Contents
- Index
Concept 3: Cost of Capital Estimation
©2009 OS Financial Trading System
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 ?c is the effective corporate tax rate, kd is the cost of debt capital and ke 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 (ke) the most widely used first pass estimate is provided from the Capital Asset Pricing Model (CAPM) estimate. This implies that ke 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 www.bloomberg.com:
We will assume a 30-year investor and set Rf = 3.71%
ii. We will work with popular web sites to get an estimate of Beta for IBM from. For example, MSN Money, Yahoo Investor and Google Finance all provide estimates. For the current example, beta for IBM was taken from the Google finance site:
Beta = 0.81
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 from 1872 to 2000 in the US on the S&P500 index is 8.81% (Fama and French, JF April 2002). If we combine this with the estimate for long term inflation in the US (as discussed in the Normal Growth section above) which equals 3.24% then the long term average equity premium for the US is 5.57%. As a first pass we will use the estimate of 5.5% however 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 21st Century"
<http://www.federalreserve.gov/BOARDDOCS/SPEECHES/1999/19991014.htm>
Similarly, an interesting paper by Pablo Fernandez at the University of Navarra, has extensively surveyed textbooks and professors to provide international estimates of current equity premiums:
<http://ssrn.com/abstract=1344209>
This paper provides estimates for the Australia, Canada, Europe, UK and US.
Cost of Equity Capital, using CAPM, for IBM
Collecting above together ke = rf + ?i*(E(RM) - rf) = 0.0371 + 0.81*0.055 = 0.08165
This number when applied to Book Value permits Residual Earnings to be computed.
Summary
Dividend per Share = Dividends/(Shares issued - Treasury Stock) = 2,585/(2,096.981860 - 757.885937) = $1.9305 equals the dividend per share.
Comprehensive Earnings Per Share = Net Income / (Shares issued - Treasury Stock) = 5,862/(2,096.981860 - 757.885937) = $4.37758
Comprehensive EPS FY 2009 $4.377*1.0175 = $4.454, Growth 0.0175
Comprehensive EPS FY 2010 $9.37*1.089 = $4.85, Growth 0.089
Projected Dividend Per Share (Next Year) = $9.37*0.2095 = $1.96
Dividend Payout Ratio = 2585/5862 = 0.440976
5-Year Growth = 0.0965
Normal Growth = 0.045
Cost of Equity Capital (ke) = 0.08165
Concept Review: IBM Example Implied Equivalence Relationship
We can verify the calculation the various earnings estimates and then apply these to illustrate the relationship between AEG at a point in time and the change in Residual Income over time.
Equivalence Relationship between Abnormal Growth and the Change in Residual Earnings
As is well presented in the textbooks the AEG model is directly related to the residual income model because the AEG for a particular year can be expressed as the difference between Residual Income for that year and the previous year.
In the current IBM example context this applies as follows:
AEG2010 = (C. Earn2010 + (ke - 1)Div2009) - keC. Earn2009
= C. Earn2010 - C. Earn2009 - (ke - 1)(C. Earn2009 - Div2009)
From the clean surplus relationship and comprehensive earnings
Book Value2009 = Book value2008 + C. Earn2009 - Div2009
Substituting in:
AEG2010 = C. Earn2010 - C. Earn2009 - (ke - 1)( Book Value2009 - Book value2008)
Rearranging we express as the differences between two residual incomes
= C. Earn2010 - (ke - 1)( Book Value2009 ) - C. Earn2009 - (ke - 1)(Book value2008)
Application:
2009 Normal earnings = 0.08165*$4.37758 = $4.735
2010 Normal earnings = 0.08165*$4.454 = $4.8177
2010 Abnormal earnings growth = $4.85 + 0.08165*$1.96 = $5.0103 - $4.8177 = 0.1927
So given current growth forecasts we expect IBM to return to positive Abnormal earnings growth.
FTS Residual Income exercise: This is verified for the same cost of equity capital as follows:
Residual Earnings Calculations for 2008, 2009, 2010 respectively:
Difference: RE 2010 3.825709 and RE2009 3.633009 = 0.1927 which equals the abnormal earnings growth above.
This verifies the analytical result for IBM
Finally, in the next section we apply this model to assess intrinsic value.