Contents
- Index
Cost of Equity Capital: A Second Look Using MCPM
©2009 OS Financial Trading System
Impact of Cost of Equity Capital
In Corporate Finance it is identified that one of the major drivers of the cost of equity capital is leverage. In particular, a levered stock is predicted to have a higher ke than does an unlevered stock. 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. Debt has a lower cost of capital than does equity and as more debt is added to the firm the cost of equity capital is predicted to increase so that the leveraged firm is expected to have a higher beta than an identical unleveraged firm. Similarly, ke is predicted to be higher than kd because debt holders must be paid in full before equity holders can receive anything in the event of bankruptcy plus the higher the leverage the larger ke becomes. As a result, in the naïve application of CAPM the effects of leverage and debt covenants are assumed to be captured in the estimate of the covariance of returns. An alternative more direct approach starts with the required rate of return from investors and imposes as a lower bound constraint that ke > kd. A reasonable example of this type of approach is provided by the MCPM model.
Inputs required for the MCPM model:
Dividend Yield
YTM on corporate debt (equivalent bond rating for IBM and say 10-year horizon).
Annualized volatility of IBM stock price
Maturity = the assumed maturity for the YTM on corporate debt.
Estimation of inputs:
The current dividend yield for IBM is: $2.20/117.67 = 0.01869
YTM on Corporate Debt: The current Fitch rating for IBM is "A" and so from the current
Turning to Yahoo's Bond Screener:
The corporate debt yield to maturity for IBM is:
For a 3-year corporate debt the YTM is 2.101 and the Fitch rating is A for IBM.
Current YTM for 3 years 2.101% but how do we estimate 10-years?
From Bloomberg the spread between 3-years and 10-years for Treasuries is around 200 basis points. However, the spread for an "A" rating will be more. To estimate this we take the average YTM of a large sample of 9-10-year Fitch rated corporate bonds. The average from 64 issues listed on Yahoo.com is:
You can mark the Yahoo results and copy and paste directly into a spreadsheet. This way you can quickly get all 64 results into a spreadsheet in a form that you can analyze.
By pasting into the spreadsheet the Yahoo results you can compute the average YTM for "A" rated bonds around 10-years to maturity as equal to 5.805% for 64 issues found (at the time of this xercise - these numbers of course will change over time).
This implies that for A rates the spread from 3-years to 10-years is around 370 basis points.
Volatility Estimates
Next we estimate volatility from the last 10-years dividend and stock split adjusted returns:
Again we download this data from www.yahoo.com <http://www.yahoo.com>:
You can then compute returns in Excel and compute the volatility of returns:
The Monthly volatility = 0.0872. To annualize this we invoke the weak form market efficiency assumption that volatility increases linearly in the square root of time. As a result, the Annualized Volatility equals 0.0872*(12^0.5) = 0.302 (i.e., 30.2% annualized).
Checking Current Implied Volatilities Using Option Prices
It is also desirable to exploit information contained in option prices for IBM, in particular the implied volatility estimate. You can do this using the FTS Option Calculator. To run, launch the FTS Real Time Client and select the "FTS Modules" tab from the top RHS of the screen. Then further select Option Calculator from the dropdown:
Run the Option Calculator. The following screen will appear:
Now complete the following steps:
Step 1: For your own stock you should enter your stock ticker beside "Get Underlying Price" and then click the button Get Underlying Price. The current stock price should come in beside Underlying Price. In the current example we enter: IBM
Tip: If a number fails to come in you can always enter it directly manually into the text box.
Step 2: Enter the ticker symbol for Option Root. You can look this up as on the web. For example, if you go to Yahoo finance, enter the IBM ticker and click on Options (LHS of the screen):
You want the longest maturity options - which are only for January 2011 in the above example. Click on Jan 11 and then select the approximately "at the money" call option:
From the screen below this is the strike 120 Call option (Ticker XBYAB.X):
Clicking on the ticker reveals the option details:
At this time the closing price of IBM was 117.67.
The four entries required for IBM into the calculator are: Stock Ticker = IBM, Option Root = XBY, Maturity = 01/22/2011, dividend yield = 0.01869 (calculated earlier), option price = 12.40 and Strike Price = 120.
In excel you can compute the number of days to maturity (current example = 503 and so the time to maturity for the option calculator = 503/365 = 1.378. Referring to the yield curve (Bloomberg.com) you can approximate the risk free rate for 1.378 years as: 0.00587
Entering the above into the calculator and finally set the calculator to Call Option, American Option, and check beside Implied Volatility and then click on Calculate.
This reveals the following:
The implied volatility estimate for IBM is currently 0.26149
The historical volatility estimate for IBM is a little higher but don't forget the maturity for the YTM is 10-years not 1.378 years. So this seems to be reasonable and so the historical volatility estimate will be used.
Summary of MCPM Estimates:
Dividend Yield = 1.869%
YTM on corporate debt (equivalent bond rating for IBM and say 10-year horizon) = 5.805%
Annualized volatility of IBM stock price: 30.2% (this is the historical volatility as opposed to the implied volatility using OPM)
Maturity = the assumed maturity for the YTM on corporate debt = 10-years