What is the break-even point per month in sales dollars?

Question

Lake Stevens Marina has estimated that fixed costs per month are $359,700 and variable cost per dollar of sales is $0.50.

 

what is the break-even point per month in sales dollars? 719,400

 

What level of sales dollars is needed for a monthly profit of $50,200? (Round answer to 2 decimal places, e.g. 15.25.)

Sales????

Answer 1

Two important observations:
    1.  All information in this problem is "per month.".
    2.  There are fixed costs (per month, as mentioned) and variable costs per dollar of sales (again, per month).
          The slope-intercept form of the equation of a line, y=mx+b, has b (the y-intercept) as the fixed costs and m (slope) as the variable costs.  Thus, we will write the equation in that form.
    3.  Considering units [which is extremely important,  (costs per dollar)*(number of dollars)=(variable costs)]

 

Each month (as mentioned already):

       Total Costs         =        Variable Costs               +         Fixed Costs

            C                  =         $0.50x                         +          $359700

 

Let x = Sales Dollars (per month)

 

Now, the important concept:  What does "break-even point" (per month) mean?  Well, if the Sales Dollars (per month) equals the Total Costs (per month), then there is a net difference of 0  (that is, no profit).  So, set them equal (or set x-C=0):

 

         x  =  $0.50x + $359700

         100x  = 50x + 35970000      [multiply by 100; note: I have trouble with fractions]

           50x = 35970000             [subtract 50x from both sides]

                x = $719,400            [divide both sides by 50]

 

Let's check (very important):

  At a monthly (as stated before) sales rate of $719400,

           there is ($0.50/$)($719400) variable cost and a $359,700 fixed cost.

      This is $359,700 + 359,700 in costs

        This is $719,400 in sales and $719,400 in costs;

             Lake Stevens Marina has "broken even."