The capital structure of William Corporation limited consists of an ordinary share capital of
Rs.20 lakhs (shares of Rs.100 per value) and Rs.20 lakhs of 10% debentures. The unit sales
increased by 20% from 2,00,000 units to 2,40,000 units, the selling price is Rs.10 per unit,
variable cost amounts to Rs.6 per unit and fixed expenses amount to Rs.2,00,000. The
income tax rate is assumed to be 50%.
You are required to calculate the following:
a. The percentage increase in earnings per share.
b. The degree of financial leverage at 2,00,000 units and 2,40,000 units
c. The degree of operating leverage at 2,00,000 units and 2,40,000 units
To calculate the required values, we need to gather the necessary information and perform a series of calculations. Let's break down each calculation step by step.
Step 1: Calculate the total sales revenue at 2,00,000 units and 2,40,000 units.
Total sales revenue at 2,00,000 units:
Sales revenue = Selling price per unit * Number of units
Sales revenue = Rs.10 * 2,00,000 = Rs.20,00,000
Total sales revenue at 2,40,000 units:
Sales revenue = Selling price per unit * Number of units
Sales revenue = Rs.10 * 2,40,000 = Rs.24,00,000
Step 2: Calculate the total variable costs at 2,00,000 units and 2,40,000 units.
Total variable costs at 2,00,000 units:
Variable costs = Variable cost per unit * Number of units
Variable costs = Rs.6 * 2,00,000 = Rs.12,00,000
Total variable costs at 2,40,000 units:
Variable costs = Variable cost per unit * Number of units
Variable costs = Rs.6 * 2,40,000 = Rs.14,40,000
Step 3: Calculate the contribution margin at 2,00,000 units and 2,40,000 units.
Contribution margin at 2,00,000 units:
Contribution margin = Total sales revenue - Total variable costs
Contribution margin = Rs.20,00,000 - Rs.12,00,000 = Rs.8,00,000
Contribution margin at 2,40,000 units:
Contribution margin = Total sales revenue - Total variable costs
Contribution margin = Rs.24,00,000 - Rs.14,40,000 = Rs.9,60,000
Step 4: Calculate the earnings before interest and taxes (EBIT) at 2,00,000 units and 2,40,000 units.
EBIT at 2,00,000 units:
EBIT = Contribution margin - Fixed expenses
EBIT = Rs.8,00,000 - Rs.2,00,000 = Rs.6,00,000
EBIT at 2,40,000 units:
EBIT = Contribution margin - Fixed expenses
EBIT = Rs.9,60,000 - Rs.2,00,000 = Rs.7,60,000
Step 5: Calculate the earnings per share (EPS) at 2,00,000 units and 2,40,000 units.
EPS at 2,00,000 units:
EPS = (EBIT - Interest) * (1 - Tax rate) / Number of shares
Interest = 10% of Rs.20,00,000 = Rs.2,00,000
EPS = (Rs.6,00,000 - Rs.2,00,000) * (1 - 0.50) / (Total shares / Face value of shares)
Total shares = Rs.20,00,000 / Rs.100 = 20,000
EPS = Rs.4,00,000 * 0.50 / 20,000 = Rs.10
EPS at 2,40,000 units:
EPS = (EBIT - Interest) * (1 - Tax rate) / Number of shares
Interest = 10% of Rs.20,00,000 = Rs.2,00,000
EPS = (Rs.7,60,000 - Rs.2,00,000) * (1 - 0.50) / (Total shares / Face value of shares)
Total shares = Rs.20,00,000 / Rs.100 = 20,000
EPS = Rs.5,60,000 * 0.50 / 20,000 = Rs.14
Now, let's calculate the required values:
a. The percentage increase in earnings per share:
Percentage increase in EPS = ((New EPS - Initial EPS) / Initial EPS) * 100
Percentage increase in EPS = ((Rs.14 - Rs.10) / Rs.10) * 100 = 40%
b. The degree of financial leverage at 2,00,000 units and 2,40,000 units:
Degree of Financial Leverage = (Percentage change in EPS) / (Percentage change in EBIT)
Percentage change in EBIT = ((New EBIT - Initial EBIT) / Initial EBIT) * 100
At 2,00,000 units:
Percentage change in EBIT = ((Rs.6,00,000 - Rs.2,00,000) / Rs.2,00,000) * 100 = 200%
Degree of Financial Leverage = 40% / 200% = 0.2
At 2,40,000 units:
Percentage change in EBIT = ((Rs.7,60,000 - Rs.2,00,000) / Rs.2,00,000) * 100 = 280%
Degree of Financial Leverage = 40% / 280% = 0.143
c. The degree of operating leverage at 2,00,000 units and 2,40,000 units:
Degree of Operating Leverage = (Percentage change in EBIT) / (Percentage change in sales)
At 2,00,000 units:
Percentage change in sales = ((New sales revenue - Initial sales revenue) / Initial sales revenue) * 100
Percentage change in sales = ((Rs.20,00,000 - Rs.20,00,000) / Rs.20,00,000) * 100 = 0%
Degree of Operating Leverage = 200% / 0% = undefined
At 2,40,000 units:
Percentage change in sales = ((New sales revenue - Initial sales revenue) / Initial sales revenue) * 100
Percentage change in sales = ((Rs.24,00,000 - Rs.20,00,000) / Rs.20,00,000) * 100 = 20%
Degree of Operating Leverage = 280% / 20% = 14
So, the answers to the calculations are:
a. The percentage increase in earnings per share is 40%.
b. The degree of financial leverage at 2,00,000 units is 0.2 and at 2,40,000 units is 0.143.
c. The degree of operating leverage at 2,00,000 units is undefined and at 2,40,000 units is 14.