1,000,000 (adv) + $900,000 (Fixed manuf. costs) + $35,000 (Alger's salary) =

$1,935,000

a. BEV = Fixed Cost/ Unit Contribution = $1935000 / $0.42 (unit contribution) =

4,607,142.9 units

b. Volume to achieve the same profit impact = (FC + Profit Impact) / Unit Contribution =

($1935000 + $581,000) / $0.42 = 5,990,476 units

c. Market share needed to achieve the same profit impact as this year = Volume to achieve

the same profit impact / Total market size = 5,990,476 units / 23 million units = 26%

d. Market share to achieve $1 million profit impact

- Volume to achieve $1m profit impact = (1935000 +1000000)/0.42 = 6988095 units

- Market share to achieve $1m profit impact = 6988095 / 23 million units = 30.4%

6. Suppose Alger decided not to raise advertising budget, instead he will raise retailer margins to

40%.

a. Raise the retailer margin to 40% and the wholesaler margin remains the same 12%. This

means the manufacturer would have to cut their price. Thus the new manufacturer selling price:

$1 * (1-40%) * (1-12%) = $0.528.

The tricky thing is now VC has changed too because the sales commission is 10% of the

manufacturer sales price. So now the new variable cost is $0.09 + $0.0528 + $0.02 = $0.1628.

Unit Contribution = Price – VC = 0.528 - 0.1628 = 0.365

Fixed cost remains the same: 900000 + 500000 + 35000 = 1435000

BEV = 1435000 / 0.365 = 3,931,507 units

b. Volume for the same profit impact = (FC + Profit impact) / UC = (1435000 + 581000) / 0.365

= 5,523,288 units

c. Market share to achieve this profit impact = 5,523,288 units / 23,000,000 units (projected

market size next year) = 24%

d. Market share to achieve $350,000 profit impact

= Volume for $350,000 profit impact / Projected market size next year

= (FC + Profit impact) / UC / Projected market size next year

= (1435000+$350,000) / 0.365 / 23,000,000

= 21.3%

=