Question

Associated Supply, Inc. is considering introducing a new product that will require a $250,000 investment of capital. The necessary funds would be raised through a bank loan at an interest rate of 8%. The fixed operating costs associated with the product would be $122,500, while the contribution margin percentage would be 42%. Assuming a selling price of $15 per unit, determine the number of units (rounded to the nearest whole unit) Associated would have to sell to generate earnings before interest and taxes (EBIT) of 32% of the amount of capital invested in the new product.

A. 32,143 units.
B. 25,575 units.
C. 23,276 units.
D. 35,318 units

Answer 1

The number of units Associated Supply, Inc. must sell to achieve an EBIT of 32% of the invested capital is approximately 35,238 units. This calculation takes into account the contribution margin ratio and total fixed costs, including interest on the capital.

Step-by-step explanation:

To calculate the number of units Associated Supply, Inc. needs to sell to generate an EBIT of 32% of the capital invested ($250,000), we must first determine the target EBIT amount. We calculate this by taking 32% of $250,000, which is $80,000. Next, we need to find the total costs incurred. Since the question mentions that the interest rate on the capital is 8%, the annual interest cost is 8% of $250,000, which equals $20,000. Adding this to the fixed operating costs of $122,500 gives us a total fixed cost of $142,500.

The contribution margin ratio of 42% means that for each unit sold at $15, $6.30 (42% of $15) will contribute to covering fixed costs and then profit. Therefore, to find the break-even point in units, we divide the total fixed costs by the contribution per unit ($142,500 / $6.30). But since we are not just breaking even, we want to achieve a target EBIT of $80,000; we will divide the total of fixed costs and desired EBIT ($142,500 + $80,000) by the contribution per unit.

The correct calculation is ($142,500 + $80,000) / $6.30, which equals approximately 35,238 units. This result is rounded to the nearest whole unit, making the answer approximately 35,238 units to achieve the desired EBIT, which most closely corresponds to option D from the given choices.