The dividend capitalization model, also known as the dividend growth model, is used to find the cost of equity.  To understand why the dividend capitalization model makes sense and is useful you must understand what influences the price of a stock.  And you must believe that the most important factor that influences the price of a stock is the future dividends that it’ll pay.

The calculation for the dividend capitalization model is as follows:

Cost of Equity = (Dividends per Share (for next year)/Current Market Value of Stock) + Growth Rate of Dividends

Dividends per share are reported in the company’s financial statements, and future ones are always disclosed in news releases.  The current market value of the stock can easily be obtained from places such as google.com/finance or finance.yahoo.com.  However, the growth rate of the dividends is an assumption estimation that you must make when valuing the company.  You can look up in the company’s annual reports the dividends that have been paid year by year by the company up to this point and figure out the growth rate.  This is a good strategy, but keep in mind that past results are not always implications of future results.  Another method would be to look at what the company’s management is prediciting for future dividend payment; remember though that management is often optimistic in their forecasts.  There is no perfect method, that’s why telling the future isn’t easy, even if Miss Cleo claims on her commercials that it is.

The dividend capitalization model is not the only model used for calcuating cost of equity.  The capital asset pricing model, CAPM, is also widely used and often more popular.  Both, however, can be used and often are for discounted cash flow anyalsis, DCF.

The capital asset pricing model ( CAPM ) is used to determine the required rate of return on a security, it is the cost of equity.  When investing in a security an investor expects a certain return.  This expectation comes from the opportunity cost of putting their money in a certain security as opposed to what it could be earning in a different security.  It also comes from the risk is associated with putting their money in that security.  The CAPM seeks to value that opportunity cost and the risk of the specific security to determine what the required rate of return the investor will have to have to invest their money in this security.  Before we go on, let’s exam the model.

The Capital Asset Pricing Model ( CAPM ) is calculated as follows:

r_a = r_f +β_a( r_m - r_f )

Where:

r_a = required rate of return of the security

r_f = risk-free rate

β_a = beta of the security

r_m = return of the market

Now that we have the formula, let’s pick it apart some more and see why it is put together the way it is as well as find where we can obtain the values for these variables.  The risk-free rate, r_f, is in the equation to signify the opportunity cost of what the money that is invested could be earning.  A United States government bond is usually used to represent the risk-free rate.  A US bond only carries risk if the US government no longer exists, because even if the US government does not have the funds they can print more funds or raise taxes.  There is considered to be a certain premium that needs to be paid for being in the market opposed to a risk-free asset like a US bond.  If there was no greater reward for being in the market, then why would you take the greater risk?  That premium is the return of the market, r_m, subtracted by the risk-free rate, r_f, and is referred to as the equity market premium.  The equity market premium needs to be multiplied by the specific security’s beta, β_a,the statisitcal measure of the security’s volatility in comparison to the market, to see what the premium needs to be for this security.  In other words, the equity market premium multiplied against the security’s beta gives you the amount you need to be compensated in order to assume that amount of risk, a risk premium.  Add that premium to the opportunity you are giving up to invest in, the risk-free rate, and you have your required rate of return on that specific security, r_a.

The capital asset pricing model ( CAPM ), however, is not perfect.  Beta is measuring past prices, and the past is not always an indication of the future.  Beta also does not ecompass all of the valuable information of a security.  There are also different ways to calculate a security’s beta, which can lead to varying required rate of returns of a security .  Smaller capitalization stocks also tended to outperform CAPM evaluations, most likely because they are not accuratley captured in the return of the market, r_m.  However, even for its shortcomings CAPM is very useful to calculate the cost of equity and is widely accepted.  Its creators even received a Nobel Prize for it in the sixties, no alternate method has had any such recognition or acceptance.  But, there is an alternative method for calculating the cost of equity, the dividend capitalization model.  CAPM and the dividend capitalization model are both used for Discounted Cash Flow analysis (DCF).

The weighted average cost of capital, WACC, is a calculation used to determine what the firm is paying in interest on their capital, what is their cost of financing.  Their capital, financing, includes all of their equity, i.e. stock, and debt.  Each piece of capital is weighted against its discount proportionally.  For instance, the interest rate on their debt would be multiplied against the amount of debt that they have (as well as their tax rate) to find the weighted average of the debt side of their capital.

