dear sir / madam

Pls help me to solve this problem.

1 L ltd needs to invest Rs 4000000. It is ascertain the cost of capital at different capital structure is as follows:

debt equity cost of debt % cost of equity%

10 90 6.00 12.00

20 80 6.50 12.50

25 75 7.00 12.50

40 60 7.00 13.00

50 50 7.25 13.50

60 40 7.50 14.00

75 25 8.00 15.00

a) yoare to suggest optimum debt equity mix base on weighted average cost of capital

b) The project has expected EBIT @ 25% and tax rate @ 35% for the debt equity mix supported by you. calculate EPS assuming capital is decided in uints of rs 100each

To tackle the problem you've presented, we need to analyze the weighted average cost of capital (WACC) for different debt-equity mixes and then determine the optimal capital structure. After that, we can calculate the earnings per share (EPS) based on the expected earnings before interest and taxes (EBIT) and the tax rate. Let's break this down step by step.

Understanding Weighted Average Cost of Capital (WACC)

The WACC is a crucial metric that reflects the average rate of return a company is expected to pay its security holders to finance its assets. It takes into account the cost of equity and the cost of debt, weighted by their respective proportions in the overall capital structure.

Calculating WACC

The formula for WACC is:

WACC = (E/V) * Re + (D/V) * Rd * (1 - Tc)

• E = Market value of equity
• D = Market value of debt
• V = E + D (Total value of financing)
• Re = Cost of equity
• Rd = Cost of debt
• Tc = Corporate tax rate

Now, let's calculate the WACC for each capital structure provided:

Capital Structures and WACC Calculation

Debt %	Equity %	Cost of Debt %	Cost of Equity %	WACC
10	90	6.00	12.00	11.40
20	80	6.50	12.50	11.80
25	75	7.00	12.50	12.05
40	60	7.00	13.00	12.70
50	50	7.25	13.50	13.00
60	40	7.50	14.00	13.50
75	25	8.00	15.00	14.25

From the calculations, we can see that the WACC is lowest at a debt-equity mix of 10% debt and 90% equity, with a WACC of 11.40%. This suggests that this mix is the most cost-effective for financing the project.

Calculating Earnings Per Share (EPS)

Now that we have identified the optimal capital structure, we can calculate the EPS based on the expected EBIT and the tax rate. The formula for EPS is:

EPS = (EBIT - Interest) * (1 - Tax Rate) / Number of Shares

Step-by-Step EPS Calculation

1. **Determine EBIT**: Given that the project has an expected EBIT of 25% on Rs 4,000,000, we calculate:

EBIT = 0.25 * 4,000,000 = Rs 1,000,000

2. **Calculate Interest**: For the optimal mix of 10% debt:

Debt = 10% of 4,000,000 = Rs 400,000

Cost of Debt = 6% of 400,000 = Rs 24,000

3. **Calculate Tax**: The tax rate is 35%, so:

Taxable Income = EBIT - Interest = 1,000,000 - 24,000 = Rs 976,000

Tax = 35% of 976,000 = Rs 342,600

4. **Net Income**:

Net Income = Taxable Income - Tax = 976,000 - 342,600 = Rs 633,400

5. **Number of Shares**: Since capital is decided in units of Rs 100 each:

Number of Shares = Total Capital / Price per Share = 4,000,000 / 100 = 40,000 shares

6. **Final EPS Calculation**:

EPS = Net Income / Number of Shares = 633,400 / 40,000 = Rs 15.84

Summary of Findings

Based on the analysis, the optimal debt-equity mix for 1 L Ltd is 10% debt and 90% equity, resulting in a WACC of 11.40%. The calculated EPS for this capital structure, given the expected EBIT and tax rate, is approximately Rs 15.84. This indicates a strong potential return for shareholders under the proposed financing strategy.