Break-Even Analysis with Multiple Products
You Are a New Consultant $\quad$

Break-even analysis with multiple products
You are a new consultant with the Boston Group and have been sent to advise the executives of Penury Company. The company recently acquired product line L from an out-of-state concern and now plans to produce it, along with its old standby K, under one roof in a newly renovated facility. Management is quite proud of the acquisition, contending that the larger size and related cost savings will make the company far more profitable. The planned results of a month's operations, based on management's best estimates of the maximum product demanded at today's selling prices are: $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { LINE K }$$\quad$$\quad$$\quad$$\quad$ $\quad$$\text { LINE L }$
$\begin{array}{|l|r|r|r|r|r|}\hline &\text { Amount } &\text { Per }& \text { Amount } &\text { Per } &\text { Total} \\&&\text { Unit }&&\text { Unit }\\ \hline\begin{array}{l} \text { Sales } \\\text { revenue }\end{array} & \$ 120,000 & \$ 1.20 & \$ 80,000 & \$ 0.80 & \$ 200,000 \\\hline \begin{array}{l}\text { Variable } \\\text { expense }\end{array} & 60,000 & 0.60 & 60,000 & 0.60 & 120,000 \\\hline \begin{array}{l}\text { Contribution } \\\text { margin }\end{array} & \$ 60,000 & \$ 0.60 & \$ 20,000 & 0.20 & 80,000 \\\hline \begin{array}{l}\text { Fixed } \\\text { expense }\end{array} & & & & & 50,000 \\\hline \begin{array}{l}\text { Net income } \\\end{array} & & & & & \$ 30,000 \\\hline\end{array}$ Required:
a. Based on historical operations, K alone incurred fixed expenses of $40,000, and L alone incurred fixed expenses of $20,000. Find the break-even point in sales dollars and units for each product separately.
b. Give reasons why the fixed costs for the two products combined are expected to be less than the sum of the fixed costs of each product line operating as a separate business.
c. Assuming that for each unit of K sold, one unit of L is sold, find the break-even point in sales dollars and units for each product.