Need Help With Marketing Math

Hi all,

I am in need of help for the following question in marketing math:

Singapore Premium Coffee is selling 60M boxes of Plain Coffee and 20M boxes of Hazelnut Coffee. A product manager suggested that Singapore Premium Coffee should add a second flavor. After substantial market research, Singapore Premium Coffee developed Caramel Coffee. Caramel Coffee requires no additional equipment, personnel, or advertising. The results of an initial test market launch showed that Singapore Premium Coffee earned a contribution of $0.30 per box of Caramel Coffee, and that the cannibalization rate was 30%. Cannibalization draws units from Plain Coffee and Hazelnut in proportion to their sales volumes. The profit per box for Plain Coffee and Hazelnut are as described in part (i): $0.50 for Plain, $0.30 for Hazelnut. Singapore Premium Coffee believes that all aspects of the test market are representative of the national rollout, except that they are worried about the cannibalization rate. In the national rollout, what is the minimum fraction of Caramel Coffee sales that must be new (and not cannibalize existing sales), assuming that the proportion of cannibalization is the same as in the market research sample, for Singapore Premium Coffee to break even?

I am not sure how to go about solving for this. I have tried to let X be the fraction and try to balance various equations

also i thought if we could look at both plain coffee and hazelnut as one unit contribution then try to solve on from there by using "new unit contribution/old unit contribution" to get the break even cannibalization rate.

my friend told me the answer is 1/3, but i cannot get that answer, and do not know if that is correct. please help!

I got 1/3. Here is what I did.

First, to break even, Caramel coffee's contribution should make up for the lost profits due to cannibalisation. Therefore, I calculate profits lost due to cannibalisation.

total volume (before new coffee flavour) is 60m+20m=80m
30% of 80m is 24m, split as follows: Plain 18m, Hazelnut 6m (in proportion to their sales)
Therefore profits lost are 18m*$0.5/box+6m*$0.3/box=$10.8 million

to compensate for these lost profits, I need to sell $10.8/0.3=36m boxes of the Caramel flavour.

The 'new sales' are 36-(18+6)=12 m boxes which is 1/3 of 36. OK?