CVP & Multiple Products

After thinking about the analysis we have done so far, Charlie is concerned about the fact that we have assumed that all sales are the same. In fact, there are two types of sales. Sales through the dealer are subject to the 10% commission, but sales to others through Charlie's own initiative are not subject to the commission. In recognition of the higher margins on these sales [and the fact that they tend to be to friends and relatives], Charlie charges only $300 per chair. As a further concession to these "preferred customers," Charlie reduces the charge for his labor to 60% of the usual amount, or $54. Charlie tells us to assume that 60% of his orders fall in this category.

In order to take into account the different contribution margin on the non-commission sales, we need to weight the respective contributions according to their proportion of Charlie's sales. This leads to the following analysis:

Charlie's Furniture Shop		With Commission	Non-Commission
Basic Data:
Sales price/unit		$ 325.00	$ 300.00
Variable mfg costs per unit
Material		$ 50.00	$ 50.00
Labor		$ 90.00
Labor factor for preferred customers	60%		$ 54.00
Supplies		$ 13.00	$ 13.00
Utilities		$ 9.50	$ 9.50
Total variable mfg costs/unit		$ 162.50	$ 126.50
Variable S & A costs (commission to dealer)	10%	$ 32.50	0
Total variable cost/unit		$ 195.00	$ 126.50
Contribution margin/chair		$ 130.00	$ 173.50
Sales mix		40%	60%
Sales mix % applied to contribution margins		$ 52.00	$ 104.10
Resulting weighted average contribution margin			$ 156.10
Breakeven point [chairs/month]			3.33
Required sales per year [monthly sales * 12]			39.97
Sales per year rounded [he can't sell a fraction of a chair]			40.00

The breakeven point has gone down. Why? Answer

The breakeven point has gone down from the previous level of 48 units annually because the effective contribution margin per unit has gone up $26.10 [from $130.00 to a weighted average of $156.10]. The cost reductions on sales to "preferred' customers more than offset the price cut.

Can you prove that the new breakeven point is correct? How? Answer

Suppose the mix is reversed [i.e., 60%/40%]. What will happen? Why? Answer

The reversal of the mix results in a higher breakeven, but because of the impact of the contribution on the preferred customer sales, the breakeven point is still lower than with the initial assumptions.

Last modified: August 03, 2005