Question

A product sells for $250 per unit, and its variable costs per unit are $181. The fixed costs are $430,000. If the firm wants to earn $25,400 pretax income, how many units must be sold

Answer 1

To earn a pretax income of $25,400 with a selling price of $250 per unit, variable costs of $181 per unit, and fixed costs of $430,000, the firm must sell 6,600 units.

Step-by-step explanation:

To calculate the number of units needed to be sold to achieve a target pretax income, we need to perform a break-even analysis and extend it to target income calculations. Here we are given that the selling price per unit is $250 and the variable cost per unit is $181. Fixed costs are $430,000. The company wants to earn a pretax income of $25,400.

The formula to calculate the number of units needed (Q) to achieve a target pretax income (TP) is: Q = (Fixed Costs + Target Pretax Income) / (Price per Unit - Variable Cost per Unit).

Substituting the given numbers into the formula:

1. Calculate the contribution margin per unit: $250 (selling price) - $181 (variable cost) = $69 per unit.
2. Add the desired pretax income to fixed costs: $430,000 (fixed costs) + $25,400 (pretax income) = $455,400.
3. Divide the total by the contribution margin: $455,400 / $69 = 6600 (rounded to nearest whole number).

The firm must sell 6,600 units to achieve a pretax income of $25,400.

Answer 2

$6600

Step-by-step explanation:

Given: Selling price= $250 per unit

Variable cost= $181 per unit.

Fixed cost= $430000.

Expected Profit= $25400.

Let´s assume the number of units sold be "x".

Revenue (R) =
`250* x= \$250x`

Cost of product (C)=
`\$ 181* x+ \$ 430000`

∴ Cost of product (C)=
`\$ 181x+ \$ 430000`

Now, finding the number of unit sold.

Forming an equation for profit.

We know, Profit=
`Revenue-cost`

⇒
`\$ 25400= 250x- (181x+430000)`

Opening parenthesis.

⇒
`25400= 250x- 181x- 430000`

⇒
`25400= 69x- 430000`

Adding both side by 430000

⇒
`455400= 69x`

Dividing both side by 69

⇒
`x= (455400)/(69)`

∴
`x= 6600 units`

Hence, total number of units sold to earn $25400 is 6600 units.