The weighted average cost of capital (WACC) is a common topic in the financial management examination. This rate, also called the discount rate, is used in evaluating whether a project is feasible or not in the net present value (NPV) analysis, or in assessing the value of an asset. Previous examinations have revealed that many students fail to understand how to calculate or understand WACC.

### How to calculate WACC

WACC is calculated as follows:

WACC = E/V x Re + D/V x Rd x (1-tax rate)

WACC is the proportional average of each category of capital inside a firm – common shares, preferred shares, bonds and any other long-term debt – 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 = firm value

E/V = percentage of financing that is equity

D/V = percentage of financing that is debt

WACC is simply a replica of the basic accounting equation: Asset = Debt + Equity. WACC focuses on the items on the right hand side of this equation.

(Most companies do not have preferred shares. For simplicity, we only use common shares and bonds in our illustrations.)

### Deriving assets by raising debt or equity

A firm derives its assets by either raising debt or equity (or both). There are costs associated with raising capital and WACC is an average figure used to indicate the cost of financing a company’s asset base.

In determining WACC, the firm’s equity value, debt value and hence firm value needs to be derived. This part is definitely not too difficult. You also need to find the cost of the equity and the cost of the debt.

Basically there are two approaches in finding the cost of equity: the dividend growth approach and the capital asset pricing model (CAPM) approach.

Using the dividend approach,

P0 = D1 / (Re – g)

where;

Po is the current stock price or price of the stock in period 0.

D1 is the dividend in period 1

Re is the cost of equity

g is the dividend growth rate

Re = D1 / P0 + g

This approach only applies to dividend-paying stock as we need to determine the dividend growth rate.

The other approach is the CAPM, which was developed by Sharpe, a Nobel Prize winner in economics in 1990.

Re = Rf + ßex (Rm – Rf )

### How best to determine the risk free rate

Using CAPM, the risk free rate (Rf ) and market return (Rm) have to be found, as does the stock’s beta. There are many arguments about how best to determine the risk free rate, market return and the beta. However, CAPM is relatively more commonly used than the dividend growth model since most stocks do not have a stable dividend history.

When calculating the cost of debt, we do not use the coupon rate of the bond as reference. Rather, we use the yield rate. For example, if a bond has coupon rate of 3% and a market price of 103, this implies that the actual yield is less than 3%.

Let me use an example to illustrate.

On the equity side, a company has 50 million shares with market price of $80 per share. The beta of the stock is 1.15 and market risk premium is 9%. The risk-free rate is 5%.

On the debt side, the company has $1 billion outstanding debt (face value). The current price of the debt is 110 and the coupon rate is 9%: the company pays semi-annual coupons with 15 years to maturity. Assume the tax rate is 15%.

To find the cost of equity,

Re = 5 + 1.15(9) = 15.35%

Remember the market risk premium is Rm-Rf. Since this is given, we need not deduct 5% from 9%.

To find cost of debt, we turn to the bond pricing equation and find r.

P = C x [1 – 1/(1 + r )t]/r + F x 1/(1 + r )t

We may assume the face value of individual bond = $1,000. Since C = $45 (remember it’s a semiannual payment), t = 30, P = $1,100, F=$1,000, we find that r = 3.9268%.