Calculation of Point of Indifference and Uncommitted Earnings

After reading this article you will learn about the Calculation of Point of Indifference and Uncommitted Earnings per Share.

Point of indifference refers to that EBIT level at which earnings per share (EPS) remains the same irrespective of different alternatives of debt-equity mix. While calculating the equivalency point, the provision for repayment of debt or obligation towards sinking fund has not been considered so far.

However, sinking fund appropriations for redemption of debt decrease the amount of earnings available for equity shareholders. Thus, a finance manager may be interested to determine the level of EBIT at which uncommitted earnings per share (UEPS) after deducting sinking fund appropriation would be the same.

The equivalency point for uncommitted earnings per share can be calculated as below:

(X-I₁)(1-T)-PD-SF/S₁ = (X-I₂)(1-T)-PD-SF/S₂

Where, X = Equivalency point or point of indifference or break even EBIT level

I₁ = Interest under alternative financial plan 1

I₂ = Interest under alternative financial plan 2.

T = Tax rate

PD = Preference dividend

SF = Sinking fund obligations

s₁ = Number of equity shares or amount of share capital under plan 1.

s₂ = Number of equity shares or amount of share capital under plan 2.

Illustration 1:

A company has the choice for raising an additional sum of Rs. 20,00,000 either by raising a 10% debt or by issue of additional equity shares of Rs. 100 each at par. The present capital structure of the company consists of 2,00,000 equity shares of Rs. 100 each and no debt.

At what level of earnings before interest and tax (EBIT) after the new funds are raised, would earnings per share (EPS) be the same whether new funds are raised either by raising debt or issue of equity shares? Also determine the level of EBIT at which Uncommitted Earnings Per Share (UEPS) would be the same, if sinking fund obligations amount to Rs. 2,00,000 per year.

Assume a 50% tax rate:

Solution:

(a) The level of EBIT where EPS will be equal under both the alternatives can be computed with the help of the following formula:

(X – I₁) × (1 – T) – PD/S₁ = (X -I₂) × (1 – T) – PD/S₂

Where, X = Indifference level of EBIT

I₁ and I₂ = Interest under alternatives 1 and 2.

T = Tax rate

PD = Preference dividend

S₁ and S₂ = Number of equity shares under alternatives 1 and 2

(X – 2,00,000) × (1 – 0.5) – 0/2,00,000 = (X – 0) × (1 – 0.5) – 0/2,20,000

0.5X – 1,00,000/2,00,000 = 0.5X-0/2,20,000

0.5X-1,00,000/20 = 0.5X/22

11X-22,00,000 = 10X

X = 22,00,000

Thus, at a level of EBIT of Rs. 22,00,000 EPS will be the same under both the alternatives.

(b) The level of EBIT where UEPS will be the same can be computed as:

(X-I₁)(1-T)-PD-SF/S₁ = (X-I₂)(1-T)-PD-SF/S₂

Where, SF = Sinking fund obligations

(X – 2,00,000) (1 – 0.5) – 0 – 2,00,000/2,00,000 = (X – 0) (1 – 0.5) – 0 – 0/2,20,000

.5X – 3,00,000/20 = 0.5X – 0/22

11X – 66,00,000 = 10X

X = 66,00,000

Thus, at a level of EBIT of Rs. 66,00,000, Uncommitted Earnings Per Share (UEPS) will be the same under both alternatives.