Question

Yellowstone Company began operations on January 1 to produce a single product. It used an absorption costing system with a planned production volume of 100,000 units. During its first year of operations, the planned production volume was achieved, and there were no fixed selling or administrative expenses. Inventory on December 31 was 10,000 units, and operating income for the year was $270,000.

Required:
1. If Yellowstone Company had used variable costing, its operating income would have been $240,000. Compute the break-even point in units under variable costing.

Answer 1

Solution:

Given the details are shown below:

Production volume = 1,00,000 units

Ending inventory = 10,000 units

Units sold = 90,000 units ( 1,00,000 - 10,000)

Net income as per Absorption costing = $ 2,70,000

Net income as per Variable costing = $ 2,40,000

Under variable costing , only variable manufacturing costs is included as a part of product costs.

Under absorption costing , product cost includes variable and fixed manufacturing costs.

The difference between net income as per variable costing and absorption costing is due to fixed manufacturing costs being a part of inventory under absorption costing .

Method                                                                               Net Income

Absorption costing $ 2,70,000

Variable costing $ 2,40,000

Fixed manufacturing cost in ending inventory $ 30,000 ($ 2,70,000 - $ 2,40,000)

Fixed manufacturing cost per unit    = Fixed Manufacturing cost / number of units in inventory

                                                                     =     $ 30,000 / 10,000

                                                                     =    $ 3.00

Total fixed Manufacturing cost = Number of units produced * fixed manufacturing cost per unit

Total fixed manufacturing cost = 1,00,000 units * $ 3.00

Total fixed manufacturing cost = $ 3,00,000

Contribution = Fixed cost + Net income as per Variable costing

Contribution = $ 3,00,000 + $ 2,40,000

Contribution = $ 5,40,000

Contribution per unit = Contribution / number of units sold

Number of units sold = Number of units produced – Ending inventory

Number of units sold = 1,00,000 units – 10,000 units

Units sold = 90,000 units

Contribution per unit = $ 5,40,000 / 90,000 units

Contribution per unit = $ 6.00

Computation of break even point in units :

Break even point (Units) = Fixed cost / Contribution per unit

Break even point (units) = $ 3,00,000 / $ 6.00

Break even point (Units) = 50,000 units

Conclusion is that Break even point (units) = 50,000 units