Concept 3: Estimating Cost of Equity Capital

Contents - Index

Concept 3: Estimating Cost of Equity Capital
©2009 OS Financial Trading System

For a 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 = 4.18%
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 = 0.82
MSN displays a beta equal to 0.82 and Yahoo a beta equal to 0.77. Taking the average we will use 0.803 as IBM's beta.
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) = 0.0418 + 0.803*0.055 = 0.08596
Note: The cost of equity capital plays a more dominating role in the RIV model than say in a FCFE model. The reason is that it directly affects the numerator (i.e., the computation of residual income). As a result, we will stick with the CAPM estimate for IBM because the obvious flaws associated with CAPM (i.e., low beta distressed related firm) do not apply to IBM. Given the valuation model places a lot of weight on the opportunity cost of capital in assessing residual earnings the theoretical measure will be applied. But this is an interesting number to perform sensitivity analysis on.
I. Application Using the FTS System
We will enter the values for IBM by gathering them together into a single location in the spreadsheet.
Once the FTS Real Time Client launches then select the trading exercise and enter your trading name, password and click on Login.

In the FTS Real Time Client the bottom RHS of the screen lets you select the analytical support from what is available. In this exercise we are using "Stocks: Residual Earnings Model" so select this support from the yellow part of the screen below.

The bottom RHS will now appear as follows. It has the main inputs from the exercise to date as well as derived values from this model. The derived values will let you make additional inferences from the current market price.

In particular the following fields are available:
RE_BV (Book Value)
RE_D (Current Dividend)
RE_D1 (Next year's dividend)
RE_EPS (Current EPS)
RE_EPS1 (Next year's EPS)
RE_EPS2 (Following year's EPS)
RE_Y1 (Number of years in abnormal growth stage)
RE_G1 (Abnormal growth --- e.g., 5-year abnormal growth)
RE_G2 (Normal Growth)
RE_Ke1 (Cost of Equity Capital abnormal growth phase)
RE_Ke2 (Cost of Equity Capital normal growth phase)
RE_PR (Payout Ratio)

In addition the derived fields are:
Market Price - Current spot stock price
PV Abnormal Earnings --- PV of residual earnings in abnormal growth phase
PV Continuing Value - PV of residual earnings in normal growth phase
Intrinsic Value (sum of PV Abnormal + PV Continuing Value + Book Value)
Premium over Book --- Value of future residual earnings stream
Over/Under --- market price relative to intrinsic value