Consider two firms. Firm A has a DOL of 3.0, an expected ROE of 9% with a standard deviation of 6%, and an EBIT of $10,000 when sales are 60,000 units. Firm B has a DOL of 6.0, an expected ROE of 12% with a standard deviation of 15%, and an EBIT of $10,000 when sales are 60,000 units. On the same graph, depict EBIT as a function of sales for the two firms. On a separate graph, depict the distribution of ROE for the two firms. Calculate the coefficient of variation for both firms.

The graphs are attached below

Explanation:

As we know that DOL = (EBIT + Fixed cost)/EBIT

So, For firm A, 3 = (10000+FC)/10000 => FC = $20000

Also EBIT = Q(P-VC)-FC, where P-VC = Contribution Margin.

So, for Firm A, 10000 = 60000*CM - 20000 => CM = $0.5

So, EBIT for Firm A = Q*0.5 - 20000

For Firm B,

DOL = (EBIT + Fixed cost)/EBIT

6 = (10000+FC)/10000 => FC = $50000

Also EBIT = Q(P-VC)-FC, where P-VC = Contribution Margin.

So, for Firm B, 10000 = 60000*CM - 50000 => CM = $1

So, EBIT for Firm A = Q*1 - 50000

Plotting 2 equation on a graph, We get

As ROE=9% for firm A, So EBIT/Equity = 9% => Equity = 111111.11

As ROE=12% for firm A, So EBIT/Equity = 12% => Equity = 83333.33

Used above equity to calculate roe for different sales quantity.

Change in ROE with sales graph

Coefficient of variation for firm A = standard deviation / expected return = 6%/9% = 0.67

Coefficient of variation for firm B = standard deviation / expected return = 15%/12% = 1.25

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