Question

Collegepak company produced and sold 85,000 backpacks during the year just ended at an average price of $45 per unit. variable manufacturing costs were $19.50 per unit, and variable marketing costs were $7.50 per unit sold. fixed costs amounted to $555,000 for manufacturing and $228,000 for marketing. there was no year-end work-in-process inventory. (ignore income taxes.)

a. Compute Collegepak’s break-even point in sales dollars for the year.
b. Compute the number of sales units required to earn a net income of $615,000 during the year.
c. Collegepak's variable manufacturing costs are expected to increase by 10 percent in the coming year. Compute the firm’s break-even point in sales dollars for the coming year.
d. If Collegepak’s variable manufacturing costs do increase by 10 percent, compute the selling price that would yield the same contribution-margin ratio in the coming year.

Answer 1

To compute Collegepak's break-even point in sales dollars for the year, we calculate the total fixed costs and the contribution margin per unit. The number of units required to earn a net income of $615,000 can be determined using the fixed costs, net income, and contribution margin per unit.

Step-by-step explanation:

To calculate the break-even point in sales dollars, we need to find the total fixed costs and the contribution margin per unit. The contribution margin per unit is the difference between the selling price per unit and the variable costs per unit. In this case, the fixed costs for manufacturing are $555,000 and the fixed costs for marketing are $228,000. The variable costs per unit are the sum of the variable manufacturing costs and the variable marketing costs, which is $19.50 + $7.50 = $27 per unit.

The contribution margin per unit is $45 - $27 = $18 per unit. The break-even point in units is calculated by dividing the fixed costs by the contribution margin per unit: ($555,000 + $228,000) / $18 = 47,500 units. To calculate the break-even point in sales dollars, multiply the break-even point in units by the selling price per unit: 47,500 units x $45 = $2,137,500.

To compute the number of sales units required to earn a net income of $615,000, we need to use the following formula: (Fixed Costs + Net Income) / Contribution Margin per Unit = Number of Sales Units. First, we need to determine the total fixed costs by adding the fixed costs for manufacturing and marketing: $555,000 + $228,000 = $783,000. The contribution margin per unit is still $18. Plugging in the values, we have: ($783,000 + $615,000) / $18 = 74,900 units.

In the coming year, if Collegepak's variable manufacturing costs increase by 10 percent, we need to adjust the variable costs per unit. The new variable manufacturing cost per unit is $19.50 x 1.10 = $21.45. The variable costs per unit are now $21.45 + $7.50 = $28.95. Using the same formula as before, we can calculate the new break-even point in sales dollars: ($555,000 + $228,000) / ($45 - $28.95) = 56,336 units x $45 = $2,535,120.

If the variable manufacturing costs increase by 10 percent, the selling price must also be adjusted to maintain the same contribution-margin ratio. Let X be the new selling price. The contribution margin ratio is the contribution margin per unit divided by the selling price per unit.

In this case, the contribution margin per unit is $18 and the selling price per unit is X. So, the contribution-margin ratio is $18 / X. To maintain the same contribution-margin ratio, we can set up the following equation: $18 / X = ($45 - $28.95) / $45. Solving for X gives us X = $27.63.