# Valuations - Discounted cash flow models

### ABSTRACT

The paper is a study of various Discounted Cash Flow Valuation Models to value both equity and organizations. The difference between cash flow to equity and to an organization is studied.

The basic Dividend Discount Model is studied with its various variants like Gordon Growth Model, two stage and three stage dividend discount models. In the last two the values of extraordinary growth is separated from the value of steady state growth.

There is a discussion of why free cash flows to equities different from dividends for a lot of organizations. The two and three stage FCFE models are described. An alternative valuing model FCFF has been described which discounts cash flows to the firm at the weighted average cost of capital.

The advantages and limitations of each model is mentioned along with conditions of which model has to be applied under what conditions.

### VALUATIONS

Determining the Present Value of the future cash flows of a company is the aim of any valuation technique. Generally investors buy stocks for as they expect that the future cash flows of the company will be high. Hence how much cash flow an asset is going to generate has to be calculated in order to determine the fair price to be paid for the particular stock. Price is that numerical figure at a moment when a transaction is completed when the market is in balance. It represents a snapshot of a dynamic market. Price is generally the function of demand and supply.

Valuations are used by Fundamental Analysts, Franchise Buyers, Chartists, Information Traders, Market Timers and Efficient Marketers in different ways to suit their respective objectives. Valuations are also required in Acquisition Analysis and Corporate Finance.

Valuations take into account future cash flows. Future cash flows can only be predicted or guessed with some amount of certainty. Hence even small errors like non payment of rent, etc could lead to an error in valuations. The more certain one is about the future cash flow, the valuations are correct to that degree of certainty. Therefore valuations a definitely uncertain.

Valuations can be done by various methods and no one method is the best. Different methods have to be used under different circumstances. Valuation methods, generally, can be divided into three approaches - Discounted Cash Flow method, Relative Valuation method and Contingent Claim Valuation method. All the above if used for the same valuation an give very different end results.

### DISCOUNTED CASH FLOW VALUATIONS

The sources of uncertainties in valuations are rational and can easily be identified. For the purpose of our study for this paper, we will concentrate on the Discounted Cash Flow valuation method. This method is based on the thought that "The actual value of any asset is its present value of the expected future cash flows that it will generate." Cash Flows will be different for every asset. To transform the value of future cash flows into present value, we use a Discount Rate. For some, this Discount Rate is the function of riskiness of estimated cash flows that is the rates will be higher for riskier assets and will be lower for safer assets.

where DPV - Value

n - life of the asset

FV - Cash Flow in time t

i - discount rate which reflects riskiness of the estimated cash flows

There is a difference between Equity Valuation and Company Valuation. Either on the equity stake can be valued in an organization or the entire organization can be valued. In both the methods, the future cash flows of the firm are discounted, the cash flows and discount rates taken into account are different. For an Equity Valuation, the expected cash flow to equity is discounted at the Cost of Equity while to value a company, the expected cash flow to the company is discounted at the Weighted Average Cost of Capital (WACC).

Discounted Cash Flow Method is firms that have positive cash flows which can be estimated with certain amount of reliability for the future. The method cannot be used for firms in trouble, cyclical firms, firms that have unutilized assets, firms with patents, firms which are restructuring, the ones involved in acquisitions, private firms.

The most commonly used methods by discounted cash flow in order to value companies are -

- Free Cash Flow which is discounted at the Weighted Average Cost of Capital
- Cash Flow to equity discounted at the Rate of Return on Equity that is required
- Capital Cash Flow which is discounted at the Weighted Average Cost of Capital before tax
- Adjusted Present Value
- Risk Adjusted Free Cash Flow to a firm discounted at the Rate of Return required to the Assets
- Risk Adjusted Equity Cash Flow to a firm discounted at the Rate of Return required to the Assets
- Economic Profit which is discounted at Rate of required Return to Equity
- Economic Value Added which is discounted at Weighted Average Cost of Capital
- Risk Free Rate Adjusted Free Cash Flows which are discounted at the Risk Free rate of Return
- Risk Free Rate Adjusted Equity Cash Flows which are discounted at the Rate of Return required to Assets

All the above methods giving the same end results is very logical as all the methods only differ in the cash flows taken at the start of the method but has the same of same reality and hypothesis.

### DIVIDEND DISCOUNT MODELS

### GORDON MODEL

A very convenient and widely used Dividend Discount model includes The Gordon Growth Model. It can only be used for firms that have a stable growth rate.

Po - Value of stock

D1 - Expected dividends during next year

k - Required rate of return for equity investors

g - Growth rate in dividends forever

This Model assumes that the growth rate in dividends is going to last till infinity and hence the same can to assumed for firms other measures of performance. A stable growth rate which has to be assumed has to be a very reasonable value as in the long term, the organizations growth rate cannot be more than that at which the economy operates.

