Contents - Index

Estimating Cost of Capital: MCPM (Volatility)
©2009 OS Financial Trading System



FTS DJIA School Case:  (Market Derived Capital Pricing Model)

References

What's Your Real Cost of Capital?  By James J. McNulty, Tony D. Yeh, William S. Shulze, and Michael H. Lubatkin  Harvard Business, October 2002.

Question:  How do you estimate the cost of equity capital for a stock from the perspective of what the investors' required rate of return is from the stock?

In this project you will learn how to answer this question by adopting a volatility based option pricing approach to the question that has been referred to as MCPM.  The required parts are provided at the end of the write-up.

Background:  Applying MCPM to Wal-Mart

In the FTS Cost of Equity Capital part 1 project, you worked through the example of estimating the cost of equity capital for Wal-Mart under CAPM.  At the beginning of February 2009 this was estimated to be 4.71%.  Wal-Mart is a low beta stock and the CAPM has often attracted criticism by practitioners for generating low estimates of the cost of equity capital especially for low beta stocks that are currently not performing well.  Wal-Mart does not fall into that latter category, but it is a low beta stock and it does have a low implied cost of equity capital.  

In this project we will consider an alternative approach to computing the cost of equity capital that starts from what the investor's required rate of return is.  To provide some intuition into this we will refer to the Wal-Mart example.  From the very latest 10-K statements for the year ending 2008 Wal-Mart made the following disclosure:



You can observe that this immediately raises questions about the cost of equity capital estimate above.  This is because the weighted average interest rate to debt-holders exceeds our estimate for the cost of equity capital even though debt holders are paid in full before equity holders in the event of corporate failure.  As a result, if we approach the problem of estimating the cost of equity capital from the perspective of the investors' required rate of return then one would argue that the cost of equity capital for Wal-Mart should exceed 4.9%.  But this leaves open the question - by how much?

Estimating the Cost of Equity Capital:  Investors Required Rate of Return Approach

An alternative method that has been proposed in the literature for estimating the cost of equity capital is the Market Derived Capital Pricing Model (MCPM).  This model was presented as an algorithm for calculating cost of equity capital in a manner that overcame some argued weaknesses of CAPM.   The technique implicitly starts with the premise that the cost of equity capital equals stock investors' required rate of return and therefore must be higher than the cost of debt capital for the firm.  MCPM computes the excess yield to maturity (YTM) that investors require from a stock over and above the corporate bond rate.   It solves the question how much excess YTM in a clever way.  The technique exploits the option pricing model to compute the cost of insuring assuming the financial cost of carry in the derivative pricing problem is the corporate bond rate.  Thus by combining a stock with a put option, guarantees that the return from the stock will not fall below the return from the risky debt.  The cost of this put option is then expressed as an ordinary annuity over the (average) life of the bond to solve for the excess YTM in terms of basis points.  The algorithm for calculating MCPM is described in detail in Appendix 1 and an application of this technique to Wal-Mart is covered next.  

The FTS Real Time Trader automates this algorithm for you which allows you to compute MCPM's cost of equity capital for a number of stocks quickly.  Furthermore, it lets you easily incorporate your estimates into standard portfolio problems if you want to as this technique simultaneously provides a revised estimate of the expected return from a stock.

The Wal-Mart example is provided in the following section.

Application:  Estimating Cost of Equity Capital using the MCPM Approach

First, the forward break-even point is computed for holding the stock.  This is defined as the price (net of dividends) that the stock must attain to provide an equal return to the corporate bond rate at the time the corporate bond matures.  For the Wal-Mart example suppose that the current weighted average corporate bond rate has approximately a 5-year maturity and from the 10-K statements filed with the SEC this s is 4.9%.  Suppose further that the dividend yield is 1.93 obtained from any of the major finance sites on the web (e.g., MSN, Yahoo, and Google):



You can now enter these numbers into the FTS Real Time Client's MCPM support as follows:


MCPMDivYield = dividend yield for MCPM = 0.0193


MCPM Yield = corporate bond rate = 0.049


The other two key inputs are volatility and debt term (weighted average time to maturity) for Wal-Mart.  For the current example, we will leave these numbers at their default FTS support numbers.  


Tip: See Appendix 2 for how to submit all values from Excel at once.


The two numbers being changed above are entered via the Parameter support as illustrated below:





With the check box "Use these values in my analytical support" on then the MCPM support appears as follows for WMT:




Observe that re-estimating WMT cost of equity capital using the MCPM approach increases this to 0.1127 if we assume that the current volatility for WMT is 35.21% annualized.  

