# Cost of Capital

Cost of capital is the opportunity cost of funds available to a company for investment in different projects. The most common measure of cost of capital is the weighted average cost of capital, which is a composite measure of marginal return required on all components of the company’s capital, namely debt, preferred stock and common stock.

Most companies are for-profit entities which must generate wealth for its shareholders and debt-holders. The projects they invest in must at least earn enough to pay off the interest on bonds and other debt and pay dividends to shareholders and/or generate enough growth to cause an increase in their stock price. It is important for companies to calculate the cost of different components of capital, identify their target mix of debt and equity and work out their weighted average cost of capital. In deciding whether to invest in a project or not, through the capital budgeting process, they must compare the return available on the project with the cost of capital and accept the project only where the return is higher than the cost of capital. If they invest in projects with return lower than the cost of capital, they are effectively destroying their shareholders wealth.

## Formula

Weighted average cost of capital is calculated by multiplying the after-tax cost of debt with the percentage of debt in total capital, multiplying the cost of preferred stock with the percentage of preferred stock in total capital, multiplying the cost of common stock with the percentage of common stock in total capital and summing all the products together.

The following equation mathematically expresses the definition of WACC:

$$ Weighted\ Average\ Cost\ of\ Capital\ (WACC)\\=w_d\times r_d\times(1-t)+w_p\times r_p+w_e\times r_e $$

Where *w _{d}*,

*w*and

_{p}*w*refer to the relative percentage of debt, preferred stock and common stock in the total target capital.

_{e}*r*,

_{d}*r*and

_{p}*r*are cost of debt, cost of preferred stock and cost of common stock respectively.

_{e}*r*is multiplied by (1 – t), where

_{d}*t*refers to the tax rate, because interest expense is allowed as deduction while calculating taxes and this tax-deductibility creates a saving which must be accounted for.

### Component Cost of Capital

If a company’s debt is publicly traded and market prices are available, cost of debt can be determined as equal to its yield to maturity. If no reasonable estimate of market price is available but a bond rating is available, a company’s cost of debt can be estimated as equal to the average cost of debt of companies in the same industry which have the same bond rating. If no market price or bond rating is available for the company’s debt, a rating might be estimated based on financial ratios.

Cost of preferred stock can be calculated using the following formula:

$$ Cost\ of\ Preferred\ Stock\\=\frac{Preferred\ Divideds\ per\ Share}{Current\ Preferred\ Stock\ Price} $$

Cost of common stock can be estimated using either the capital asset pricing model. Under the capital asset pricing mode, cost of common equity is calculated as follows:

$$ Cost\ of\ Common\ Stock\\=r_f+\ beta\times MRP $$

Where *r _{f}* stands for risk-free rate, typically estimated as equivalent to 10-year government bond rate. Beta is the beta coefficient of the company, a measure which assesses the sensitivity of the company’s common stock to movement in market interest rates.

MRP stands for market risk premium (also called equity risk premium) which equals the expected return on the broad market index such as S&P500 i.e E_{m} minus the risk-free rate i.e. r_{f}.

$$ Market\ Risk\ Premium\ (MRP)\\=E_m-r_f $$

If no reliable estimate of MRP is available, the historical risk premium approach maybe used, which bases market risk premium on the historical average of market risk premium.

Under the dividend discount model, cost of common stock can be estimated as follows:

$$ Cost\ of\ Common\ Stock=\frac{D_1}{P_0}+g $$

Where *D _{1}* is the dividend per share expected in 1 year and

*P*is the current market price of the stock and g is the sustainable growth rate.

_{0}### Relative weights

The weighted average cost of capital weighs different component cost of capital in proportion of their relative weight in the target capital structure.

The proportions must be calculated based on market values instead of book values and they should be based on target capital structure, the capital mix the company wants to ultimately achieve, even if it differs materially from its current capital structure.

## Example

Let’s calculate weighted average cost of capital of The Walt Disney Company (NYSE: DIS).

The following information is available from Morningstar for the FY 2017:

Dividend per share | $1.56 |

5-year average return on equity | 18.47% |

Dividend payout ratio | 27.6% |

Debt to equity ratio | 0.46 |

Current stock price | $109.20 |

From Yahoo Finance, we find that the company’s beta coefficient is 1.37, from NYU Stern website’s historical implied risk premiums, we find that the latest is 5.9% (as compared to the historical geometric average of 4.8%). The latest US 10-year treasury bond yield is 2.8%. Assume that the weighted average effective interest rate on the company’s borrowings is 4.5% and its tax rate is 30%.

First, we need to find the component cost of capital.

The cost of debt is 4.5% because it is the effective interest rate on debt.

The company has no preferred stock.

The cost of common stock can be calculated using three approaches:

- the capital asset pricing model,
- the dividend discount model and
- the historical equity risk premium approach.

Under the capital asset pricing model, cost of common stock equals 10.88%:

$$ Cost\ of\ Common\ Stock\ (CAPM)\\=2.8\%+1.37\times5.9\%\\=10.88\% $$

To calculate the cost of equity using the dividend discount model, we need to work out the sustainable growth rate, which equals the product of return on equity and retention rate (which in turn equals 1 minus the dividend payout ratio).

$$ Growth\ Rate\ (g)\\=(1\ -\ Dividend\ Payout\ Ratio)\times ROE\\=(1-27.6\%)\times18.47\%\\=13.37\% $$

Under the dividend discount model, cost of common stock works out to 14.99%:

$$ Cost\ of\ Common\ Stock\ (DDM)\\=\frac{$1.56\times(1+13.37\%)}{$109.20}+13.37\%\\=14.99\% $$

Under the historical equity risk premium approach, DIS cost of common stock is 9.38%:

$$ Cost\ of\ Common\ Stock\ (HRPA)\\=2.8\%+1.37\times4.8\%\\=9.38\% $$

Since DIS is a well-established large-cap company, using the CAPM cost of equity estimate is appropriate.

We need to find their relative proportions which we can work out from the debt to equity ratio.

$$ Debt/Equity=0.46 $$

$$ Debt/(Assets-Debt)=0.46 $$

$$ Debt=0.46\times(Assets\ -\ Debt) $$

$$ Debt\ +\ 0.46\ \times\ Debt=0.46\ \times Assets $$

$$ \frac{Debt}{Assets}=\frac{0.46}{1.46}=31.5\% $$

$$ \frac{Equity}{Assets}=1\ -\ \frac{Debt}{Assets\ }=1-\ 31.5\%\ =68.5\% $$

Now that we have all the necessary figures, we just need to plug the relevant numbers in the WACC formula:

$$ WACC=31.5\%\times4.5\%\times(1-30\%)+68.5\%\times10.88\%=8.45\% $$