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Mathematical Method

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In order to calculate the break-even point of a business mathematically, it is necessary to determine the gross income percentage of the business or marginal income per unit.

Example:

The marginal income ratio is calculated as follows:

Marginal income ratio = marginal income ÷ income

R80 000 ÷ 200 000 = 0.4 or 40%

The ratio can now be used to calculate the break-even point.

Break-even point in units = Tot fixed cost ÷ marginal income per unit

= R20 000 ÷ R0.80 = 25 000 units

Break-even point in rand = Tot fixed cost ÷ marginal income

= R20 000 ÷ 40% = R50 000.00

Jimco Ltd. BALANCE SHEET December 31, 1981(Thousands of Rands)

Current assets:

 

  Cash

1 400

  Marketable securities  (market value, R320)

300

  Account receivable

10 000

  Inventories

12 000

  Prepaid expenses

300

  Total current assets

24 000

 

 

Fixed assets:

 

  Land

2 000

  Plant and equipment

12 300

  Less:  Accumulated depreciation

7 300

  Net plant and equipment

5 000

  Total fixed assets

7 000

  Total assets

31 000

LIABILITIES AND OWNER’S EQUITY

Current liabilities:

 

  Accounts payable

3 000

  Notes payable, 9%, March 1, 1982

3 400

  Accrued salaries, wages and other expenses

3 100

  Current portion of long term debt

500

  Total current liabilities

10 000

 

 

Non-current liabilities:

 

  Deferred income taxes

1 500

  First mortgage bond, 7%, due January 1, 1995

6 300

  Debentures, 8.5%, due June 30, 1991

2 900

  Total long-term liabilities

10 700

 

 

Owner’s equity

 

  Common stock (par value R 1.00)

100

  Additional paid-in capital

2 000

  Retained earnings

8 200

  Total owner’s equity

10 300

  Total liabilities and owner’s equity

31 000

Income statement for Jimco for the year ended December 31, 1981(Thousands of Rands)

Net sales

 

51 000

Cost of goods sold

 

(38 000)

Gross profit

 

13 000

 

 

 

Operating expenses

 

 

    Selling expense

3 100

 

    Depreciation expense

500

 

    General and administrative expense

5 400

(9 000)

    Net Operating Income (NOI)

 

4 000

   

 

 

    Interest expense

 

(1 000)

    Earnings before taxes (EBT)

 

3 000

   

 

 

    Income taxes

 

(1 200)

    Net income (NI)

 

1 800