managerial accounting break-even sales revenue question need help

Question

Lincoln Corporation produces and sells two products : Standard and Deluxe. The info on the two products sold for the last month is given below. The common fixed cost is $15,000.

Standard : Sales : $45,000 Variable Expenses : $36,000

Deluxe : Sales : $33,000 Variable Expenses : $16,500

Suppose total sales revenue for the coming month stays the same, but the sales (revenue) mix changes such that Deluxe increases by 20% (i.e. additional 20% to current %) and Standard decreases by 20% from the present levels. What will be the impact of this change on the break even sales revenue of Lincoln?

Answer was Break Even sales will decrease by $7,115 but I don't get how , please show help with steps.

Answer 1

the formula for Break Even in $ = [ Fixed costs / (average unit price - average variable cost/unit) ] x average unit price

 

since no unit sales are available, we will use 1 unit of each model, so Pav = $78/2 = $39, and Cav = ($36+16.5)/2 = $26.25

 

OLD BE = [ $15,000 / ($39,000 - 26,250) ] x 39000 = $45,882

 

in order to calculate the new variable cost, we will expect a decrease in VC for the standard from $36,000 to $28,800, and an increase of 20% for the deluxe model, from $16,000 to $19,800, which will give a Cav of ($28,800+19,800)/2 = $24,300

it was given that sales will remain the same at $78,000, or an average of $39,000/unit

 

NEW BE = [ $15,000 / ($39,000 - 24,300) ] x 39000 = $39,795; when we subtract the OLD BE from the NEW BE we get -$6,086

 

you wrote that the "answer" is a decrease of $7,115, which can only be achieved if the Cav in the NEW system is $23,910.  I was unable to obtain that number.