# Answer to Question #9083 in Economics of Enterprise for Harry

Question #9083

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,

returns of small caps over 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

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 =

*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 excessreturns of small caps over 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

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