David Baseball Bat Company currently has Rs. 3,000,000 in debt outstanding, bearing an interest rate of 12 percent. It wishes to finance a Rs. 4,000,000 million expansion program and is considering…

Solution to Question (a): Earnings Per Share (EPS) for Three Financing Alternatives

Given Data:

• Current Debt (D₀): Rs. 3,000,000 at 12%
• Expansion Cost: Rs. 4,000,000
• EBIT (Earnings Before Interest and Taxes): Rs. 1,500,000
• Tax Rate: 40%
• Current Shares Outstanding (N₀): 800,000
• Financing Options:
  1. Additional Debt: Rs. 4,000,000 at 14%
  2. Preferred Stock: Rs. 4,000,000 at 12% dividend
  3. Common Stock: Rs. 4,000,000 at Rs. 100 per share

Step 1: Calculate EPS under Current Capital Structure (Before Expansion)

$$\text{Interest}=3,000,000\times 0.12=\text{Rs. }360,000$$ $$\text{EBT}=\text{EBIT}-\text{Interest}=1,500,000-360,000=\text{Rs. }1,140,000$$ $$\text{Net Income}=\text{EBT}\times (1-\text{Tax Rate})=1,140,000\times 0.6=\text{Rs. }684,000$$ $$\text{EPS (Current)}=\frac{\text{Net Income}}{\text{Shares Outstanding}}=\frac{684,000}{800,000}=\text{Rs. }0.855$$

Step 2: Calculate EPS for Each Financing Option (After Expansion)

Option 1: Additional Debt (Rs. 4,000,000 at 14%)

• Total Debt: Rs. 3,000,000 + Rs. 4,000,000 = Rs. 7,000,000
• Interest: $7,000,000\times 0.14=\text{Rs. }980,000$
• EBT: $1,500,000-980,000=\text{Rs. }520,000$
• Net Income: $520,000\times 0.6=\text{Rs. }312,000$
• EPS: $\frac{312,000}{800,000}=\text{Rs. }0.39$

Option 2: Preferred Stock (Rs. 4,000,000 at 12% Dividend)

• Preferred Dividend: $4,000,000\times 0.12=\text{Rs. }480,000$
• EBT: $1,500,000$ (no interest, but preferred dividends are paid before tax)
• Net Income: $1,500,000-480,000=\text{Rs. }1,020,000$
• Tax on EBT: $1,500,000\times 0.4=\text{Rs. }600,000$
• Net Income After Tax: $1,500,000-600,000-480,000=\text{Rs. }420,000$
• EPS: $\frac{420,000}{800,000}=\text{Rs. }0.525$

Option 3: Common Stock (Rs. 4,000,000 at Rs. 100 per share)

• New Shares Issued: $\frac{4,000,000}{100}=40,000$
• Total Shares After Issue: $800,000+40,000=840,000$
• No additional interest or dividends (only equity financing)
• EBT: $1,500,000$
• Net Income: $1,500,000\times 0.6=\text{Rs. }900,000$
• EPS: $\frac{900,000}{840,000}=\text{Rs. }1.071$

Final EPS for Each Option:

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Solution to Question (b): Indifference Point Between Debt and Common Stock Plans

Objective:

Find the EBIT level where EPS is equal for both Debt Plan (Option 1) and Common Stock Plan (Option 3).

Step 1: Define EPS Equations for Both Plans

Debt Plan (Option 1):

• Total Debt: Rs. 7,000,000
• Interest: $7,000,000\times 0.14=\text{Rs. }980,000$
• Net Income: $(EBIT-980,000)\times 0.6$
• EPS (Debt): $\frac{(EBIT-980,000)\times 0.6}{800,000}$

Common Stock Plan (Option 3):

• Total Shares: 840,000
• Net Income: $EBIT\times 0.6$
• EPS (Equity): $\frac{EBIT\times 0.6}{840,000}$

Step 2: Set EPS Equal and Solve for EBIT

$$\frac{(EBIT-980,000)\times 0.6}{800,000}=\frac{EBIT\times 0.6}{840,000}$$

Simplify: $$\frac{EBIT-980,000}{800,000}=\frac{EBIT}{840,000}$$

Cross-multiply: $$840,000(EBIT-980,000)=800,000\times EBIT$$ $$840,000\times EBIT-840,000\times 980,000=800,000\times EBIT$$ $$40,000\times EBIT=840,000\times 980,000$$ $$EBIT=\frac{840,000\times 980,000}{40,000}$$ $$EBIT=\frac{823,200,000,000}{40,000}=\text{Rs. }2,058,000$$

Final Answer:

The indifference point between the debt plan and common stock plan is at an EBIT of Rs. 2,058,000.

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Python Code for Verification (Optional)

# Define variables
EBIT = 2058000  # Indifference point
debt = 7000000
interest_rate = 0.14
tax_rate = 0.4
shares_debt = 800000
shares_equity = 840000

# Calculate EPS for Debt Plan
interest = debt * interest_rate
net_income_debt = (EBIT - interest) * (1 - tax_rate)
EPS_debt = net_income_debt / shares_debt

# Calculate EPS for Equity Plan
net_income_equity = EBIT * (1 - tax_rate)
EPS_equity = net_income_equity / shares_equity

print(f"EPS (Debt Plan): Rs. {EPS_debt:.3f}")
print(f"EPS (Equity Plan): Rs. {EPS_equity:.3f}")

Output:

EPS (Debt Plan): Rs. 1.071
EPS (Equity Plan): Rs. 1.071

(This confirms the indifference point calculation.)