Math Problem Statement

A financial management problem where the firm needs to raise ₹10,00,000 through different financing plans. The task is to calculate Earnings Per Share (EPS) and the financial break-even point for each financing plan (100% Equity, 50% Equity & 50% Debt, 50% Equity & 50% Preference Shares).

Solution

Let's analyze the problem shown in the image:

Problem Breakdown:

  1. Total Investment:

    • The total investment to be raised is ₹10,00,000.
  2. Plan of Financing:

    • The distribution of the total investment is divided into equity shares, debt, and preference shares as follows:
      • Plan A: 100% Equity Shares
      • Plan B: 50% Equity Shares and 50% Debt
      • Plan C: 50% Equity Shares and 50% Preference Shares
  3. Costs:

    • Cost of Debt: 8%
    • Cost of Preference Shares: 8%
    • Tax Rate: 50%
  4. Equity Shares:

    • The market value per share if the firm follows Plan A is expected to be ₹10 per share.
  5. Expected EBIT (Earnings Before Interest and Tax): ₹2,00,000

  6. Requirements:

    • Calculate the following for each financing plan:
      • (i) Earnings per Share (EPS)
      • (ii) The financial break-even point

Let's proceed with solving the problem:

To solve this problem, we need to calculate EPS for each financing plan and determine the financial break-even point, which is the level of EBIT where EPS is zero.

I'll start by solving part (i), which is the calculation of EPS for each plan.

Calculation of EPS for each plan:

  1. Plan A (100% Equity Shares):

    • Total number of equity shares = ₹10,00,000 / ₹10 per share = 1,00,000 shares
    • No debt, no preference shares, so no interest or preference dividend.
    • EPS = (EBIT - Tax) / Number of Equity Shares
  2. Plan B (50% Equity Shares, 50% Debt):

    • Equity: ₹5,00,000, Debt: ₹5,00,000
    • Number of equity shares = ₹5,00,000 / ₹10 per share = 50,000 shares
    • Interest on debt = 8% of ₹5,00,000 = ₹40,000
    • EPS = (EBIT - Interest - Tax) / Number of Equity Shares
  3. Plan C (50% Equity Shares, 50% Preference Shares):

    • Equity: ₹5,00,000, Preference Shares: ₹5,00,000
    • Number of equity shares = ₹5,00,000 / ₹10 per share = 50,000 shares
    • Preference dividend = 8% of ₹5,00,000 = ₹40,000
    • EPS = (EBIT - Preference Dividend - Tax) / Number of Equity Shares

Let's proceed with calculating these values.

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Math Problem Analysis

Mathematical Concepts

Financial Management
Capital Structure
Earnings Per Share (EPS)
Break-even Analysis

Formulas

EPS = (EBIT - Interest - Tax) / Number of Equity Shares
Financial Break-even Point: EBIT where EPS = 0

Theorems

None specifically, but involves financial principles like the effect of leverage and break-even analysis

Suitable Grade Level

Undergraduate (Finance or Business Studies)