Explanation:
Let's analyze the information given step by step:
1. The current selling price of the product is $42 per unit.
2. The variable cost per unit is $36.
3. The fixed cost for the year is $540,000.
Now, let's calculate the current profit per unit:
Profit per unit = Selling price per unit - Variable cost per unit
Profit per unit = $42 - $36 = $6
To determine the current profit for the year, we need to know the number of units sold. Let's assume the number of units sold is N.
Current profit for the year = Profit per unit × Number of units sold
Current profit for the year = $6 × N
Next, we are told that the selling price will be increased to $45 per unit. Let's calculate the new profit per unit:
New profit per unit = New selling price per unit - Variable cost per unit
New profit per unit = $45 - $36 = $9
To find the new profit for the year, we still need to know the number of units sold. Let's assume the number of units sold next year is M.
New profit for the year = New profit per unit × Number of units sold next year
New profit for the year = $9 × M
Now, let's consider the fixed cost for the year. The fixed cost remains the same, regardless of the selling price or number of units sold. So, the fixed cost for the year is still $540,000.
To calculate the total profit for the year, we add the profit from selling units to the fixed cost and set it equal to the total profit for the next year:
Current profit for the year + Fixed cost = New profit for the year
$6 × N + $540,000 = $9 × M
Since we don't have the specific values of N and M, we can't determine their relationship directly. However, we can provide an equation that relates the number of units sold this year to the number of units sold next year. Let's call the percentage increase in units sold as P.
Number of units sold next year = (1 + P) × Number of units sold this year
M = (1 + P) × N
Now, we can substitute this relationship into the equation:
$6 × N + $540,000 = $9 × (1 + P) × N
From here, you can solve for P, the percentage increase in units sold, by rearranging the equation and isolating P:
P = (($9 × N - $6 × N) / ($6 × N)) * 100
Simplifying the equation:
P = (($3 × N) / ($6 × N)) * 100
P = 50%
Therefore, to achieve the same profit for the next year with the increased selling price of $45 per unit, the number of units sold needs to increase by 50%.