Dividend Discount Model

Present Value Models

Dividend Discount Model


1.  If a company pays regular dividends

The dividend discount model (DDM) values a share of common stock as the present value of its expected future cash flows (dividends).

When an investor sells a share of common stock, the value that the purchaser will pay equals the present value of the future stream of cash flows (i.e. the remaining dividend stream).

Therefore, the value of the stock at any point in time is still determined by its expected future dividends.

When this value is discounted to the present, we are back at the original dividend discount model.



2.  If a company pays no dividends currently

If a company pays no dividends currently, it does not mean that its stock will be worthless.

There is an expectation that after a certain period of time the firm will start making dividend payments.

Currently, the company is reinvesting all its earnings in its business with the expectation that its earnings and dividends will be larger and will grow faster in the future.



3.  If the company is making losses

If the company does not make positive earnings going forward, there will still be an expectation of a liquidating dividend.  

The amount of this dividend will be discounted at the required rate of return to compute the stock's current price.




Additional notes:

The required rate of return on equity is usually estimated using the CAPM.

Another approach for calculating the required return on equity simply adds a risk premium to the before-tax cost of debt of the company.

Introduction to Present Value

Compound Interest: Present Value/Future Value

Understanding Valuation Principles

The basics of valuation are:

1.  The Time Value of Money:  This states that $1 received today has a different value from $1 received a year ago or $1 received a year from now.

2.  Present Value:  This is the concept that money spent tomorrow must be worth less today because of the time value of money.  It is calculated by using the formula

PV = CF  /  (1+r)^n

where

PV = present value
CF = cash flow for the period
r = discount rate
n = period


Methods of valuation are:

1. Replacement method
This method tends to be the simplest to explain but the most time-consuming to produce.

This method would measure all the costs involved in creating an exact duplicate company.  Those costs might include:
Land
Buildings
Machinery
Equipment
Working capital.

2.  Capitalization of Earnings
This is one of the more common and relatively straightforward methods of valuation.This method uses a risk rate to assess the value needed to generate the same amount of income as the business being valued.

A company is expected to generate exactly $10,000 each year in income indefinitely.  Assuming that the buyer can earn a guaranteed rate of interest of 5% elsewhere, an investment of $200,000 would earn $10,000 in interest each year.  Therefore, the company has a value of $200,000.

Unfortunately, such risk-free situations rarely exist.  Thus, with increased risk, a higher capitalization rate would have to be assessed to estimate fair value.  These rates vary, and some might argue that they are entirely arbitrary.  The result will prove highly sensitive to this rate.  As a result, many believe the capitalization of earnings method is problematic.


3.  Discounted Cash Flow Valuation
This is one of the most commonly used methods.

The entire process can be condensed into four steps:
1.  Calculate projections for future cash flows.
2.  Calculate the cost of capital, or the discount rate.
3.  Calculate the present value for each year's cash flow.
4.  Finally, take total of those present value cash flows.

Completing these four steps provides a very close estimate of the valuation for the company.  The sum of these discounted cash flows is the company's valuation ... well, almost.

However, the company doesn't simply dissolves at the end of the DCF study period.  The company continues to operate long after those projections end, meaning there is residual value that has to be considered.

To account for what happens after the projections end, the concept of terminal value is employed.  Terminal value is a concept used to calculate the value of an asset that continues after the projections end, or into perpetuity.

The method of choice involves using the present value of a perpetuity.  A perpetuity is an instrument that makes payments year after year without end.  You can use the formula to calculate a perpetuity that assumes growth or a simpler formula to calculate one without growth.  The two formulas are given here:

Perpetuity without growth = CF / r
Perpetuity with growth = CF / (r - g)

where

CF = cash flow
r = discount rate
g = growth rate


For example:

• Given the 5 year cash flow projections.  
• Find the present value of these 5 year cash flows.
• The next step is to get a year 6 cash flow estimate.  Having this cash flow estimate, assume it stays constant each year after that or it grows at a low rate.  
• Then calculate the present value of that perpetuity.  The present value of this perpetuity is treated as the value at the beginning of year 6.  
• Then calculate the present value of that perpetuity in today's dollars by discounting it back 5 years by using the present value formula.  
• Add the present value of perpetuity to the total discounted cash flows for the first five years. 
• That results in the company valuation and at this point, the analysis of this company has concluded.  

