Untitled-29

(^322) Financial Management
Exhibit 3: Relation between ROI and ROE Under Capital Structures A and B
Exhibit 4: Relationship between ROI and ROE Under Alternative Capital Structure
Looking at' the relationship between ROI and ROE we find that:

1. The ROE under capital structure A is higher than the ROE under capital structure
   B when ROI is less than the cost of debt.


2. The ROE under the two capital structures is the same when ROI is equal to the
   cost of debt. Hence the indifference (or breakeven) value of ROI is equal to the
   cost of debt.


3. The ROE under capital structure B is higher than the ROE under capital structure
   A when ROI is more than the cost of debt.

Mathematical Relationship

The influence of ROI and financial leverage on ROE is mathematically as follows:

ROE =[ROI + (ROI - r) D/E] (1 - t)

where ROE = return on equity

ROI = return on investment

Capital Structure A Capital Structure B

ROI 5% 10% 15% 20% 25% 5% 10% 15% 20% 25%

EBIT (Rs in million) 5 10 15 20 25 5 10 15 20 25

Interest 0 0 0 0 0 5 5 5 5 5

·Profit after tax 5 10 15 20 25 0 5 10 15 20

Tax 2.5 5 7.5 10 12.5 0 2.5 5 7.5 10

Profit after tax 2.5 5 7·5 10 12.5 0 2.5 5 7.5 10

Return an equity 2.5% 5% 7.5% 10% 12.5% 0% 5% 10% 15% 20%

Relationship between ROI and ROE Under Alternative Capital Structure

20

15

10

5

ROE

B

A

ROI