The cost of equity capital for the firm as a whole is different from the cost of equity capital for the stock issued by the firm.  The difference arises whenever a firm uses both debt and equity in their financing mix.  For the firm as a whole as introduced in the beginning of this write-up the cost of capital is a weighted average cost of capital.  The usual formulation is in terms of the after tax weighted average cost of capital. 

Where τ_c is the effective corporate tax rate, k_d is the cost of debt capital and k_e is the cost of equity capital.  The above equation works with the after tax cost of debt because interest expense is tax deductible whereas dividend payments are not.   For the stock (k_e) the most widely used first pass estimate is provided from the Capital Asset Pricing Model (CAPM) estimate.  This implies that k_e is a function of three major inputs:

i.                    Risk free rate (Estimated from US Treasury bonds)

ii.                  Beta (Measures how much volatility the stock contributes to the market as a whole)

iii.                Equity Premium (Excess return expected from stocks over the risk free rate)

 

i.                     First, you can get current estimates for the risk free rate from the Valuation Tutor: 

 

 

At the time of this current example the 30-year bond rate was 4.19% and so we will use this rate for the risk free rate.

ii.                  We will work with popular web sites to get an estimate of Beta for IBM from.  For example, MSN Money, and Yahoo Investor provide estimates:

The estimate for IBM’s beta at the time of this example is 0.76.

iii.                Again, like expected return the equity premium cannot be observed because it requires an estimate of the expected return from the market.  So again this needs to be estimated.  We do so from historical averages as discussed below.

“The average real return for 1872-2000 on the S&P index (a common proxy for the market portfolio, also used here) is 8.81% per year. The average real return on six-month commercial paper (a proxy for the riskfree interest rate) is 3.24%. This large spread (5.57%) between the average stock return and the interest rate is the source of the so-called equity premium puzzle: stock returns seem too high given the observed volatility of consumption (Mehra and Prescott, 1985).” Fama and French (2002). 

Also in the last chapter we saw that in a recent extensive survey of analysts, the consensus estimate is 5.1% to 5.3%.  As a result, there is a large amount of agreement in the range of 5.1-5.5% for the US Equity premium.

As a first pass, we will use the more conservative estimate of 5.5%, though we note that the equity premium fluctuates over time.  For example, in the 1990’s it was commonly speculated that the equity premium had declined and some estimates were as low as 3.5%.  For example, interested readers are encouraged to read the speech by Allan Greenspan “Measuring Financial Risk in the 21^st Century.”   Similarly, an interesting paper by Professors Pablo Fernandez and Javier Del Campo Baonza at the University of Navarra, provides an extensive survey textbooks and professors to provide international estimates of current equity premiums.  This paper provides estimates for the Australia, Canada, Europe, UK and US.  Both of these can be accessed from Valuation Tutor:

Collecting above together k_e = r_f + β_i*(E(R_M) – r_f) = 0.0419 + 0.76*0.055  = 0.0837

Current Summary on a Per Share Basis: 

IBM Adjusted Cash Flows from Operations = 18.873/1.341 = 14.07

CAPEX per Share = 6.519/1.341 = 4.86

Derived Value: FCFF per share = 12.381/1.341 = 9.21

Debt Ratio = 0.239

Derived Value: FCFE per share = 13.939/1.341 = $10.39

5-year Stage 1 Growth:  0.10 

Normal Growth:  0.045

Risk free rate (both stages) = 0.0419

Beta IBM = 0.76

Years in Stage 1:  5-years

Equity Premium = 0.055

Derived Value (CAPM):  Cost of Equity Capital = 0.0837