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%