The above method is highly sensitive to the input of growth rate. As the growth rate will converge on discount rate, the value goes to infinity. It is best used for organizations whose growth rates can be compared to the nominal growth rate of the economy.

### TWO STAGE DIVIDEND DISCOUNT MODEL

Another method is called the Two Stage Dividend Discount Model. It takes into account two stages of growth - the first one which has a high growth rate and the next one which has a stable growth rate and is expected to be that way for a long time.

Value of stock at present = (from 1 to n) ? (Expected dividends per share in year t / ((1 + Required rate of return)^t)) + Price at the end of year n / ((1 + Required rate of return)^n)

where Price at the end of year n = Expected dividends in the year n + 1 / (Required rate of return - Growth rate forever after year n)

The above Model faces a problem in specifying the length of the high growth period, as the growth is expected to decline and come to stable after this period, increasing this time period will increase the value. In reality, the shift from high growth rate to a stable growth rate happens gradually over time but this model assumes that it happens suddenly which may only be the practical case for few.

However the method can be used for firms which are expected to maintain the high growth rate for some time after which the reasons for high growth rate disappear.

### VALUE OF GROWTH

The value of Growth is important to estimate which can be done using the two stage dividend model as high growth companies tend to have a very high price/earnings and price/book value ratios. Due to this investors end up paying higher premiums to own the stock. There are several factors which determine the value of growth.

It depends on growth rates when the growth period is extraordinary. The higher is the growth rate during this period, higher will be the value of growth.

It depends on How long will the extraordinary growth period last. The longer is this period, hence greater will be the value of growth.

As and when projects start becoming more and more profitable, the growth rate increases and so does the resulting value from extraordinary growth.

If the risk of the stock increases the corresponding discount rate will also increase thereby decreasing the present value to extraordinary growth.

### H MODEL

There is The H Model which is used for valuing growth. It is a two stage growth model where the initial high growth rate decreases linearly with time to reach the steady state growth rate. If the growth rate suddenly drops from a high value to a low one, then the above value proves to be wrong. Also assuming that payout ratio is constant is also incorrect here as it usually increases and is not the same or both the phases.

### THREE STAGE DIVIDEND DISCOUNT MODEL

There is also a Three Stage Dividend Discount Model which combines both the Two Stage model and the H model. It requires a very large number of inputs but also eliminates a lot of drawbacks from the above models. It should be used for organizations that have an extraordinary present growth rate, will maintain so for sometime then with a gradual decline will reach the steady state stable growth rate period.

The Dividend Discount model is simple to use but is not really used for valuations due to its drawbacks and has limited applications in high dividend paying equities. The model can also be used for firms which are high growth and are not paying dividends with the consideration that the dividend/payout ratio is adjusted to show the changes in the expected growth rate. This model creates a tax disadvantage in case where dividends are taxed at a greater rate than capital gains. The model does show very impressive results over long periods of time. The model generally outperforms the markets in five year time frames. It is also biased towards finding low price/earnings with high dividends and high price/earnings with low dividends.

### FREE CASH FLOW TO EQUITY (FCFE) MODELS

FCFE = Net Income + Depreciation - Capital Spending - ? Working Capital - Principal repayments + New debt issues

FCFE = Net Income + (1 - ?) (Capital expenditure - Depreciation) + (1 - ?) ? Working capital

Dividends are different from FCFE. FCFE measures how much an organization can afford to pay as dividends. Dividends paid from FCFE are different for different organizations for the below four reasons

Organizations have a Desire for Stability where in they do not want to change the dividends as variations in dividends is considered to be a lot lower than variations in earnings and cash flows.

Organizations may not pay dividends at all to meets its Future Investment Needs. It might require a lot of capital expenditure in the future and raising capital again is an expensive process.

Tax Factors come into play where if Dividends are taxed higher than Capital gains then firms might again not pay out dividends.

Organizations also use dividends as a sign of saying, with the increase in dividends implying is a positive sign while decrease in dividends a negative one. It is nothing more than a Dividend Prerogative.

### CONSTANT GROWTH FCFE MODEL

The Constant Growth FCFE Model values organizations that are in a steady state ie have a stable growth rate.

Po - Value of stock today

FCFE1 - Expected FCFE over the next year

r - Cost of equity

gn - Growth rate in FCFE forever for the firm

The model is very similar the the Gordon Growth model and hence all the above advantages and limitations apply to this model as well.

### TWO STAGE FCFE MODEL

The above heading also contains a Two Stage FCFE Model and a Three Stage FCFE Model (E - Model). The two stage FCFE Model has the same concept as had been described above.

