Question

Riviera Incorporated produces flat panel televisions. The company has annual fixed costs totaling $10,000,000 and variable costs of $600 per unit. Each unit of product is sold for $1,000. Riviera expects to sell 70,000 units this year. This is the base case. Assume a tax rate of 20%.

REQUIRED:

a.    Find the break-even point in units.

b.    How many units must be sold to earn an annual profit of $2,000,000?

c.     Find the margin of safety in units.

d.    What amount of sales dollars is required to earn an annual profit of $500,000 after taxes?

e.    Find the contribution margin per unit for Riviera Inc.

f.     How much will operating profit change if sales increase by 1,000 units?

g.    Go back to the base case. How much will operating profit change if fixed costs are 15 percent higher than anticipated? Would this increase in fixed costs result in higher or lower operating leverage?

h.            Go back to the base case. What will operating profit (loss) be if the variable cost per unit increases 10%?

Answer 1

a)At breakeven ,there is no profit no loss situation so fixed cost is equal to contribution

BEP (units) =Fixed cost /(price -variable cost)

        = 10,000,000/(1000-600)

         = 10,000,000/ 400

        = 25000 units

b)Profit desired before tax =Profit desired /(1 -tax)

       = 2,000,000/(1-.20)

         = 2500000

Units to sell =[Fixed cost +target profit ]/[price -variable cost]

        = [10,000,000+2,500,000]/[1000-600]

         = 12500000/400

             = 31250 units

c)Margin of safety = Actual unit sales -BEP unit sales

          = 70000-25000

         = 45000 units

d)Profit before taxes = 500000/(1-.20) = 625000

CM ratio = [price -variable cost]/price

        = [1000-600]/1000

         = 400/1000

           =.40 or 40%

Sales in $ desired= [fixed cost+ profit before tax ]/CM ratio

           =[10,000,000+625000]/.40

         = 10625000/.40

          = $ 26,562,500