a) The number of toys needed to be sold in order to break even is 8,000 units. b) The breakeven sales value is $120,000. c) 11,000 toys must be sold to generate a profit of $15,000.
To calculate the breakeven point, we can use the formula:
Break-even point (in units) = Fixed costs / (Selling price per unit - Variable cost per unit)
For this question, the fixed costs are $40,000, the selling price is $15 per unit, and the variable cost is $10 per unit. Plugging in these values into the formula, we get:
Break-even point = $40,000 / ($15 - $10) = $40,000 / $5 = 8,000 units
So, the number of toys needed to be sold in order to break even is 8,000 units.
The breakeven sales value can be calculated by multiplying the breakeven point by the selling price per unit:
Breakeven sales value = Break-even point * Selling price per unit = 8,000 units * $15 = $120,000
Therefore, the breakeven sales value is $120,000.
To determine the number of toys that must be sold to generate a profit of $15,000, we can use the formula:
Number of toys sold = (Fixed costs + Desired profit) / (Selling price per unit - Variable cost per unit)
Substituting in the given values, we have:
Number of toys sold = ($40,000 + $15,000) / ($15 - $10) = $55,000 / $5 = 11,000 units
Therefore, 11,000 toys must be sold to generate a profit of $15,000.
To calculate the sales revenue that must be made to earn a profit of $17,000, we can use the formula:
Sales revenue = (Fixed costs + Desired profit) / (1 - (Variable cost per unit / Selling price per unit))
Plugging in the given values, we get:
Sales revenue = ($40,000 + $17,000) / (1 - ($10 / $15)) = $57,000 / (1 - 0.67) = $57,000 / 0.33 = $172,727.27
Therefore, the sales revenue that must be made to earn a profit of $17,000 is $172,727.27.
To determine the sales volume that would earn a profit of $18,000, we can use the formula:
Sales volume = (Fixed costs + Desired profit) / (Selling price per unit - Variable cost per unit)
Substituting in the given values, we have:
Sales volume = ($40,000 + $18,000) / ($15 - $10) = $58,000 / $5 = 11,600 units
Therefore, the sales volume that would earn a profit of $18,000 is 11,600 units.
To calculate the sales value that should be made to earn a profit of $24,000, we can use the formula:
Sales value = (Fixed costs + Desired profit) / Number of units
Plugging in the given values, we get:
Sales value = ($40,000 + $24,000) / Number of units
Since the number of units is not given, we cannot determine the exact sales value. We would need to know the number of units to calculate the sales value.
Finally, to determine the percentage increase in sales volume needed to earn a profit of $30,000 after tax compared to the profit of $24,000, we can use the formula:
Percentage increase = (Desired profit - Previous profit) / Previous profit * 100
Plugging in the given values, we get:
Percentage increase = ($30,000 - $24,000) / $24,000 * 100 = $6,000 / $24,000 * 100 = 25%
Therefore, the firm should increase its sales volume by 25% over the previous sales volume to earn a profit of $30,000 after tax.