QUESTION

Free Cash Flow (FCF) is the cash that is left over in the firm’s coffers from its net after-tax income after providing for all planned capital expenditure and working capital requirements. It measures the cash generated by a firm prior to servicing the debt-holders and paying any dividends to equity-holders. As per the FCF-based firm valuation model, the value of a firm can be estimated as the present value of all future expected FCFs. The formal model is as follows (see page 279 of textbook):

V0 = FCF1/(1 + rwacc) + FCF2/(1 + rwacc)2 + … + FCFn/(1 + rwacc)n + Vn/(1 + rwacc)n … (i)

Here V0 is the present value of the firm, FCFn is the FCF for the n-th year, Vn is the value of the firm in the n-th year and rwacc is the firm’s weighted average cost of capital. Assuming gFCF to be a constant growth rate of FCFs beyond the n-th year, Vn may be estimated using the following formula:

Vn = FCFn x (1 + gFCF)/(rwacc – gFCF) … (ii)

Substituting for Vn from equation (ii), one may choose to re-write equation (i) as follows:

V0 = FCF1/(1 + rwacc) + FCF2/(1 + rwacc)2 + … + FCFn/(1 + rwacc)n + [FCFn x (1 + gFCF)/(rwacc – gFCF)]/(1 + rwacc)n

= FCF1/(1 + rwacc) + FCF2/(1 + rwacc)2 + … + [FCFn /(1 + rwacc)n][1 + (1 + gFCF)/(rwacc – gFCF)] … (iii)

What you are required to do:

I. Derive the FCF-based valuation model as stated in equation (iii): Your methodology can be EITHER formal/mathematical OR descriptive/argumentative. If you are going for a formal/mathematical derivation you will need to clearly state the underlying assumptions of the model, clearly explain each of the terms involved and give a detailed, step-by-step algebraic exposition that mathematically justifies the exact form in which equation (iii) has been expressed.

On the other hand, if you choose to go for a descriptive/argumentative derivation, you will still need to clearly state the underlying assumptions of the model and clearly explain each of the terms involved. But instead of providing a step-by-step algebraic exposition, you will justify; using lucid arguments; why the firm valuation model essentially needs to be a sum of discounted cash flows. You are also required to supply a hypothetical numerical example using an Excel spreadsheetdemonstrating that the value of the firm in year n indeed ‘converges’ to FCFn x (1 + gFCF)/(rwacc – gFCF) if one assumes a constant rate of growth of the free cash flows beyond the n-th year. (50 marks)

II. Compare and contrast the FCF-based valuation with the dividend discount model: The FCF-based valuation model has been advanced as a better alternative to the dividend discount model of valuation. The former takes into account future expected streams of all free cash flows to the firm whereas the latter only takes into account future expected streams of dividends to equity holders. Clearly explain where the two models are similar and where they differ. Which one do most analysts seem to prefer? Is a FCF-based model necessarily always better than the dividend discount model? You are strongly encouraged to provide suitable numerical examples to make your point. (25 marks)

SOLUTION

1. Introduction

The value the firm is estimated using the  Free Cash flow model .The complete value of the firm can be can be estimated using the (FCFF) and the Free cash flow to equity (FCFE) and discounting these cash flows by the suitable rate of return. The paper derives the free cash flow model mathematically as well as analyses the strengths and the weaknesses of the model. The paper also compares and contrasts the model with respect dividend discount model.

2. Derivation of the Free Cash Flow Model

The free cash flow is the measure of the company’s true cash flow that is obtained after the payment to all parties including tax payments. It is the true measure of the company’s cash flow position. The most appreciated standards of valuation of any corporation is to estimate the present discounted value of free cash flow have been discussed below. The availability of free cash flow is a basis of the long term financial growth of the corporation. Based on the availability of the free cash flow the firm is able to undertake the long term capital budgeting decision. The capital outlay of the project required on a yearly basis can be determined through the availability of free cash flows to the firm.

(Evans, 1998)

2.1 Free cash flow to equity (FCFF)

To estimate the free cash flows available to the shareholders of the firm is calculated by firstly obtaining the net income of the corporation, and eventually adding the earnings back to the net income and then subtract any re investing opportunities available to the firm.

Therefore to estimate the availability of free cash flow to the firm the following calculations are to be undertaken.

