Question

The Lucjia’s Café is a very popular restaurant in Skedattle Washingtoon. Below is an income statement for Lucjia’s Café the year ended December 31, 2011. Lucjia’s Café Income Statement For the year ended December 31, 2011 Revenues $2,098,400 Cost of Goods Sold, (all variable) 1,246,500 Gross Profit 851,900 Operating Expenses: Variable 222,380 Fixed 170,700 393,080 Administrative Expenses (all fixed) 451,500 Net Income $7,320 The average Dinner costs $40 each and the average lunch costs $20 each. Lucjia’s Café sells twice as many lunches as it does dinners. The variable cost, as a percentage of sales for both lunches and dinners is the same. Assume that Lucjia’s Café is open 305 days per year. For 2011, the current year, fixed operating expenses will increase by $41,215 and fixed Administrative Expenses will increase by $20,993. Required: a) Compute the number of Dinners and Lunches that Lucjia’s Café will have to sell per day in 2010 in order to break even.

Answer 1

Daily break-even volume is 85 dinners and 170 lunches:

              First compute contribution margins on lunches and dinners:

              Variable cost percentage = ($1,246,500 + $222,380) ÷ $2,098,400

                                                                      = 70%

              Contribution margin percentage = 1 - variable cost percentage

                                                                                       = 1 - 70% = 30%

              Lunch contribution margin   = .30 x $20 = $6

              Dinner contribution margin = .30 x $40 = $12

              Annual fixed cost is $170,700 + $451,500 = $622,200

              Let X = number of dinners and 2X = number of lunches

              12(X) + 6(2X) - $622,200 = 0

              24(X) = 622,200

              X = 25,925 dinners annually to break even

              2X = 51,850 lunches annually to break even

              On a daily basis:

              Dinners to break even = 25,925 ÷ 305 = 85 dinners daily

              Lunches to break even = 85 x 2 = 170 lunches daily or 51,850 ÷ 305 =    170 lunches daily.