 # Net Operating Income Approach of Capital Structure By Yuriy Smirnov Ph.D.

## Definition

The net operating income approach claims that valuation of a firm is irrelevant to capital structure. In other words, the market value of a firm will be the same regardless of the proportion of debt. The reason is that any benefit from the increase of cheaper debt will be offset by a higher required rate of return on equity. Thus, the weighted average cost of capital (WACC) and the market value of a firm remain fixed at any level of financial leverage. In turn, the market value of a firm depends on earnings before interest and taxes and the weighted average cost of capital.

## Assumptions

The net operating income approach works best if the following assumptions are met:

1. The weighted average cost of capital is constant and irrelevant to capital structure
2. The valuation of a firm is determined by operating income and WACC
3. The cost of debt (kd) is constant at any level of financial leverage
4. The cost of equity (ke) is larger than the cost of debt at any level of financial leverage, i.e., ke > kd

## Formula

As has been mentioned before, the market value of a firm (V) depends on operating income (earnings before interest and taxes, EBIT) and WACC.

 V = EBIT WACC

Please note that if assumptions are met, both EBIT and WACC are irrelevant to capital structure.

The market value of shareholders’ equity (E) is calculated as the market value of a firm less the market value of debt (D).

E = V - D

As far as the cost of debt is constant, the formula to calculate the required rate of return on equity (cost of equity) is as follows:

 ke EBIT - I E

## Graph

The main proposition of the net operating income approach of capital structure is the constant weighted average cost of capital at any level of financial leverage. In other words, the mix of debt and equity is irrelevant to the market value of a firm.

The reason why replacing equity by cheaper debt will not result in a decrease of WACC is that risk increases as financial leverage increases. Thus, investors will claim a higher required rate of return on equity to compensate for the higher risk they take. Therefore, using higher financial leverage will be offset by an increase in the cost of equity; consequently, the WACC remains constant at any mix of debt and equity.

We should also note that an increase in financial leverage results in a decrease of the price-earnings ratio (P/E). *The graph illustrating the net operating income approach of capital structure will be slightly different depending on whether a debt-to-equity ratio or a debt ratio is used as a measure of financial leverage.

## Example

Total S.E. Inc. has declared earnings before interest and taxes of \$360,000, and the book value of total capital is \$2,500,000. The cost of borrowing is 8%. Let’s calculate the cost of equity at different levels of financial leverage.

At debt ratio of 0.00

Equity = \$2,500,000 × (1-0.00) = \$2,500,000

Debt = \$2,500,000 × 0.00 = \$0

I = \$0 × 8% = \$0

 V = \$360,000 = \$3,000,000 0.12

E = \$3,000,000 - \$0 = \$3,000,000

 ke = (\$360,000 - \$0) = 12.0% \$3,000,000

At debt ratio of 0.25

Equity = \$2,500,000 × (1-0.75) = \$1,875,000

Debt = \$2,500,000 × 0.25 = \$625,000

I = \$625,000 × 8% = \$50,000

 V = \$360,000 = \$3,000,000 0.12

E = \$3,000,000 - \$625,000 = \$2,375,000

 ke = (\$360,000 - \$50,000) = 13.1% \$2,375,000

At debt ratio of 0.50

Equity = \$2,500,000 × (1-0.50) = \$1,250,000

Debt = \$2,500,000 × 0.50 = \$1,250,000

I = \$1,250,000 × 8% = \$100,000

 V = \$360,000 = \$3,000,000 0.12

E = \$3,000,000 - \$1,250,000 = \$1,750,000

 ke = (\$360,000 - \$100,000) = 14.9% \$1,750,000

At debt ratio of 0.75

Equity = \$2,500,000 × (1-0.75) = \$625,000

Debt = \$2,500,000 × 0.75 = \$1,875,000

I = \$1,875,000 × 8% = \$150,000

 V = \$360,000 = \$3,000,000 0.12

E = \$3,000,000 - \$1,875,000 = \$1,125,000

 ke = (\$360,000 - \$150,000) = 18.7% \$1,125,000

At debt ratio of 1.00

Equity = \$2,500,000 × (1-1.00) = \$0

Debt = \$2,500,000 × 1.00 = \$2,500,000

I = \$2,500,000 × 8% = \$150,000

 V = \$360,000 = \$3,000,000 0.12

E = \$3,000,000 - \$2,500,000 = \$500,000

 ke = (\$360,000 - \$200,000) = 32.0% \$500,000

As we can see, the market value of a firm and WACC are definitely constant at any level of financial leverage under the net operating income approach of capital structure. However, the cost of equity (required rate of return for investors) grows as financial leverage increases.