Verifying the MCPM Cost of Equity Capital Number for Wal-Mart (0.1127)

Observe that the Put Value is 13.5171 for Wal-Mart in the MCPM support.  This is the cost of insuring the Wal-Mart stock so that it provides at least a dividend adjusted return of 4.9% which is the same as the corporate debt.

How is this put price number arrived at?

Answer:  This is computed from a regular Black Scholes computation assuming the following inputs:

1. Forward break even point for the stock (see step 1 of the algorithm in the appendix).  This is $56.54811 = $48.85*(1+(0.049-0.0193))^5
2. Volatility = 0.3521 annualized (i.e., 35.21%)
3. Time to maturity 5-years
4. Financial cost of carry for the option calculation = 4.9% (MCPM Yield).  
Aside:  Unlike a normal Black-Scholes option pricing problem 4.9% is not the risk free rate, but in this exercise we compute the cost of insuring the downside of the stock returns assuming the financial cost of carry is the corporate bond rate (i.e., the debt-holders required rate of return).    
5.  The dividend yield is 0.0193.

You can verify separately the put value (13.5171) computed by the FTS Real Time Trader using the FTS option calculator (accessible from the System Manager) as follows:



Step 2:  Computing the Excess Equity Return (see appendix part 4)





From the above you can verify that the excess equity return = 0.063737
Finally, the cost of equity capital for MCPM = 0.049+0.063737 = 0.112737

That is, from this approach the cost of equity capital and thus the expected return from investing in Wal-Mart currently (February 2009) is much higher than our previous estimate from CAPM.

Clearly, however an important number to get correct is the current volatility for Wal-Mart.

Question:  Is our volatility estimate for Wal-Mart of 0.3521 reasonable?

To answer this we will check the current implied volatility for a longer maturity Wal-Mart put option.  For example, consider the 2011 January put with strike equal to $55.  What is the implied volatility of this option?

Again this can be answered using the FTs Option Calculator:
Referring to the web (e.g., options trading on WMT, Yahoo):




You can compute the implied volatility for this option by entering the following from the option's contract, the current US yield curve (2-year rate) and current other market information:




Here the implied volatility is 36.78% (make sure you check the checkbox Implied Volatility as displayed above) which is very close to the number actually used in the MCPM calculation above.  So this appears to be a reasonable volatility estimate for Wal-Mart.

Answer To Original Question:  From the above analysis the estimate of the cost of equity capital for Wal-Mart provided from CAPM appears to be too low.  In this exercise if this is recomputed starting from the assumption that the cost of equity capital should be at least as large as the bond holder's required rate of return from Wal-Mart.  Starting from this premise the estimate is revised upwards significantly to 11.3% for Wal-Mart.  Furthermore, it is likely that many CAPM estimates would be revised upwards currently if a MCPM method is applied to the DJIA stocks.  You are encouraged to test this out because this is not an unreasonable conjecture in this current recessionary economy.

Required:  Complete the following steps

Step 1:  Select a high beta, middle beta and low beta stock from among the DJIA stocks and download the latest 10-K filings with the SEC.  If you have previously completed the CAPM cost of capital project then you should select the same three stocks.  You can download this from the web and for example the link for WMT is:

<http://moneycentral.msn.com/investor/sec/filing.asp?Symbol=WMT>


Just substitute the ticker for the companies that you are looking at.  In the footnotes to the financial statements you will find current interest information regarding their corporate debt.
An alternative useful site is:


<http://screen.yahoo.com/bonds.html>


This provides a great corporate bond screener that again provides current YTM information for corporate debt.


Step 2:  Go to Google, MSN or Yahoo's financial sites and record the current dividend yield information for the stocks you have selected.  If the stock does not pay a dividend then the dividend yield is zero.


Step 3:  Enter your estimates into the FTS Real Time Client to update the Parameters for the MCPM analytical support.  How you do this is described in the first part of the Wal-Mart example above.  If the time to maturity for debt is different from 5-years you should also change this number.


Step 4:  By using your parameters check the MCPM analytical support for the three companies you have selected.  You should record the revised estimate of the "Cost of Capital" as well as the "Put Value"


Step 5:  For one of your stocks repeat the steps described in the above section titled: "Verifying the MCPM Cost of Equity Capital Number for Wal-Mart (0.1127)"


Note:  To complete step 5 you will need to use the FTS Option Calculator referred to in the Wal-Mart example above.  You can access this calculator from the FTS System Manager drop down as displayed below:






Once you launch the Calculator you can enter the numbers directly as described in this handout for the Wal-Mart example.  Be sure to set the settings to Put Option and European for the MCPM option verification.  In addition, you will use the corporate debt rate for the stock you are working with as the "Interest Rate" for this exercise.


