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

Quizplus · Accepted Answer

First, we need to calculate the profit before taxes. We can do this by subtracting total costs from total revenue:

Total revenue = 45,000 units x $40 per unit = $1,800,000
Total costs = $1,320,000 (variable costs of $900,000 + fixed costs of $420,000)
Profit before taxes = $480,000 ($1,800,000 - $1,320,000)

Next, we need to calculate the profit after taxes. We can do this by multiplying the profit before taxes by (1 - tax rate):

Profit after taxes = $480,000 x (1 - 0.4) = $288,000

Finally, we need to calculate how many units must be sold to achieve this profit. We can use the contribution margin ratio (CMR) to do this:

CMR = (selling price - variable cost) / selling price
CMR = ($40 - $20) / $40 = 0.5

Break-even point (in units) = fixed costs / CMR
Break-even point = $420,000 / 0.5 = 840,000 / 5 = 168,000

To achieve a profit of $288,000, we need to sell an additional:

Additional units = (target profit + fixed costs) / CMR
Additional units = ($288,000 + $420,000) / 0.5
Additional units = $708,000 / 0.5 = $1,416,000 / 5 = 283,200

Total units = 45,000 + 283,200 = 328,200

However, we need to adjust this for the fact that we have already sold 45,000 units. So the additional units we need to sell are:

Additional units = 328,200 - 45,000 = 283,200

Therefore, the total units we need to sell to achieve a profit of $180,000 after taxes is:

Total units = 45,000 + 283,200 = 328,200

Since the question is asking for how many units must be sold in the coming year, we can assume that the fixed costs and variable costs will remain constant, and the selling price and tax rate will also remain constant.

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