Net Operating Income Question Accounting Need Help

Question

White Corporation is a wholesaler that sells a single product. Management has provided the following cost data for two levels of monthly sales volume:

Sales Units : 6,000

Cost of Goods Sold : $457,800

Selling And Adminstrative Expenses : $621,000

Selling Price Per Unit : $180

 

Sales Units : 7,000

Cost of Goods Sold : $510,800

Selling And Adminstrative Expenses : $639,000

Selling Price Per Unit : $180

 

Question : The best estimate of net operating income if 6,300 units are sold is?

A) 1,200 B) 31,200 C) 33,900 D) 39,300 E) None of Above

 

Answer was C) but I need help with steps as to how.

Answer 1

Jon offered the ideal way to do this problem. Here is a less efficient method that analyzes each of the expenses. I have not done the actual calculations but it should give the same answer. Perhaps it can offer additional insight. 

 

For this problem, you need to analyze how the cost are changing from when you sold 6000 units to when you sold 7000 units. The Selling and Administrative Expenses only increase a relatively small amount. This means that the Selling and Administrative cost consists both of a variable and fixed amount with the vast majority of the expense being a fixed amount. So you need to figure out the equation of the line that represents the selling and administrative expenses associated with the units sold. To do this use the two points given (6000, 621,000) and (7000, 639,000). Use these two points to determine the slope and then use the point slope formula to write the equation of the line that represents the selling and administrative expenses associated with the units sold. Once you have this equation, plug in 6300 to determine the selling and administrative expenses associated with selling 6300 items. Alternatively, and more simply, you could take the slope and multiply it by 300 and add to this 621,000 to get the same answer. 

Now look at the costs of goods sold. Figure out the cost of each item when 6000 were sold (457,800/6000) and then figure out the cost of each item when 7000 units were sold (510800/7000) You will see that the unit cost has decreased meaning that the 1000 extra items that were sold had an average unit cost that was less than the average unit cost of the first 6000 that were sold. So what you need to do is figure out the difference in the cost of goods sold (510,800-457800) and divide this by 1000. This is the average unit cost of the extra 1000 units that were sold. Multiply this number by 300 and add to that number, the cost of selling the 1st 6000 items (457,800). This will give you the cost of selling 6300 items. Now add this cost to the selling and administrative expense calculated in the first paragraph to get your total expenses in selling 6300 items. Now multiply 6300 by 180 (the selling price) to get your revenue. Subtract from this revenue your total expenses in selling 6300 items which was just calculated. This should give you the answer.

Answer 2

Let's suppose there is a linear relationship between total costs and units sold.  That is, there is some fixed cost, plus some cost per unit.

 

The TOTAL cost at 6000 units is $1,078,800 and the total cost at 7000 units is $1,149,900.  We obtain these figures by adding the Cost of Goods Sold to the Selling And Administrative Expenses.  We want to find the cost at 6300 units, which we can do by interpolating between the costs at 6000 and 7000 units.  There are a number of ways to do this, but a simple way is to find the variable cost per unit and add 300 units worth of variable cost to the cost at 6000 units. 

 

So, the per unit cost would be the difference between the two total costs divided by the difference between the number of units.  So that is ($1,149,900 - $1,078,800) /1000 = $71,000 / 1000, or $71 per unit.

 

So the total cost at 6300 units would be the cost at 6000 units plus 300 * $71 = $1,078,800 + $21,300 = $1,100,100.

 

The gross revenue from the sales of 6300 units is 6300 * $180 (since the sales price per unit is fixed).  That comes to $1,134,000.

 

To calculate the net operating income, subtract the costs from the revenue:  $1,134,000 - $1,100,100, which equals $33,900.