This document provides a detailed solution to a quantitative analysis exercise on marketing arithmetic terms. It calculates key metrics like unit contribution, break-even volume and market share under different scenarios. Specifically: 1. It first calculates the unit contribution, break-even volume and market share based on current pricing, margins and costs. 2. It then analyzes the impact of doubling the advertising budget and calculates the new break-even volume, market share needed to achieve the same profit. 3. Finally, it considers increasing the retailer margin instead of advertising, and recalculates the break-even volume and market share required for the original profit level and a new profit target.

1. 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%

2. 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%