Read the article “Note on Marketing Arithmetic and Related Marketing Terms” and answer all the following questions:

Horatio Alger has just become product manager for Brand X. Brand X is a consumer product with a retail price of $1.00. Retail margins on the product are = 33%, while wholesalers take a 12% margin.

Brand X and its direct competitors sell a total of 20 million units annually; Brand X has 24% of this market. Variable manufacturing costs for Brand X are $0.09 per unit. Fixed manufacturing costs are $900,000.

The advertising budget for Brand X is $500,000. The Brand X product manager's salary and expenses total $35,000. Salespeople are paid entirely by a 10% commission. Shipping costs, breakage, insurance, and so forth are $0.02 per unit.

1) What is the unit contribution for Brand X? (This is a critical calculation that if incorrect will render all subsequent calculations using it also wrong)

a. If the retail price is $1, what is the price the retailer pays per unit to the wholesaler?

b. What is then the price the wholesaler pays the manufacturer (Horatio’s company)?

c. Which of the costs of Brand X are variable with respect to the number of units sold? Which are fixed and therefore not variable with units sold?

2) What is Brand X’s break-even point, both in units and in dollars?

3) What market share does Brand X need to break even?

4) What is Brand X’s profit impact?

5) Industry demand is expected to increase to 23 million units next year. An increase in the ad budget to $1 million is being considered.

a. If the ad budget is raised, how many units will Brand X have to sell to break even?

b. How many units will Brand X have to sell in order for it to achieve the same profit impact it did this year?

c. What will Brand X’s market share have to be next year for its profit impact to be the same as this year?

d. What will Brand X’s market share have to be for it to have a $1 million profit impact?

6) Upon reflection, the product manager decides against increasing the ad budget for the coming year. Instead, he things sales would be increased more if the company gives retailers an incentive to promote Brand X, by temporarily raising their margins from 33% to 40%. The margin increase would be achieved by lowering the price of the product to retailers. Wholesaler margins would continue to remain at 12%.

a. If retailer margins are raised to 40% next year, how many units will Brand X have to sell to break even?

b. How many units will Brand X have to sell to achieve the same profit impact next year as it did this year?

c. What would be Brand X’s market share have to be for its profit impact to remain at this year’s level?

d. What would Brand X’s market share have to be for it to generate a profit impact of $350,000?

**Subject Business Mathematical Finance**