In our studies of corporate finance, we said that the right choice of a project would be the one with the higher net present value. We had some problems or quizzes that analyze the case in which we have two projects. One has a higher rate of return but the other has the higher NPV. At that time we said that given the NPV paradigm, we have to stick to the first one, the one with the higher NPV. In this episode, we will study, not an exception to that, but the special point of view that forces us to keep in mind that oftentimes in reality managers at companies and projects they have to make decisions based on specific constraints. So, in this discussion, we will take a look at the product mix under capacity constraints. So, we will see that some factor is limited, and in this case, we will have to make decisions that maximize the profit with respect to this special limiting factor. So, that will be product mix under capacity constraint. As always, we will have an example. So, here we analyze the assembly plant that makes engines for gardening equipment, for garden trimmers and for lawnmowers. The first one is a two-stroke engine and the second one is a four-stroke engine. So, the second one is a little bit more complex. The capacity of the assembly machine that is used there is limited, so we have a limited amount of machine hours. Now, we have to analyze what decision we have to make with respect to this production. First of all, we analyze costs and prices and profits. So, we have here trimmers, trimmer engines, and here we have lawnmower engines. Well, this is the price, and the prices will be 200 here and 160 here. By the way, we make an assumption that regardless of how many engines or whichever kind we make, they all can be easily sold. Now, we have a variable cost per unit, and here, it will be 120, and here, it will be 125. So, the result is the contribution margin per unit, which is here clearly 75, and here, just 40. So, the next line will be just contribution margin ratio, so this is the ratio of that to the selling price. That would be 25 percent here, 40 over 160, and 37.5 percent here, 75 over 200. So, clearly based on this analysis, our choice would be make more lawnmower engines. But let's say that we have a constraint. So, overall, we have only 120 machine hours available for making these engines, and for trimmer, this is two hours, while for lawnmower, this is five hours, because this is a more complicated piece to make. If this is the case, then we have another analysis. So, we have here, we start with contribution margin, and this is lawnmower engine and this is the trimmer engine. Well, the contribution margin here was 40 weighed on a per-unit basis, and here it was 75. But now the next line will be machine hours to produce. Here, this is five, and here, this is two. So, the next very important piece will be contribution margin per one machine hour per unit over limiting factor. Here, this is clearly 20, and here, this is just 15. So, we can see that although the contribution margin for lawnmower engine is almost double that of the trimmer, but because you have 2.5 times more hours to make it, then the overall contribution margin per one machine hour is lower for lawnmowers, and if we used up for all 120 machine hours, so here our potential contribution margin would be, we multiply that. That would be 2,400 here and just 1,800 there. So, we can see that it's better to make trimmer engines. Why? Because they have the higher contribution margin on a unit of the constraint factor. Now, in reality, that is what people do when they analyze projects. Let's say there are two projects and each of them requires let's say, a piece of land or a special piece of equipment, then, they would like to take the one that although might have a lower NPV but has the higher NPV per unit or with respect to this very limiting factor. Strictly speaking, that allows you to make up for the quoted loss of this NPV by using your other capital resources to find another project that will have a sufficient NPV that if we added that to the first one then the combined would be higher compared to the case if we made the first choice. Now, this is clearly seen on problems rather than these discussions, but the illustrations in this episode was clear to show that sometimes the right decision is based on the idea of the highest contribution margin per unit of a constraint factor.
