# 2. COST OF CAPITAL

The cost of capital is the rate of return that:

• The suppliers of capital —bondholders and owners—require as compensation for their contribution of capital.
• Investors demand for the average-risk investment of a company.
##### Calculate WACC.

WACC = WdRd(1 – t) + WpRp + WeRe
Rd RE都是用Market value 而不是 book value.

##### 2.1Tax

Takingthe tax-deductibility of interest as the base case, we adjust the pre-tax cost of debt for this tax shield. Multiplying rd by (1 − t) results in an estimate of the after-tax cost of debt.

##### Target Value

target > forecast > current
Target value 是一个公司未来希望达到的一种资本结构。但如果无法获得target value的话，也有以下几种办法。

• Assume the company’s current capital structure, at market value weights for the components。(使用最多）

• Examine trends in the company’s capital structure or statements by management regarding capital structure policy to infer the target capital structure.

• Use averages of comparable companies’ capital structures as the target capital structure.

##### 2.3. Applying the Cost of Capital to Capital Budgeting and Security Valuation

A company’s marginal cost of capital (MCC) may increase as additional capital is raised.
Investment opportunity schedule are generally believed to decrease as the company makes additional investments

image.png

If NPV > 0 , the company accepy the project. If we choose to use the company’s WACC in the calculation of the NPV of a project, we are assuming that the project:

• has the same risk as the average-risk project of the company
• will have a constant target capital structure throughout its useful life.

Project risk > average risk discount rate: project rate > WACC
Project risk < average risk discount rate: project rate < WACC

# 3 COSTS OF THE DIFFERENT SOURCES OF CAPITAL

##### 3.1 Cost of debt
• 3.1.1Yield to maturity

image.png

使用的是market rate

• 3.1.2 Debt rating approach
如果无法获得当前市场Debt的价格，就找一个与之评级相近的公司

##### 3.2 Cost of preferred dividends

A company has committed to pay preferred stockholders as a preferred dividend when it issues preferred stock. In the case of nonconvertible, preferred stock that has a fixed dividend rate and no maturity date

image.png
image.png

• Pp = the current preferred stock price per share
• Dp = the preferred stock dividend per share
• rP = the cost of preferred stock

the dividend on preferred stock is not tax-deductible by the company; therefore, there is no adjustment to the cost for taxes.

##### 3.3 Cost of Common Equity
• 3.3.1 Capital Asset Pricing Model

image.png

E(Rm) = the expected return on the market
RF = is the sum of the risk-free rate of interest,
βi = the return sensitivity of stock i to changes in the market return
E(RM) − RF = the expected market risk premium

``````Example
the risk-free rate is 5 percent, equity risk premium is 7 percent,
and Valence’s equity beta is 1.5.
What is Valence’s cost of equity using the CAPM approach?
Solution:
Cost of common stock = 5 percent + 1.5(7 percent) = 15.5 percent.
``````

The expected market risk premium, or E(RM − RF), is the premium that investors demand for investing in a market portfolio relative to the risk-free rate. When using the CAPM to estimate the cost of equity, in practice we typically estimate beta relative to an equity market index. In that case, the market premium estimate we are using is actually an estimate of the equity risk premium。

Historical Rates of Return model requires compiling historical data to find the average rate of return of a country’s market portfolio and the average rate of return for the risk-free rate in that country.

``````Example：
Suppose that over the last 100 years is an unbiased estimator for the risk-free rate and amounts to 5.4 percent. over the last 100 years，the average rate of return of the market was 9.3 percent. Calculate the equity risk premium.
Solution Re = Rm - Rf = 3.8
``````
• 3.3.2. Dividend Discount Model Approach

image.png

image.png
• P0 is the current market value of the equity market index,
• D1 are the dividends expected next period on the index,
• re is the required rate of return on the market,
• g is the expected growth rate of dividends. g = (1 – D/EPS)ROE
• 3.3.3. Bond Yield plus Risk Premium Approach
re = bond yield + Risk premium

# 4. TOPICS IN COST OF CAPITAL ESTIMATION

##### 4.1. Estimating Beta and Determining a Project Beta

pure-method

image.png

image.png

• Beta is using historical returns data.
• Estimates of beta for small-captitalization firms may need to be adjusted upward.
##### 4.2. Country Risk

Country premium(CRP) = Sovereign yield spread × (Annualized standard deviation of equity index/Annualized standard deviation of the sovereign bond market in terms of the developed market currency)
r = Rf + B * [ Rm - Rf + CRP]

##### 4.3. Marginal Cost of Capital Schedule

Break-point = capital变化的价格点 / weight of capital

##### 4.4. Flotation Costs
• 第一种办法，CFA不鼓励的
R = D1 / [p* (1 - f)] + g
• 第二种方法，先求出f 剪掉的钱 F
NPV = - N0 - F + N1 + N2 +...

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