By Yuriy Smirnov Ph.D.

The traditional approach to capital structure assumes that an increase in the proportion of debt to some extent does not result in an increase in the cost of equity, i.e., it remains fixed or grows slightly. That is the reason why it becomes possible to reduce the weighted average cost of capital (WACC) by increasing the proportion of debt financing in total capital. Thus, firms using financial leverage within certain limits are valued higher by the market than similar companies with lower financial leverage.

The traditional theory of capital structure is based on the following assumptions:

- Cost of debt (k
_{d}) remains stable with an increase in the debt ratio to a certain limit after which it begins to grow. - Cost of equity (k
_{e}) remains stable or grows slightly with an increase in the debt ratio to a certain limit after which it begins to grow rapidly. - Weighted average cost of capital decreases to some degree with an increase in the debt ratio and then begins to grow.
- Cost of equity is larger than the cost of debt at any capital structure, i.e., k
_{e}>k_{d}at any value of debt ratio. - The traditional approach to capital structure believes the existence of optimal capital structure. It is such a mix of debt and equity at which WACC reaches the minimal value and the value of a firm will be maximized.

Assumptions of the traditional approach to capital structure are illustrated in the figure below.

**financial leverage is measured as a debt ratio*

When financial leverage equals to 0, i.e., the capital of a firm is represented by equity only, its WACC is equal to the cost of equity. As the financial leverage increases, the WACC will decrease until the marginal cost of debt is lower than the marginal cost of equity. The minimal value of WACC is reached when the marginal cost of debt equals the marginal cost of equity. Such a capital structure is considered as optimal under the traditional approach. A further increase of financial leverage will result in an increase of WACC as far as the marginal cost of debt will be higher than the marginal cost of equity due to higher risks.

When the optimal capital structure is reached, the value of a firm is maximized as shown in the figure below.

Total capital of STAR S.E. Inc. is $3,000,000 and expected earnings before interest and taxes are $510,000. Management needs to determine the optimal capital structure in which the market value of a company will be maximized. The information about cost of debt (k_{d}) and cost of equity (k_{e}) at different values of debt ratio is presented in the table below.

We should use the formula below to calculate the WACC at different values of debt ratio

WACC = k_{d}×w_{d} + k_{e}×w_{e}

where w_{d} is the proportion of debt in total capital (debt ratio) and w_{e} is the proportion of equity (1 - debt ratio).

WACC at D/E of 0 = 12% × 0.00 + 17%×(1-0.00) = 17.00%

WACC at D/E of 0.15 = 12%×0.15 + 17%×(1-0.15) = 16.25%

WACC at D/E of 0.30 = 12%×0.30 + 17%×(1-0.30) = 15.50%

WACC at D/E of 0.40 = 12%×0.40 + 18%×(1-0.40) = 15.60%

WACC at D/E of 0.50 = 14%×0.50 + 21%×(1-0.50) = 17.50%

WACC at D/E of 0.60 = 17%×0.60 + 24.5%×(1-0.60) = 20.00%

WACC at D/E of 0.75 = 22%×0.75 + 30%×(1-0.75) = 24.00%

WACC at D/E of 1.00 = 30%×1.00 + 40%×(1-1.00) = 30.00%

Management of STAR S.E. Inc. may reach the minimum WACC of 15.5% when its capital structure is represented by 30% of debt and 70% of equity.

Let’s see if the value of STAR S.E. Inc. will be maximized under the traditional approach to capital structure. To do this, we need to calculate its value (V) for all variants of capital structure using the following formula:

V = E + D

where E is the current value of equity, and D is the current value of debt.

In turn, the value of equity can be calculated using the equation below

E = | EBIT - I |

k_{e} |

where I is interest expense.

Let’s calculate the value of STAR S.E. Inc. for all variants of capital structure.

__At wd = 0.00__

D = $3,000,000 × 0.00 = $0

I = $0

E = | $510,000 | = $3,000,000 |

0.17 |

V = $3,000,000 + $0 = $3,000,000

__At wd = 0.15__

D = $3,000,000 × 0.15 = $450,000

I = $450,000 × 0.12 = $54,000

E = | ($510,000 - $54,000) | = $2,682,353 |

0.17 |

V = $2,682,353 + $450,000 = $3,132,353

__At wd = 0.30__

D = $3,000,000 × 0.30 = $900,000

I = $900,000 × 0.12 = $108,000

E = | ($510,000 - $108,000) | = $2,364,706 |

0.17 |

V = $2,364,706 + $900,000 = $3,264,706

__At wd = 0.40__

D = $3,000,000 × 0.40 = $1,200,000

I = $1,200,000 × 0.12 = $144,000

E = | ($510,000 - $144,000) | = $2,033,333 |

0.18 |

V = $2,033,333 + $1,200,000 = $3,233,333

__At wd = 0.50__

D = $3,000,000 × 0.50 = $1,500,000

I = $1,500,000 × 0.14 = $210,000

E = | ($510,000 - $210,000) | = $1,428,571 |

0.21 |

V = $1,428,571 + $1,500,000 = $2,928,571

__At wd = 0.60__

D = $3,000,000 × 0.60 = $1,800,000

I = $1,800,000 × 0.17 = $306,000

E = | ($510,000 - $306,000) | = $832,653 |

0.245 |

V = $832,653 + $1,800,000 = $2,632,653

__At wd = 0.75__

D = $3,000,000 × 0.75 = $2,250,000

I = $2,250,000 × 0.22 = $495,000

E = | ($510,000 - $495,000) | = $50,000 |

0.30 |

V = $50,000 + $2,250,000 = $2,300,000

The calculations above prove that the value of STAR S.E. Inc. will be maximized at a debt ratio of 0.30.

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