1. Capital expenditures like acquisitions are to be subtracted from the free cash flow as they represent the out flow of cash from the business, whereas on the other hand the expenses such as depreciation and amortization are too added back as they represent the non-cash charges on the business. These expenses are referred to as net capital expenditures and are often the indicator of the growth function of the organization.  High growth firms usually have greater capital expenditures with respect to the earnings to the corporation and vice – versa.
2. To obtain the model we have to obtain the non-cash working capital. Working capital explains the out flow of funds from the corporation. High growth firms require higher amount of working capital to facilitate their operations.
3. The effect of debt is also taken into account; debt refers to the outflow of cash from the firm on account of debt charges being paid to fund the operations of the firm. Debt can also be accounted as new debt taken to fund a capital budgeting decision of the corporation, in such a case the new debt indicates the inflow of cash within the organization and therefore has to be added back to the cash flow.

Thus the Free Cash Flow obtained after subtracting all the above charges

(Source: Pages.stern.nyu.edu- accessed on 3/5/2012)

Dividends can be paid using these cash flows. The equation can be further simplified if we undertake the following assumptions

If the net working capital and the capital expenditures are funded, using both debt and equity. Therefore assuming if δ is the proportional change in the net working capital and the capital expenditures raised by financing from debt then the change in the free cash flow can be represented as.

Change in the equity cash flow associated with the change in the working capital needs can be represented as

Thus the free cash flow available to investors is a mix of financing the cash flow from debt and equity after meeting the working capital needs and the capital expenditure of the firm. Thus the free cash flow can now be represented as:

(Source: Pages.stern.nyu.edu- accessed on 3/5/2012)

Thus if any debt is issued, then the issue of the new debt represents the inflow cash in the organization and thus, will be simply added to the free cash flow and in case any re payments are made it would be subtracted from the free cash flow equation.

Let us take an example to understand the concept of free cash flow: Given below is the Net Cash flow of ABC Corporation over a 5 year period .Based on which the FCF is also calculated.

The average Net Income for ABC corporation over the 5 Year Period is $1321 , The depreciation average for the 5 year period is $267 , the capital spending over the 5 year period is $2880 , Now assuming the debt ratio at 25% , therefore below is calculated the FCFE for ABC below

Thus in the case of the above firm ABC ltd has negative FCF over the 5 year period indicating a stringent liquidity condition for the corporation. Large capital expenditures have been consistently taken by the organization to expand their operations; this however has had an effect on the cash flow of the firm.

(Pages.stern.nyu.edu- accessed on 3/5/2012)

2.2 The 2 Stage FCFE model for Growth

The 2 stage FCFE model has been designed for firms expecting to achieve a higher rate of growth over a given period of time. The model states that the present value of the FCFE is per year for the extra ordinary growth plus the present value of the stock and the end of the period. Thus mathematically the model can be presented as

Where FCF is the future cash flow in time period t

Ke is the cost of equity

Pn is the extraordinary growth over the time period t

3. The 3 Stage Growth Model

The three stage growth model also assumes similar assumptions, but under lines that the firm experiences 3 stages of growth during a particular time period. The firm first experiences a high rate of growth, then experiences a transition phase and eventually experiences a stable rate of growth for the organization. This can mathematically be denoted as

Where,

P0 is the Price of the stock today ,FCFEt is the free cash flow in the year t  ,ke is the  Cost of equity

Pn2 is referred as the  Terminal price at the end of transitional period calculated as

N1 can be classified as the ending of the initial high growth period

N2 can be classified as the ending of transition period

Thus the models can be effectively applied considering the various stages of growth the corporation is in.

(Source: Pages.stern.nyu.edu- accessed on 3/5/2012)

3. FCF vs. Dividend Discount Model

3.1 Similarities between FCF and Dividend Discount Model

The discounted cash flow model may be seen as an alternative to the dividend discount model. Though the means and methods of calculation of both the methods may be very different but both provide the nearly same measure of the value. However there may be conditions where the dividend discount model may be similar to the FCF model, this similarity arises when the dividends that are paid out are equal to the free cash flow available. The second similarity is when the FCFE is greater than the dividends paid out i.e. (free cash flow – dividends) is then invested in projects with NPV as 0.  The third similarity arises when the rate of discount is assumed same for both the models. If however these 3 conditions do not exist then the dividend discount model is very different from the FCF model.

The basic differences between the dividend discount model and the FCF are highlighted below.

