By Yuriy Smirnov Ph.D.

Firms can employ several sources of financing: debt, preferred stock, and common stock. The proportion between those components of capital is called capital structure. The different components of capital have different required rates of return because of the differences in risk. On the other side, the required rate of return is the cost that a firm carries for financing provided by investors (stockholders and debtholders). The weighted average cost of capital or WACC is the sum of the after-tax cost of each component multiplied by the relevant proportion in capital structure.

The WACC can be calculated with the formula

WACC = w_{d}×r_{d}×(1 - T) + w_{ps}×r_{ps} + w_{cs}×r_{cs}

where r_{d}×(1-T) is the after-tax cost of debt; r_{ps} is the cost of preferred stock; r_{cs} is the cost of common stock or retain earnings; w_{d}, w_{ps} and w_{cs} represent the proportion of debt, preferred stock, and common stock in capital structure; and T is a marginal tax rate.

It is strongly recommended to use the market value of debt, preferred stock, and common stock when the weighted average cost of capital is being estimated. The book value of those components may only be employed if their market value can’t be assessed properly.

The target or optimal capital structure is a proportion of debt and common and preferred equity that maximize the shareholder’s value. When a firm is going to raise additional capital, it must ensure that previous proportions are stable. In other words, the w_{d}, w_{ps} and w_{cs} should not change in further WACC calculations.

The proportion between components of capital depends on risk and return trade-off, e.g., the higher portion of debt in capital structure means a greater degree of risk in a firm’s earnings and results in the higher required rate of return for debtholders. This leads to a firm’s lower market value and a lower stock price.

Company A has 10,000 bonds outstanding of $1,000 par value and a fixed annual coupon rate of 8.5%. The bond issue matures in three years, and the current required rate of return is 9.75%. The number of shares of common stock outstanding is 2,000,000 of $25 par value, the current market price is $19.85, the beta (β) is 1.15, the expected market return (r_{M}) is 15.5%, and the risk-free rate (r_{RF}) is 3.5%. The preferred equity is represented by 300,000 shares of preferred stock of $60 face value and annual dividends of 10%. Their current required rate of return is 11.5%, and the marginal tax rate is 25%.

First, we need to calculate the market value and proportion of each component of capital to give an accurate WACC estimation.

To find the current market value of a bond, we have to perform the following calculations:

Annual coupon = $1,000 × 0.085 = $85

The current market bond price is equal to the present value of all future cash flow:

Current bond price = | $85 | + | $85 | + | $85 + $1,000 | = $968.78 |

(1 + 0.0975)^{1} |
(1 + 0.0975)^{2} |
(1 + 0.0975)^{3} |

So, the current market value of debt is $9,687,800 ($968.78×10,000).

The current market value of common equity is $39,700,000 ($19.85×2,000,000).

To find the current market price of preferred stock, we should use the equation

P_{ps} = |
D_{ps} |

r_{ps} |

where D_{ps} is the annual preferred dividend.

D_{ps} = $60 × 0.1 = $6

P_{ps} = $6 ÷ 0.115 = $52.17

The current market value of preferred equity is $15,651,000 ($52.17×300,000).

The market value of capital = $9,687,800 + $39,700,000 + $15,651,000 = $65,038,800

w_{d} = $9,687,800 ÷ $65,038,800 = 0.15

w_{ps} = $39,700,000 ÷ $65,038,800 = 0.24

w_{cs} = $15,651,000 ÷ $65,038,800 = 0.61

As a second step of WACC calculation, we have to estimate the cost of each component of capital.

After-tax cost of debt = 8.5% × (1 - 0.25) = 6.375%

To estimate the cost of common stock, we should employ the CAPM approach.

r_{s} = r_{RF} + β×(r_{M} - r_{RF}) = 3.5% + 1.15×(15.5% - 3.5%) = 17.3%

WACC = 0.15 × 6.375% + 0.24 × 10% + 0.61 × 17.3% = 13.91%

If we calculate WACC using the book value of each component of capital, their proportion will be different.

Book value of debt = $1,000 × 10,000 = $10,000,000

Book value of preferred equity = $60 × 300,000 = $18,000,000

Book value of common equity = $25 × 2,000,000 = $50,000,000

Book value of capital = $10,000,000 + $18,000,000 + $50,000,000 = $78,000,000

w_{d} = $10,000,000 ÷ $78,000,000 = 0.13

w_{ps} = $18,000,000 ÷ $78,000,000 = 0.23

w_{cs} = $50,000,000 ÷ $78,000,000 = 0.64

WACC = 0.13 × 6.375% + 0.23 × 10% + 0.64 × 17.3% = 14.2%

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