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?
2. What is Brand X's break-even point?
3. What market share does Brand X need to break even?
4. What is Brand X's profit impact? Industry demand is expected to increase to 23 million units next year. Mr. Alger is considering raising his advertising budget to $1 million.
a. If the advertising 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 that 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?
5. Upon reflection, Mr. Alger decides not to increase Brand X's advertising budget. Instead, he thinks he might give retailers an incentive to promote Brand X by raising their margins from 33% to 40%. The margin increase would be accomplished by lowering the price of the product to retailers. Wholesaler margins would 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 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?

Answer:

Horatio Alger

1. The unit contribution for Brand X is = $0.79

2. Brand X's break-even point (in units) = 1,816,456 (in sales dollars) = $1,816,456

3. The market share that Brand X needs to break-even

= 9.1%

4. Brand X's profit impact is 48.9% or $2,347,000

a. If the advertising budget is raised, units that Brand X have to sell to break-even is:

= 2,449,367 units

b. The units that Brand X have to sell in order for it to achieve the same profit impact that it did this year is:

= 5,865,886 units

c. Brand X's market share have to be 25.5% next year for its profit impact to be the same as this year.

d. Brand X's market share have to be 16.2% for it to have a $1 million profit impact.

5. a. Break-even sales units = 2,474,138 units

b. Break-even sales units = 6,520,690 units

c. Brand X's market share have to be 32.6% for its profit impact to remain at this year's level.

d. Brand X's market share have to be 15.4% to generate a profit impact of $350,000.

Explanation:

a) Data and Calculations:

Retail price of Brand X = $1.00

Units sold = 24% of 20 million = 4,800,000 units

Total sales revenue =              $1.00  $4,800,000

Variable costs:

Manufacturing                         $0.09

Selling commision (10% of $1) $0.10

Other selling expense            $0.02

Total variable costs per unit   $0.21  $1,008,000

Contribution margin per unit $0.79  $3,782,000

Fixed costs:

Manufacturing                $900,000

Advertising                       500,000

Brand X manager's salary 35,000    $1,435,000

Net income =                                     $2,347,000

Fixed costs/Contribution margin per unit = $1,435,000/$0.79 = 1,816,456 units

The market share that Brand X needs to break-even

= 1,816,456/20,000,000

= 9.1%

Brand X's profit impact = 48.9% ($2,347,000/$4,800,000 * 100)

With increase in advertising budget to $1 million next year,

a. Units to break-even = $1,935,000/$0.79 = 2,449,367 units

b. Units to achieve same profit impact:

Sales increased by 15% (3/20 * 100)

Net income will increase to = $2,699,050 ($2,347,000 * 1.15)  to make the same impact

Therefore, the units to achieve same profit impact = ($1,935,000 + $2,699,050)/$0.79

= $4,634,050/$0.79

= 5,865,886 units

Market share next year = 25.5% (5,865,886/23,000,000)

Market share to achieve $1 million profit impact

= (FC + Profit target)/$0.79

=  $1,935,000 + $1,000,000)/$0.79

= $2,935,000/$0.79

= $3,715,190

= $3,715,190/$23,000,000 * 100 = 16.2%

Fixed costs = $1,435,000

Retailer's margin raise = 40% from 33%, a 21.2% increase or decrease in price

Therefore, the new selling price = $1.00 * (1 - 0.212) = $0.79

Variable cost = $0.21

Contribution margin = $0.58

To break-even, FC/Contribution margin per unit

= $1,435,000/$0.58

= 2,474,138 units

Break-even units to achieve profit of $2,347,000 = ($1,435,000 + $2,347,000)/$0.58

= 6,520,690 units

Sales = $5,151,345 (6,520,690 * $0.79)

Market sales revenue = $15,800,000 (20,000,000 * $0.79)

= $5,151,345/$15,800,000 * 100

= 32.6%

Market impact of $350,000

Break-even units ($1,435,000 + $350,000)/$0.58

= 3,077,586 units

Sales revenue = $2,431,293 (3,077,586 * $0.79)

Market revenue = $15,800,000 (20,000,000 * $0.79)

Market share = $2,431,293/$15,800,000 * 100

= 15.4%

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Additional paid in capital 400 320
Retained earnings 825 675
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Cash dividends paid 12,192
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