A simple 10-Year Valuation Model
A step by step DCF model for calculating the equity value of a company (Source: Morningstar, Inc.)


Step 1:  Forecast free cash flow (FCF) for the next 10 years.

Step 2:  Discount these FCFs to reflect the present value.

Step 3:  Calculate the perpetuity value, using the FCF of the 10th year, and discount it to the present.

• Perpetuity Value = FCF(10th Year)  x  (1 + g)  /  (R - g)
• Discounted Perpetuity Value = Perpetuity Value / (1 + R) ^ 10

Step 4:  Calculate total equity value by adding the discounted perpetuity value to the sum of the 10 discounted cash flows (calculated in step 2)

• Total Equity Value = Discounted Perpetuity Value + 10 Discounted Cash Flows

Step 5:  Calculate per share value by dividing total equity value by shares outstanding:

• Per Share Value = Total Equity Value  / Shares Outstanding

4.  Comparable Multiple Valuation

The final method of valuation is the most commonly used and probably the easiest to use as well.

It is based on benchmarking one company against an industry-average multiple such as the P/E (price-to-earning) ratio.  This could also be applied to other variations on this multiple, such as P/EBIT or P/EBITDA.

Generally speaking, if a company's P/E ratio is greater than the industry average, it is fair to say that the company is overvalued.  If the company's P/E ratio is less than the industry average, it is fair to say that the company is undervalued.  However, be caution, no rules are without exception.    Many companies are seemingly undervalued, but for good reason.  For example, a company might be a party in a pending lawsuit, and the market has undervalued the company because it is unclear what the ruling will be.

The comparable multiple method of valuation forms at least a starting point for making some basic assumptions about a company's value.  

The Time Value of Money

"A bird in hand (today) is worth two in the bush (tomorrow)."

Everyone would rather have a dollar in his or her pocket today than to receive a dollar far into the future.  Today's dollar is worth more - that it has more value - than a dollar received tomorrow.

The three main reasons for this difference in value are:

1.  Inflation.
Inflation does reduce purchasing power (value) over time.  With a 5% per year inflation, a dollar received a year from today will only buy 95c worth of goods.

2.  Risk
There is always the chance that the promise of a dollar in the future will not be met and you will be out of luck.  The risk could be low with a CD at an FDIC insured bank; or the risk could be high if it is your brother-in-law who is promising to repay a personal loan.

3.  Opportunity Cost.
If you loan your dollar to someone else, you have lost the opportunity to use it yourself.  That opportunity has a value to you today that makes today's dollar worth more than tomorrow's.

These three concepts - inflation, risk, and opportunity cost - are the drivers of present value (PV) and future value (FV) calculations used in capital budgeting and investing.

Present value (PV) calculations are used in business to compare cash flows (cash spent and received) at different times in the future.  Converting cash flows into present values puts these different investments and returns onto a common basis and makes capital budgeting analysis more meaningful and useful in decision-making.

Nominal dollars are just the actual amount spent in dollars taken out of your wallet.  Real dollars are adjusted for inflation.  When you take out inflation (i.e. convert from 'nominal dollars' into 'real dollars') the price difference becomes much more comparable and easy to explain.

Capital Budgeting

In capital budgeting, different projects require different investment and will have different returns over time.  In order to compare projects "apples to apples" and "oranges to oranges" on a financial basis, we will need to convert their cash flows into a common and comparable form.  That common form is present value.

Simply put, a little bit of cash that is invested today followed by lots of cash returned in the near future would be a REALLY GOOD financial investment.  

However, lots of cash invested today followed by a little bit of cash returned in a long time would be a REALLY  BAD investment.

Capital budgeting analysis is as simple as that.