Problem 4 Beakeven, target profit, cost changes, selling price Laraby Company pr

Question

Problem 4
Beakeven, target profit, cost changes, selling price Laraby Company produces a single product.
It sold 25,000 units last year with the following results.
Sales $625,000
Variable costs 375,000
Fixed costs 150,000
Income before taxes 100,000

In an attempt to improve its product, Laraby’s managers are considering replacing a component part that costs $2.50 with a new and better part costing $4.50 per unit during the coming year. A new machine would also be needed to increase plant capacity. The machine would cost $18,000 and have a useful life of 6 years with no salvage value. The company uses straight-line depreciation on all plant assets.

A. What was Laraby Company’s breakeven point in units last year?
B. How many units of product would Laraby Company have had to sell in the past year to
earn $77,000 in profit?
C. If Laraby Company holds the sales price constant and makes the suggested changes, how
many units of product must be sold in the coming year to break even?
D. If Laraby Company holds the sales price constant and makes the suggested changes, how many
units of product will the company have to sell to make the same profit as last year?
E. If Laraby Company wishes to maintain the same contribution margin ratio, what selling
price per unit of product must it charge next year to cover the increased materials costs?

Explanation / Answer

A. What was Laraby Company’s breakeven point in units last year?
    Contribution per unit = (Sales - variable costs) / units sold
                                    = ($625,000 - $375,000) / 25,000 units
                                    = $10 per unit

    Break even point (units) = Fixed cost / Contribution per unit
                                         = $150,000 / $10 = 15,000 units

B. How many units of product would Laraby Company have had to sell in the past year to
earn $77,000 in profit?
Units to be sold = (Fixed cost + desired profit) / Contribution per unit
                         = ($150,000 + $77,000) / $10
                         = $227,000 / $10   = 22,700 units

C. If Laraby Company holds the sales price constant and makes the suggested changes, how
many units of product must be sold in the coming year to break even?

Existing variable cost = $375,000 / 25,000 units = $15 per unit
Revised Variable Cost per unit = $15.00 + Cost of new part ($4.50 - $2.50)
                                             = $17 per unit

Revised contribution per unit = ($625,000/25000 units) - $17 = $8 per unit
Revised Fixed cost = $150,000 + New machine depreciation($18,000/ 6 years)
                             = $153,000

Break even point (units)   = $153,000 / $8 = 19,125 units

D. If Laraby Company holds the sales price constant and makes the suggested changes, how many
units of product will the company have to sell to make the same profit as last year?

Units to be sold to earn profit of $77,000   = ($153,000 + $77,000) / $8
                                                               = $230,000 / $8 = 28,750 units

E. If Laraby Company wishes to maintain the same contribution margin ratio, what selling
price per unit of product must it charge next year to cover the increased materials costs?

          Existing Contribution margin ratio   = $10 / $25 = 40%
          Selling Price per unit = $17 / (100 - 40) = $28.33
           

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