Question

As a recently hired MBA intern, you are working in a consulting capacity to provide an analysis for Al Dente's Italian Restaurant. A financial income Statement is presented below: Sales $2,698,000 Cost of sales (all variable) $1,557,563 Gross Margin $1,140,438 Operating expenses: Variable $277,975 Fixed $213,675 Total operating expenses: $491,650 Administative expenses (all fixed) $564,375 Net operating income $84,413 This income statement presents the sales, expenses and pre-tax operating income for a local eating facility. At Al Dente, the average meal cost for lunches and dinners are $20 and $40 respectively. Al Dente serves both lunch and dinner 300 days per year and serves twice as many lunches as dinners. As the MBA intern you are to prepare a managerial accounting focused report to the owners of Al Dente's Italian Restaurant, to include the following:

2. Compute the break-even volume of the number of lunches and dinners. Assume that the CM% for each meal category is the same as the average CM% as calculated in #1. Hint: To solve a break even sales mix, use the horizontal formula:

Net operating income = ($Sales – $Variable costs) – $fixed costs

Net operating income = $CM – $fixed costs

At Breakeven, NOI = $0

Therefore, $CM = $ Fixed costs

Now solve for the unit $CM for each item. Let X be the number of dinners, 2X the number of lunches. $CM is the combined total of the $CM for dinners, and the $CM for lunches.

Answer 1

Let the present sales of lunches be 2Y units and dinners be Y units

Hence, 2Y x 20 + Y x 40 = 2,698,000

40Y + 40Y = 2,698,000

80Y = 2,698,000

Y = 67,450

Present sale of dinners = 67,450

Present sale of lunches = 67,450 x 2

= 134,900

Total of lunches and dinners = 67,450 + 134,900

= 202,350

Present variable costs = Cost of goods sold + Variable operating costs

= 1,557,563 + 277,975

= $1,835,538

Variable cost per lunch/dinner = Present variable costs/Total of lunches and dinners

= 1,835,538/202,350

= $9.07

Contribution margin per unit = Selling price per unit - Variable cost per unit

Contribution margin per lunch = 20 - 9.07

= $10.93

Contribution margin per dinner = 40 - 9.07

= $30.93

Let X be the number of dinners, 2X the number of lunches at the break even level.

At the break even level, Contribution margin is equal to fixed costs.

Total fixed costs = Fixed operating expenses + Administrative expenses

= 213,675 + 564,375

= $778,050

Total contribution = 10.93 x 2X + 30.93 x X

= 21.86X + 30.93X

= 52.79X

Hence, 52.79X = 778,050

X = 14,739

Hence, number of dinners at break even = 14,739

Number of lunches at break even = 14,739 x 2

= 29,477

Exact answers may slightly differ due to rounding off.