CFA Level 1: Degree of Total Leverage (DTL) Calculation

Degree of Total Leverage (DTL)

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Question

Alvarez Technologies has sales of $3,000,000. The company's fixed operating costs total $500,000 and its variable costs equal 60 percent of sales, so the company's current operating income is $700,000. The company's interest expense is $500,000. What is the company's degree of total leverage (DTL)?

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A. B. C. D. E.

B

DTL = (S - VC)/(EBT - I)

= ($3,000,000 - $1,800,000)/($700,000 - $500,000)

= 6.

To calculate the degree of total leverage (DTL), we need to first calculate the degree of operating leverage (DOL) and the degree of financial leverage (DFL), and then multiply them together.

The degree of operating leverage (DOL) measures the sensitivity of operating income to changes in sales. It is calculated as the percentage change in operating income divided by the percentage change in sales.

DOL = (ΔOperating Income / Operating Income) / (ΔSales / Sales)

In this case, the company's current operating income is $700,000. Let's assume there is a 10% increase in sales. We can calculate the new operating income using the given information:

Operating Income = Sales - Variable Costs - Fixed Costs

Operating Income = $3,000,000 - (0.60 * $3,000,000) - $500,000 Operating Income = $3,000,000 - $1,800,000 - $500,000 Operating Income = $700,000

Now, let's calculate the percentage change in operating income:

ΔOperating Income = New Operating Income - Current Operating Income ΔOperating Income = $700,000 - $700,000 = $0

Percentage change in operating income = ΔOperating Income / Current Operating Income Percentage change in operating income = $0 / $700,000 = 0%

Similarly, let's calculate the percentage change in sales:

ΔSales = New Sales - Current Sales ΔSales = 10% * $3,000,000 = $300,000

Percentage change in sales = ΔSales / Current Sales Percentage change in sales = $300,000 / $3,000,000 = 10%

Now, let's calculate the degree of operating leverage (DOL):

DOL = (0% / $700,000) / (10% / $3,000,000) DOL = 0 / 0.1 DOL = 0

The degree of operating leverage (DOL) is 0, which implies that the operating income is not sensitive to changes in sales.

Next, we need to calculate the degree of financial leverage (DFL). The degree of financial leverage (DFL) measures the sensitivity of earnings per share (EPS) to changes in operating income. It is calculated as the percentage change in EPS divided by the percentage change in operating income.

DFL = (ΔEPS / EPS) / (ΔOperating Income / Operating Income)

In this case, the interest expense is $500,000. Let's assume there is a 10% increase in operating income. We can calculate the new EPS using the given information:

EPS = (Operating Income - Interest Expense) / Number of Shares

EPS = ($700,000 - $500,000) / Number of Shares

Since the number of shares is not provided, we cannot calculate the actual EPS. However, for the purpose of calculating the DFL, we can assume a constant number of shares, which cancels out in the calculation.

Now, let's calculate the percentage change in EPS:

ΔEPS = New EPS - Current EPS ΔEPS = (New Operating Income - Interest Expense) / Number of Shares - (Current Operating Income - Interest Expense) / Number of Shares ΔEPS = (New Operating Income - Current Operating Income) / Number of Shares ΔEPS = 10% * $700,000 / Number of Shares

Percentage change in EPS = ΔEPS / Current EPS Percentage change in EPS = (10% * $700,000 / Number of Shares) / ($700,000 / Number of Shares) Percentage change in EPS = 10%

Now, let's calculate the