# Answer to Question #6207 in Economics of Enterprise for LaMarcus Streeter

Question #6207

Analyze the various ways to determine the cost of capital and determine which is the most difficult to get right. Explain your rationale.

Expert's answer

The cost of capital determines how a company can raise money (through a stock issue, borrowing, or a mix of the two). This is the

rate of return that a firm would receive if it invested in a different vehicle

with similar risk. Cost of capital = interest rate at zero level risk + premium for business risk + premium for

financial risk. There are other different ways to determine the cost of capital:

1.The cost of debt is relatively simple to calculate, as it is composed of the rate of interest paid. It is computed by

taking the rate on a risk free bond whose duration matches the term structure of

the corporate debt, then adding a default premium. The formula can be written as

(Rf + credit risk rate)(1-T), where T is the corporate tax rate and Rf is the

risk free rate.

2.The cost of equity is more challenging to calculate as equity does not pay a set return to its investors. It is therefore inferred by comparing the investment to other investments

(comparable) with similar risk profiles to determine the "market" cost of

equity. It is commonly equated using the Capital Asset Pricing Model (CAPM) formula:

An alternative to the estimation of the required return by the CAPM as above, is the use of the Fama–French three-factor

model.

r =

Here r is the portfolio's rate of return,

big caps and of value stocks over growth stocks.

3. The Weighted Average Cost of Capital (WACC) is used in finance to measure a firm's cost of capital.

Its calculation is an iterative procedure which requires estimation of the fair

market value of equity capital:

Where:

Re = cost of equity

Rd = cost of debt

E = market value of the firm's equity

D = market value of the firm's debt

V = E + D

E/V = percentage of financing that is equity

D/V = percentage of financing that is debt

Tc = corporate tax rate

rate of return that a firm would receive if it invested in a different vehicle

with similar risk. Cost of capital = interest rate at zero level risk + premium for business risk + premium for

financial risk. There are other different ways to determine the cost of capital:

1.The cost of debt is relatively simple to calculate, as it is composed of the rate of interest paid. It is computed by

taking the rate on a risk free bond whose duration matches the term structure of

the corporate debt, then adding a default premium. The formula can be written as

(Rf + credit risk rate)(1-T), where T is the corporate tax rate and Rf is the

risk free rate.

2.The cost of equity is more challenging to calculate as equity does not pay a set return to its investors. It is therefore inferred by comparing the investment to other investments

(comparable) with similar risk profiles to determine the "market" cost of

equity. It is commonly equated using the Capital Asset Pricing Model (CAPM) formula:

An alternative to the estimation of the required return by the CAPM as above, is the use of the Fama–French three-factor

model.

r =

*R*_{f}+ β (*K*_{m}-*R*_{f}) + bs * SMB + bv * HML + α.Here r is the portfolio's rate of return,

*R*_{f}is the risk-free return rate, and*K*_{m}is the return of the whole stock market. The "three factor" β is analogous to the classical β but not equal to it, since there are now two additional factors to do some of the work.*S**M**B*stands for "small (market capitalization) minus big" and*H**M**L*for "high (book-to-market ratio) minus low"; they measure the historic excess returns of small caps overbig caps and of value stocks over growth stocks.

3. The Weighted Average Cost of Capital (WACC) is used in finance to measure a firm's cost of capital.

Its calculation is an iterative procedure which requires estimation of the fair

market value of equity capital:

Where:

Re = cost of equity

Rd = cost of debt

E = market value of the firm's equity

D = market value of the firm's debt

V = E + D

E/V = percentage of financing that is equity

D/V = percentage of financing that is debt

Tc = corporate tax rate

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