### THREE STAGE FCFE MODEL OR E MODEL

The E Model is used for organizations which are expected to initially grow with very high growth rates then come into a transition period where in the growth rate decline and then comes to a stable period where it is at steady state. Here assumptions about variables have to be consistent with the assumption of growth rates. As the organization moves from a high growth organization to a stable stead state one, the relationship between capital expenditure and depreciation is bound to change. Also as the growth patterns of the firm changes so does the Risk pattern consequently.

The Model is very similar to Three stage dividend discount model. It is appropriate to use it in organizations which currently have a very high growth rate.

### Comparison between FCFE Valuations and Dividend Discount Model Valuations

Same values can be obtained by using the above two only when either dividends and FCFE are equal or when FCFE is more than dividends, but the remaining cash is invested in projects which have Net Present Value as zero.

The above two also provide with a different estimate when FCFE is more than dividend but the difference between the two earns interest lower than the market rates or is invested in negative NPV projects. If an organization pays out small dividends as compared to what it can afford, the debt/equity ratios decrease hence making the organization underleveraged which will also decrease value. In another case if too much dividends are paid out then simply loss of wealth happens with there are capital constraints to good projects.

### FREE CASH FLOW TO FIRM MODELS (FCFF)

FCFF = FCFE + Interest expense (1 - tax rate) + Principal repayments - New debt issues + Preferred dividends

FCFF = EBIT (1 - tax rate) + Depreciation - Capital expenditure - ? Working Capital

### Difference in Growth of FCFE and FCFF

The main reason for the difference in the growth rates in FCFF and the growth rates in FCFE is leverage. Generally, due to leverage, growth increases in FCFE. It affects the growth rate in Earning Per Share. However, growth rates in Earnings Before Interest and Tax, growth rates in depreciation, growth rates in capital expenditure and growth rates in capital spending all remain identical.

### STABLE GROWTH FIRM MODEL

The above method includes Stable Growth Firm Model.

Value of firm = FCFF1/ (WACC - gn)

where FCFF1 - Expected FCFF over next year

WACC - Weighted Average Cost of Capital

gn - Growth rate in the FCFF

To use the above model, the growth rate used has to be relative and reasonable as compared to the nominal growth rate in the economy at that particular time. Also, depreciation and capital spending should have a relationship which support the assumption of stable growth. A stable firm, generally, cannot have depreciation significantly lower than capital expenditure as there in no high growth and hence there is no need for additional high capital expenditure.

The model is also highly sensitive to the expected growth rates that are used for calculations. It is also sensitive to assumptions about capital expenditure with respect to depreciation. The value of FCFF can be adjusted by adjusting the value of capital expenditure with respect to depreciation.

### TWO AND THREE STAGE FCFF MODEL

There are also a General Version of the FCFF Model which are also the Two and Three Stage versions of the FCFF Model

It can be used to value any firm where FCFF can be forecasted with available sufficient information.

Value of a Firm

where FCFFt - Free Cash Flow to firm in year t

The above model values organizations and not equity, however, the value of equity can be calculated by subtracting the market value of debt which is outstanding. The advantage of using FCFF over FCFE is that cash flows related to debts do not have to be accounted for separately. Where ever there is leverage which is expected to change largely with time, this turns out to be a significant saving. Also FCFF does not required any information regarding debt ratios or even interest rates to find out the Weighted Average Cost of Capital.

The model is best suited to use for by organizations that have a high leverage or the organizations that are in the process of transforming their leverage. Using FCFE has a drawback that it frequently turns out to be negative in cases with high leverage and cyclical organizations.

### CONCLUSION

After looking at a number of different models applicable to various situations, it is a fact that a lot of time and resources get wasted in trying to fit the data to a valuation model. We cannot call any one model as best. It depends upon the following factors

What are the level of earnings of an organization. Has it lost or gained money, the ones that have gained money are easier to value than those which have lost it.

The choice of the model also depends upon the level of current growth found in earnings. For firms with stable growth rates, the Gordon growth model, and stable FCFE and FCFF models should be used.

Examining the sources of growth is also important. High growth can be due to competitive advantage due to brand building or reducing production costs or patent advantages. There can be other competitive advantages the speed of whose loss depends upon the competences of the organizations management and the entry barriers for that particular industry.

Also, the ease of use decides the choice between cash flows to organization and cash flows to firms.

### REFERENCES

- Security Analysis for Investment and Corporate Finance, Valuation by Damodaran
- wikipedia.org
- http://pages.stern.nyu.edu/~adamodar/
- Price and worth - practice paper by Robert Peto, Nick French and Gillian Bowman
- Value Innovation Management and Discounted Cash Flow - Tony Carter and Demissew Diro Ejara, College of Business, University of New Haven, West Haven Connecticut, USA (Emerald Insight Research Paper)
- Valuing companies by cash flow : ten methods and nine theories - Pablo Fernandez, IESE Business School, University of Navarra, Madrid, Spain (Emerald Insight Research Paper)