The Value of the Firm: Relevance of Debt–Equity Mix

Why do investors buy shares of a company?

Ans:

  • For dividend
  • For capital appreciation
  • For profit

 

Debt equity mix

What determines whether a company is valuable or not?

Ans: The value of a firm is determined by its ability to generate future earnings and cash flows.

A firm is financed by:

  • Equity shareholders
  • Debt holders

So naturally,

Value of the Firm (Market Value Concept)

Value of the firm = Market value of Equity + Market value of Debt

V=S+D

Where:

S=No. of equity shares × Market Price per Share

D=No. of debentures × Market Price per Debenture

So,


Why Market Value (Not Book Value)?

In finance theory (especially capital structure decisions):

  • We use market values
  • Because they reflect investors’ expectations
  • They capture risk and return perception
  • They are relevant for shareholder wealth maximization

Suppose:

  • 1,00,000 shares
  • MPS = Rs. 50
  • 10,000 debentures
  • Market price per debenture = Rs. 95

Then:

Market value of equity = 1,00,000 × 50 = Rs. 50,00,000
Market value of debt = 10,000 × 95 = Rs. 9,50,000

Value of Firm+ Rs. 59,50,000

All capital structure theories use market values:

  • NI Approach
  • NOI Approach
  • MM Hypothesis
  • Trade-off Theory

Under Net Income (NI) Approach

  • More debt → Increases value of firm
  • WACC decreases
  • Ko =( D/V)kd + (S/V)Ke      v= total  value of firm

                                                     S= value of equity

                                                     D= value of debt

Under Net Operating Income (NOI) Approach (MM without tax)

  • Value of firm is constant
  • Capital structure irrelevant

               V= EBIT/Ko

  • The value of equity S is found as S = V-D
  • Ke = EBIT-I/S

 Under MM with Tax

Where:

  • = Levered firm value
  • = Unlevered firm value
  • = Tax shield value
Debt equity mix

What Trade-Off Theory Says

Trade-Off Theory accepts MM tax shield but adds:

  • Expected bankruptcy cost
  • Financial distress cost
  • Agency cost of debt

So the equation becomes:

Now:

  • Initially value increases (tax benefit dominates)
  • After some point value decreases (distress dominates)

Under:

  • Net Income (NI) Approach → Value changes with leverage
  • Net Operating Income (NOI) Approach → Total value remains constant
  • MM without tax → Capital structure irrelevant
  • MM with tax → Value increases with debt (due to tax shield)

Let us take go trough this comparative table

  •  NI Approach
  •  NOI Approach
  •  MM Approach (without tax)
  • MM Approach (with tax)
  • Trade -Off theory—- in a comparative table format.

Comparative Table

TheoryOptimal Structure?Reason
NI100% DebtDebt cheaper
NOIIrrelevantMarket adjusts
MM (No Tax)IrrelevantArbitrage
MM (With Tax)100% DebtTax shield
Trade-OffYesBalance benefit & cost

Let us take one common numerical example and compute

Assume

EBIT = Rs. 2,00,000
Total Capital = Rs. 10,00,000
Debt = Rs. 4,00,000
Equity = Rs. 6,00,000
Interest Rate = 10%
Cost of Equity (unlevered) = 12%
Overall Cost of Capital (Ko under NOI/MM) = 12%

Interest = 10% of 4,00,000 = Rs. 40,000

EBT = 2,00,000 – 40,000 = Rs. 1,60,000

Net Income (NI) Approach

Assumptions:

  • Cost of equity constant
  • Cost of debt constant
  • WACC declines with leverage

Step 1: Value of Equity

Step 2: Value of Firm

Net Operating Income (NOI) Approach

Assumptions:

  • Overall cost (Ko) constant
  • Market capitalizes EBIT
  • Value independent of capital structure

Value of Equity:

MM (without tax) gives same result as NOI:

Hence,

Equity Value = Rs. 12,66,667

MM with Corporate Tax

EBIT = Rs. 2,00,000
Debt = Rs. 4,00,000
Interest Rate = 10% → Interest = Rs. 40,000
Tax Rate = 40%
Unlevered Cost of Capital (Ko) = 12%

Step 1: Value of Firm under MM (Without Tax)

This is value of firm if no debt.

Step 2: Tax Shield Value

Under MM with tax:

Step 3: Levered Firm Value

Step 4: Value of Equity

Complete Comparative Table

ParticularsNINOIMM (No Tax)MM (With Tax)
EBIT2,00,0002,00,0002,00,0002,00,000
Interest40,00040,00040,00040,000
Tax Rate00040%
Value of Firm17,33,33316,66,66716,66,66718,26,667
BehaviourValue ↑ with DebtConstantConstantValue ↑ due to tax shield

Why doesn’t Big Company operate with 90% debt?

Ans: Because of

  • Credit rating risk
  • Bankruptcy risk
  • Loss of control
  • Agency problems

That is Trade-Off Theory in action and Trade-Off Theory leads to an Optimum Capital Structure.

Debt equity mix

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