Question

Grixdale Tax Services prepares taxes for individuals. Grixdale offers a simplified pricing model with two alternatives for taxpayers: Standard Deduction or Itemized Deduction. Price and variable costs for the two services are listed below.

Standard Itemized
Sales price (per return) $50.00 $250.00
Variable costs (per return) 10.00 30.00

The annual fixed costs at Grixdale are $262,500. Based on experience, the owner estimates that Standard Deduction returns represent 25 percent of the firms business.

How many Standard Deduction and Itemized Deduction returns must be filed annually to break even?

Answer 1

Answer: Grixdale Tax Services must file 375 Standard Deduction returns and 1,125 Itemized Deduction returns annually to break even

Step-by-step explanation:

To determine the break-even point, we need to calculate the total contribution margin, which is the difference between the sales price and variable costs. For the Standard Deduction service, the contribution margin is:

$50.00 - $10.00 = $40.00

For the Itemized Deduction service, the contribution margin is:

$250.00 - $30.00 = $220.00

Next, we need to determine the proportion of total returns that are Standard Deduction returns. We are given that 25 percent of the firm's business is Standard Deduction returns, so the proportion of Itemized Deduction returns is:

1 - 0.25 = 0.75

Now we can set up the equation to solve for the break-even point:

Contribution margin × Total number of returns = Fixed costs

Let x be the total number of returns. Then, the number of Standard Deduction returns is 0.25x, and the number of Itemized Deduction returns is 0.75x. Plugging in the values from the problem, we get:

(40.00 × 0.25x) + (220.00 × 0.75x) = 262,500

Simplifying the equation, we get:

10x + 165x = 262,500

175x = 262,500

x = 1,500

Therefore, the break-even point is 1,500 total returns. To find the number of Standard Deduction and Itemized Deduction returns required to break even, we can multiply the total number of returns by the proportion of each type of return:

Number of Standard Deduction returns = 0.25 × 1,500 = 375

Number of Itemized Deduction returns = 0.75 × 1,500 = 1,125

Therefore, Grixdale Tax Services must file 375 Standard Deduction returns and 1,125 Itemized Deduction returns annually to break even.