Part III work out question (6pts)
1. A firm has a base level of 10,000 units of sales and increase to 12,500 units. The sales price per unit is \( \$ 40.00 \) and variable costs per unit are \( \$ 20 \). Total annual operating fixed costs are \( \$ 150,000 \), and the annual interest expense is \( \$ 40,000 \). The firm paid 10,000 for preferred stock holders and has 10,000 outstanding shares of common stock. The firm tax rate is \( 40 \% \).
A. What is the firm' earning per share at an output level of 10,000 and 12,500 units? (2pts)
B. What is the firm's EBIT, Degree of operating leverage (DOL) and degree of financial leverage at output level of 10,000 (DFL)? (2pts)
C. What is the firm's Degree of combined leverage (DCL)? (2pts)
A. To calculate the firm's earnings per share at an output level of 10,000 units, we need to calculate the firm's net income first. Net income is calculated as follows:
Net income = (Sales - Variable costs) - Fixed costs - Interest expense - Taxes
Sales = 10,000 units * $40.00/unit = $400,000
Variable costs = 10,000 units * $20.00/unit = $200,000
Fixed costs = $150,000
Interest expense = $40,000
Taxes = 40% of (Sales - Variable costs - Fixed costs - Interest expense) = 40% of (400,000 - 200,000 - 150,000 - 40,000) = $12,000
Net income = ($400,000 - $200,000) - $150,000 - $40,000 - $12,000 = $-2,000
Since the net income is negative, the firm has a loss at an output level of 10,000 units. Therefore, the earnings per share cannot be calculated.
To calculate the firm's earnings per share at an output level of 12,500 units, we follow the same steps as above but with the new sales figure.
Sales = 12,500 units * $40.00/unit = $500,000
Variable costs = 12,500 units * $20.00/unit = $250,000
Taxes = 40% of (500,000 - 250,000 - 150,000 - 40,000) = $24,000
Net income = ($500,000 - $250,000) - $150,000 - $40,000 - $24,000 = $36,000
Since the firm has 10,000 outstanding shares of common stock, the earnings per share is calculated by dividing the net income by the number of shares:
Earnings per share = $36,000 / 10,000 = $3.60
Therefore, the firm's earnings per share at an output level of 12,500 units is $3.60.
B. To calculate the firm's EBIT (Earnings Before Interest and Taxes) at an output level of 10,000 units, we use the following formula:
EBIT = (Sales - Variable costs) - Fixed costs
EBIT = ($400,000 - $200,000) - $150,000 = $50,000
The degree of operating leverage (DOL) measures the responsiveness of a firm's operating income to changes in sales. It is calculated as follows:
DOL = (Percentage change in operating income) / (Percentage change in sales)
Since the firm's output level is 10,000 units, we can calculate the DOL by comparing it to the output level of 12,500 units:
DOL = ([EBIT at 12,500 units - EBIT at 10,000 units] / EBIT at 10,000 units) / ([Sales at 12,500 units - Sales at 10,000 units] / Sales at 10,000 units)
DOL = ([($400,000 - $200,000) - $150,000 - $40,000 - $24,000 - ($400,000 - $200,000) - $150,000] / ($400,000 - $200,000) - $250,000) / (($400,000 - $200,000) / $400,000)
DOL = ($36,000 / $200,000) / ($200,000 / $400,000) = 0.18 / 0.5 = 0.36
The degree of financial leverage (DFL) measures the responsiveness of a firm's earnings per share to changes in EBIT. It is calculated as follows:
DFL = (Percentage change in earnings per share) / (Percentage change in EBIT)
Since the firm's output level is 10,000 units, we can calculate the DFL by comparing it to the output level of 12,500 units:
DFL = ([EPS at 12,500 units - EPS at 10,000 units] / EPS at 10,000 units) / ([EBIT at 12,500 units - EBIT at 10,000 units] / EBIT at 10,000 units)
DFL = ([($3.60 - 0) / $3.60] / ($50,000 - $0) / $50,000) = 1 / 1 = 1
Therefore, the firm's EBIT at an output level of 10,000 units is $50,000, the DOL is 0.36, and the DFL is 1.
C. The degree of combined leverage (DCL) measures the responsiveness of a firm's earnings per share to changes in sales. It is calculated as follows:
DCL = DOL * DFL
DCL = 0.36 * 1 = 0.36
Therefore, the firm's degree of combined leverage at an output level of 10,000 units is 0.36.