Breakeven Point When Price Is Independent of Demand An engineering consulting firm measures its output in a standard service hour unit, which is a function of the personnel grade levels in the professional staff. The variable cost ( cv) is $62 per standard service hour. The charge-out rate [i.e.,

Question

Breakeven Point When Price Is Independent of Demand
An engineering consulting firm measures its output in a standard service hour unit, which is a function of the personnel grade levels in the professional staff. The variable cost ([latex]c_{v}[/latex]) is $62 per standard service hour. The charge-out rate [i.e., selling price (p)] is $85.56 per hour. The maximum output of the firm is 160,000 hours per year, and its fixed cost ([latex]C_{F}[/latex]) is $2,024,000 per year. For this firm,

(a) what is the breakeven point in standard service hours and in percentage of total capacity?

(b) what is the percentage reduction in the breakeven point (sensitivity) if fixed costs are reduced 10%; if variable cost per hour is reduced 10%; and if the selling price per unit is increased by 10%?

Accepted Answer

(a)
Total revenue = total cost (breakeven point)

[latex]p D^{\prime} =C_{F}+c_{v} D^{\prime} \D^{\prime} =\frac{C_{F}}{\left(p-c_{v}\right)^{\prime}}[/latex] (2-13)

and

[latex]D^{\prime} =\frac{\$ 2,024,000}{(\$ 85.56-\$ 62)}=85,908 \text { hours per year } \[/latex]
[latex]D^{\prime} =\frac{85,908}{160,000}=0.537,[/latex]

or 53.7% of capacity.

(b) A 10% reduction in [latex]C_{F}[/latex] gives

[latex]D^{\prime}=\frac{0.9(\$ 2,024,000)}{(\$ 85.56-\$ 62)}=77,318 \text { hour per year }[/latex]

and

[latex]\frac{85,908-77,318}{85,908}=0.10,[/latex]

or a 10% reduction in D′.
A 10% reduction in [latex]c_{v}[/latex] gives

[latex]D^{\prime}=\frac{\$ 2,024,000}{[\$ 85.56-0.9(\$ 62)]}=68,011 \text { hours per year }[/latex]

and

[latex]\frac{85,908-68,011}{85,908}=0.208,[/latex]

or a 20.8% reduction in D′.
A 10% increase in p gives

[latex]D^{\prime}=\frac{\$ 2,024,000}{[1.1(\$ 85.56)-\$ 62]}=63,021 \text { hours per year }[/latex]

and

[latex]\frac{85,908-63,021}{85,908}=0.266,[/latex]

or a 26.6% reduction in D′.

Thus, the breakeven point is more sensitive to a reduction in variable cost per hour than to the same percentage reduction in the fixed cost. Furthermore, notice that the breakeven point in this example is highly sensitive to the selling price per unit, p.

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