3.2 Difference between Dividend Discount and FCF model

3.2.1 Initial Assumption

The dividend discount model assumes that once the dividends have been repaid , the remainder amount is invested back into the business in both operating assets as well as securities On the other hand the FCF model assumes that the after the FCFE is paid to the shareholders the amount is re invested in the operating assets of the business.

3.2.2. Measure of Growth

The dividend discount models measures the growth in both income and cash, and uses the return on equity measure to calculate the following. On the other hand the FCF model also calculates the income in terms of operating assets and uses the rate of growth over the given period and the estimated value of equity over the time period to calculate the measure of growth.

3.2.3 Cash and Marketable securities

The dividend discount model does not need to account for the cash received from the marketable securities as the earnings already reflect the amount. Whereas the FCF model enables the choice to consider the cash received from marketable securities. Income from these securities can be projected and the value of the equity can be taken out .Or they can be completely ignored and their value can be added to the equity value.

(Pages.stern.nyu.edu- accessed on 3/5/2012)

3.3 Analysts View

Authors and analysts reflect the view top managerial levels lay heavy importance to the valuation models. Mac Kinsey a top consultant to some of the world’s largest corporation views that the FCF is a better indicator of the valuation of the company than the discounted dividend model. Authors are of the view the FCF is a long term model and enables to access the long term feasibility of the corporation. The DCF is a better indicator of the different growth stages which the corporation goes through during a particular period of time.

(Gibson, 2009)

Let us undertake a numerical example to understand the difference between the 2 models.

3.4 Example

The basic Dividend Discount model equation

Where DPS is the dividend expected  per share received in the time period t and ke  represents is the cost of equity.

The Gordon Growth Model

DPS is the dividend paid by the firm in the current, therefore using the above formula to estimate the use: Let us utilise the stable growth model to estimate the value of equity for a bank over a period of time g for the given period is assumed at 7.16% and the cost of Equity ke is maintained at 12.67%.

Therefore the growth rate calculation for the bank is:

Thus using the Gordon-Growth Model

The discounted cash flow is calculated on the basis of dividends paid, whereas the FCF is based on the availability of free cash flow in the business. The DCF method is however more popular among analysts and because it provides a better valuation of the firm based on the real cash flows available to the firm.

4. Weaknesses of FCF

There may be occurrence of several forecasting errors which might occur in while calculating the value through the FCF method. Aggressive assumptions to assume a high degree of inflation rate may be assumed in the calculation .Which can significantly overstate the value of the firm at the time. Certain expense items may not be accounted for which may produce misleading results in the valuation of the corporation. Neglecting the contribution of “other” income can result in the undervaluation. Equally, a high expectation estimation of the “other” income can result in a flawed valuation. The DCF analysis in some cases may however fail to recognise the market conditions of the economy at that time and this may result in the, operating statements not being able to reflect the true market conditions resulting in a flawed estimation.

Thus despite the many weakness of the FCF analysis the FCF analysis continues to be a popular choice among analysts and researchers of top consultancies to measure the valuation of the business.

5. Conclusion

The paper has evaluated the FCF and the Dividend discount models in detail, the importance of each of the models in estimation of the value of the firm cannot be ignored. The importance of the FCF model has also been recognised by analysts companies in the estimation of future valuation and the capital budgeting decisions. Therefore despite the weaknesses the model continues to be a popular choice.

6. References

• “CHAPTER 14 FREE CASH FLOW TO EQUITY DISCOUNT MODELS.” pages.stern.nyu.edu. N.p., n.d. Web. 3 May 2012. <http://pages.stern.nyu.edu/~adamodar/
• DISCOUNTED CASHFLOW MODELS: WHAT THEY ARE AND HOW TO CHOOSE THE           RIGHT ONE.. .” Welcome to Pages at the Stern School of Business, New York University. N.p., n.d. Web. 3 May 2012. <http://pages.stern.nyu.edu/~adamod
• “Pitfalls of Discounted Cash Flow Analysis in the Valuation of Certain Income Producing Special Purpose Properties A.” www.specialpurposeproperty.com. N.p., n.d. Web. 3 May 2012. <http://www.specialpurposeproperty.com
• Gibson, Charles H.. Financial reporting & analysis: using financial accounting information. 10th ed. Mason, OH: Thomson/South-Western, 2007. Print.
• Schön, Dennis. The relevance of Discounted Cash Flow (DCF) and Economic Value Added (EVA) for the valuation of banks. München: GRIN Verlag, 2007. Print.

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