Kermit's Hardware's (KH) fixed operating costs are $20.8 million, and its variable cost ratio is 0.30. The firm has $10 million in bonds outstanding with a coupon interest rate of 9%. KH has 200,000 shares of common stock outstanding. The firm has revenues of $32.2 million, and its marginal tax rate is 40%. Compute KH's degree of operating leverage.
A) 14.81
B) 5.19
C) 12.95
D) 4.54

Question

Quizplus · Accepted Answer

Degree of operating leverage (DOL) = (% change in operating income) / (% change in revenue)

First, we need to calculate KH's total costs:

Fixed costs = $20.8 million
Variable costs = (0.30)(revenue) = (0.30)($32.2 million) = $9.66 million
Total costs = fixed costs + variable costs = $30.46 million

Next, we can calculate KH's operating income:

Operating income = revenue - total costs = $32.2 million - $30.46 million = $1.74 million

Now, we can calculate KH's DOL:

Let's assume that revenue increases by x%. Then:

New revenue = $32.2 million + (x%)($32.2 million) = $32.2 million(1 + x%)

New variable costs = (0.30)(new revenue) = (0.30)($32.2 million)(1 + x%) = $9.66 million(1 + x%)

New total costs = fixed costs + new variable costs = $20.8 million + $9.66 million(1 + x%) = $30.46 million + $2.9324 million(x%)

New operating income = new revenue - new total costs = $32.2 million(1 + x%) - [$30.46 million + $2.9324 million(x%)] = $1.74 million + $1.6748 million(x%)

Therefore:

% change in operating income = [new operating income - old operating income] / old operating income
= [$1.74 million + $1.6748 million(x%)] - $1.74 million / $1.74 million
= $1.6748 million(x%) / $1.74 million
= 0.9632(x%)

% change in revenue = x%

DOL = (% change in operating income) / (% change in revenue)
= (0.9632(x%)) / x%
= 0.9632

Finally, we can check our answer using another formula for DOL:

DOL = contribution margin / operating income
= (revenue - variable costs) / operating income
= [$32.2 million - (0.30)($32.2 million)] / $1.74 million
= $22.54 million / $1.74 million
= 12.95

Either way, the answer is C: 12.95.

Kermit's Hardware's (KH) Fixed Operating Costs Are $20