Question

Blue Seas Cruiseline offers two types of dinner​ cruises: Regular and Executive. The contribution margin per ticket sold is​ $30 for the regular​ cruise, and​ $90 for the executive. Fixed costs are​ $210,000. It expects to sell four regular dinner cruises for every one executive dinner cruise. What is the total number of regular cruises Blue Seas must sell in order to​ breakeven?

A.

​1,750

B.

​1,000

C.

​5,000

D.

​4,000

The answer 5000 is wrong, can someone explain why?

Answer 1

Answer = 4000 units.

Break even sales (in units) = total fixed cost / contribution margin per unit.

But in case where there are multiple products,

Break even sales(in units) = total fixed cost /weighted average contribution margin per unit.

Where,

Weighted average contribution margin per unit = [(contribution margin per unit for regular × ratio of sales ) + (contribution margin per unit for Exicutive × ratio of sales) ]

Ratio of sales = four Regular for every one Exicutive = 4:1

That is, 4/5 for Regular and 1/5 for Exicutive.

So, weighted average contribution margin per unit = [($30×4/5) + ($90×1/5)} = [$24 +$18] = $42

So break even units = 210000/$42 = 5000 units.

Now this 5000 units are not of only Regular but also includes Excutives.

Therefore,

To know the proportion of Regular units in it, multiply with Regular sales ratio.

The number of Regular units to be sold to break even = (5000 units ×4)×5

= 4000 units.

Verification : when 4000 units of regular sold, total contribution margin from regular = 4000 ×$30 = $120000

When 4000 units of regular sold, it means that 1000 units of Exicutive is also sold. So total contribution margin from Exicutive = 1000 ×$90 = $90000

Total contribution margin from both = $120000 + $90000 = $210000.