Step 6:  Compare your estimated cost of capital using MCPM with your estimates from the CAPM project for the same three stocks.  Alternatively, if you have not completed this earlier project then you can use the default cost of capital estimates provided in the FTS Dow School Case (see analytical support for "Stocks Index Model").  In this support the column header for the stocks is "Expected Return."   However, recall that in CAPM the expected return equals the cost of equity capital.  
Finally, discuss briefly which estimate of cost of equity capital you prefer along with support reasons as to why.

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Appendix 1:  Algorithm for Calculating MCPM

The objective of this measure is to estimate the risk premium that investors value in the market which in turn would reflect what the investor's required rate of return.  Consider corporate debt.  By comparing the price of the corporate debt to the price of the equivalent Treasury debt it is possible to immediately infer the default risk premium from the relative values.  MCPM extends this idea to equity by using option pricing combined with financial engineering principles in a four stage approach.  

1.  Calculate the Forward Break-Even Price of the Stock

This is defined as the minimal price an investor requires to be compensated for holding a stock as opposed to a bond.  Operationally, the return on equity equals:



Calculate the minimal capital gains which MCPM defines as follows.  From dividend policy the minimal capital gain rate is as follows:



And the forward break-even price is computed as follows:



Where P0 equals the spot stock price and t = the time horizon in years.

2.  Estimate the Stock's Return Volatility for the Given Time Horizon

This can be estimated using implied volatility from an at-the-money option price (if available) or past price data.  The implied volatility is preferred as it provides an ex ante estimate for volatility.

Where P0 equals the spot stock price and t = the time horizon in years.

3.  Calculate the Cost of Downside Insurance

By combining the stock with a put option you can insure against downside losses.  MCPM computes the cost of the downside insurance by calculating the value of a put option with the life equal to the time horizon and strike equal to the forward break-even price.  

Note:  In this step you apply the option calculator to compute the downside insurance cost from the predicted price of the put option.  The inputs into this calculation are:  The spot stock price = current market price of the stock, the strike price =  forward break-even price (step 1 above), time to maturity = investment horizon, volatility = estimated volatility for the underlying process (step 2), financial cost of carry (i.e., risk free rate in a traditional option pricing problem) = the MCPM rate for the time to maturity,  and the dividend yield.  

4. Derive the annualized excess equity return

This step re-expresses the dollar cost of the insurance calculated in step 3 as an annualized rate.  This rate is the Excess Equity Return that will be added to the company's bond rate to provide the volatility based estimate of the cost of equity capital.  The step is expressed as follows:



The intuition behind the above formula is as follows.

The Option Price/Stock Price is proportion of the spot stock price that an investor would be willing to pay to buy out of the downside risk of earning a lower rate than the bond.  The Excess Equity Return is merely the re-expression of this proportion as an ordinary annuity using the standard annuity formula and solving for "C" when the PV of the annuity equals the Option Price/Stock Price.



Where solving for  C = Excess Equity Return in the MCPM step 4.

5. The last step then combines the corporate debt rate with excess equity premium to provide the  MCPM estimate of the cost of equity capital.


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Appendix 2:  Entering all Parameter changes at once to populate analytical support with your own estimates

For control and convenience it is easiest to keep all personal parameter overrides for the Parameter support in Excel.  This is because you can then copy and paste from Excel to immediately update all your parameters without requiring any typing.

Step 1:  Format is as follows: (adjacent columns) and enter the values of your parameters or link to other cells that may be computing/receiving personal support values in Excel

Column 1:  Security Name
Column 2:  Field Name
Column 3:  Value

Major Tip:  It is most important to use precisely the same security name and field name as is used by the FTS Real Time Trader.  As a result, make use of the Copy Security Names and Copy Field Names in the Edit menu item and first paste them into the Excel spreadsheet that you are working with.  This will ensure that all names are identical.

Step 2:  Once you have a contiguous block of Security Names, Field Names and Values then mark and copy from Excel to the windows clipboard, give focus to the Parameters window in FTS Real Time Client and select menu item Edit, Paste and Submit Values 

Now your personal parameters are immediately used.