Econ Pty Ltd produced and sold 45 000 units of a single product last year. Data concerning the year's profit and loss statement is as follows:
Assuming all cost relationships will remain constant for the coming year, how many units must be sold for the company to earn an after-tax profit of $180 000 if the income tax rate is 40 per cent?

Question

Econ Pty Ltd produced and sold 45 000 units of a single product last year. Data concerning the year's profit and loss statement is as follows: 
Assuming all cost relationships will remain constant for the coming year, how many units must be sold for the company to earn an after-tax profit of $180 000 if the income tax rate is 40 per cent?

Quizplus · Accepted Answer

First, we need to calculate the current after-tax profit:
Profit before tax = $240,000
Income tax = 40% x $240,000 = $96,000
Profit after tax = $240,000 - $96,000 = $144,000

Next, we need to find the number of units needed to earn an after-tax profit of $180,000:
Let x be the number of units to be sold
Revenue from selling x units = x x $18 = $18x

Variable cost per unit = ($8 + $1)/unit = $9/unit
Total variable cost for x units = $9x

Fixed costs = $210,000

Profit before tax = Revenue - Total variable cost - Fixed costs
$180,000 + $96,000 (income tax) = $18x - $9x - $210,000
$276,000 = $9x - $210,000
$486,000 = $9x
x = 54,000 units

However, we must check if selling 54,000 units will achieve an after-tax profit of $180,000:
Revenue from selling 54,000 units = 54,000 x $18 = $972,000
Total variable cost for 54,000 units = $9 x 54,000 = $486,000
Fixed costs = $210,000
Profit before tax = $276,000

Income tax = 40% x $276,000 = $110,400
Profit after tax = $276,000 - $110,400 = $165,600

Therefore, we need to sell more than 54,000 units to achieve an after-tax profit of $180,000. The closest option is 61,000 units, thus the answer is C.

Econ Pty Ltd Produced and Sold 45 000 Units of a Single