The equation for calculating WACC is as follows:

WACC = (E/V)Re + (D/V)Rd(1-Tc)

Where:

E = market value of the firm’s equity

V = the total capital of the firm, equity + debt (E+D)

Re = the cost of equity

D = market value of the firm’s debt

Rd = the cost of debt

Tc = the corporate tax rate

Finding most of the values for these variables is fairly simple, but a few of them can be a little tricky.  E, the market value of the firm’s equity, will be found on the company’s financial statements, add up all the equity accounts.  (Remember these can usually be found on the company’s website under at term similar to “investor relations” or at google.com/finance or finance.yahoo.com.) D, the market value of the firm’s debt, will also be found on the company’s financial statements, add up their liabilities.  Add E and D together and you will get V, which is the value of the firm’s capital, however, not yet appropriately weighted).  E/V is the percentage of the firm’s financing that is done through equity, and E/D is the percentage of the firm’s financing that is done through debt.  Re, the cost of equity, is more difficult to calculate and requires another model.  The capital asset pricing model ( CAPM ) is the most recognized and popular model for calculating the cost of equity and uses beta, risk free rates, and expected market return to calculate.  Another method is the dividend calculation model which uses current dividends being paid by the company’s stock, the current market value of the stock, and the growth rate of those dividend payments.  Rd, the cost of the firm’s debt, is easier to find as it is the current rate they are paying on their debt and should be disclosed.  A company is able to benefit on their taxes from the interest that they pay so it is important to also multiply their debt by 1 minus their tax rate to get a more appropriate valuation, (1-Tc).

Now that you know how to calculate the WACC, it’s valuable to know how to apply it and how to value what you are applying.  Because assumptions have to be made when calculating Re, the cost of equity, (assumptions either about how to calculate the beta or what the dividend growth rate will be) the number one person gets for their calculation of WACC can vary from another’s.  However, WACC still gives you a good idea of at what value cash flows should be discounted at to get their present value.  Another way to think of the WACC is the required return that a company has, as this is what they need generate in order to cover their interest on their financing activites.  The WACC is often used in Discounted Cash Flow anaylsis (DCF) to find the appropriate value to discount the cash flows at for Net Present Value (NPV).

For financial purposes a moving average is applied to a time series.  The moving average is used to smooth out the noise of every day market volatility and fluctuations so that trends can be recognized.  These trends can show possible momentum in a security’s price as well as possible points of support and resistance.

Now there are two ways to do this, calculate it yourself, or have someone else (like a computer) do them for you.  I aim to prove to you that calculating them yourself is time consuming and complicated, and that using a computer program that is programmed to do the many, many math equations in a matter of seconds is the way to go.  finance.yahoo.com offers a great charting program that will calculate the moving average over any time period for any stock in seconds.  However, it is important to understand what the program is doing so you can interpret what it is telling you completley and know how to use the information to its fullest advantage.

As a simple example, take the closing stock price of your favorite stock for the past six days.  My favorite stock for this example is an imaginary stock called ZMRP.  Below are the closing prices for ZMRP over the past six days:

Day 1: $10 Day 2: $14 Day 3: $12 Day 4: $17 Day 5: $15 Day 6: $18

If you simply took the average of the six days you would have the average price of the stock, $14.3, but not have a good idea of which way the price of the stock is moving; unless, of course, you had additional sets of data.  However, if you took the 3-Day Moving Average of stock ZMRP you would have an idea of which way the stock price is moving as well as a smoothed curve that shows deeper trends.  To plot the points first take the first three prices, in my example $10, $14, $12, and divide by the period of your moving average, in this example three.  You should note that a moving average does not have to be day, it could be any period you desire, seconds, minutes, hours, weeks, months, years, etc., however, when looking at stock prices it is usually best to look at days as they will give you the best gauge of a trend.  So, going back to the math our first point is going to be $12 ($10+$14+$12/3days).  For the next point you simply move over another day, this time giving us the prices of $14, $12, and $17.  Divide by the period, usually denoted by the variable n, and you have the second point for our 3-Day Moving Average, $14.33 ($14+$12+$17/3days).  The next point’s prices are $12, $17, and $15, giving an average of $14.67.  And the final point for our series has the prices of $17, $15, and $18, giving an average of $16.67.  When you plot this you should see something like below:

As you can see the moving average heads in the same direction as the stock price, but takes out some of the dramatic shifts that the price itself shows.  This fact would be more pronounced and useful if the value of the period, n, in our case 3, were larger.  You may have already figured out that the method above is not the method that you would want to use to calculate a moving average.  With much higher amount of periods, such as a 50-Day Moving Average, and for years of data to calculate the average like the way above would take way too much time and would make the information you receive from your analysis possibly more valuable in a measure of your time than the return on a spectacular trade!

To calculate the moving average quicker with larger amounts of numbers you will need to be a little fancier (or use a program that does the fancy dance for you).  The equation for calculating the n-period moving average for continuous functions or extremely large data sets is:

Where the variables are defined as:

=moving average for continuous functions

n=the amount of the length of the period; if a 50-Day Moving Average then n would equal 50

x=the data point you begin calculating the moving average for

f(b)=the function that the original data moves upon.  Note that the “b” is a dummy variable, meaning it could be anything it just needs to be a place holder.

In as easy to understand speech as possible the equation says, “The moving average for continuous functions equals one over the n-unit of the moving average multiplied against the integral of the function that the data creates over the data point you are calculating at and the data point you are calculating at subtracted by the n-unit of the moving average.”  Did that make sense??  Haha, maybe the equation was easier to understand than that sentence.  However, even if you do have a complete understanding of that equation and how to calculate integrals there is another problem.  Finding the f(b) is not the easiest thing to do.  You must find the function that the original data follows, and with highly fluctuating data such as stock prices this can be a difficult task.  A goodness of fit test, a stastical model that aims to test how well a model fits a set of observations, can be used to give an estimation of the function for the data as well as a spline function, a function made up of “piecewise” polynomials.  Obviously a whole new can of mathematical worms has been opened up!  But now that the worms are before you, you can see what is going on behind the scenes when the computer program tosses that fishing line into the water and pulls you out a nice bass of a moving average.  Sorry, maybe I got too carried away with that metaphor, haha, but I hope you see my point and have a better understanding of what a moving average represents.

Return on Investment (ROI) is a valuable ratio to look at when comparing two different investment’s returns.

Here is an example:

If you invested in two seperate business ventures, one produces footballs and the other produces basketballs, and the football business had a return of $100,000 and the basketball business had a return of $200,000, which one would you say is better?  Your answer should be, “I don’t know yet, what is the ROI for each business, how much was invested in each venture?”  If you knew that $500,000 was invested in the football business and $2,000,000 was invested in the basketball business then you would be able to give your answer, you would be able to compute the ROI.

The equation for computing return on investment (ROI) is:

ROI = Operating income/Average operating assets

In our example of footballs and basketballs the ROI for the football business is .2, or 20%, (operating income of $100,000/average operating assets of $500,00) and the ROI for the basketball business is .1, or 10%, operating income of $200,000/average operating assets of $2,000,000).  Obviously the football production business is better than basketballs, its ROI is 20% compared to 10%; double!  Think if you used that $2,000,000 that you invested in the basketball venture to invest in more football production ventures at $500,000 per venture with the 20% ROI on footballs you would have had a total return for the period of $500,000 instead of $300,000 an ROI of 25% (operating income of $500,000/average operating assets of $2,500,000) instead of your original ROI of 12% (operating income of $300,000/average operating assets of $2,500,000) when you were investing in basketballs and footballs.  Good thing you understand ROI so you know to move your money out of basketballs and into footballs!

ROI does not always come out of cash, even though in our example it did, an investment can of course include other assets such as securities, inventory, land etc.

Operating income is explained in detail in this article here and average operating assets are explained in detail in this article here.

It should be noted that ROI can also be calculated by multiplying margin against turnover.  However, because margin and turnover both include sales in their calculation the equation can be simpliflied to operating income/average operating assets.