Discuss Whether the Dividend Growth Model or the Capital Asset Pricing Model Offers the Better Estimate of Cost of Equity of a Company3

Finance Notes by Dr. J. Kashefi

BUSINESS VALUATION MODELS This paper deals with the basic theory underlying valuation models. It begins by discussing such concepts as free cash flow, cost of capital, and epected growth rates, as they are basic to an understanding of valuation theory. The ultimate ultimate goal of a corporate corporate manager manager is to maim maimi! i!ee the wealth wealth of sharehol shareholders ders.. "hareholders wealth wealth is the value of the firm firm #s collectiv collectivee assets. To maimi!e maimi!e the shareholders shareholders wealth, in general, is e$uivalent to maimi!ing the value of the firm. Therefore, it is imperative that the corporate corpora te officers %now how to determine the value of the firm. firm. Determining the value of a company is a difficult tas%, since there are various definitions of &value&, depending on the needs and usage of different users. &'alue& can be considered from two different perspectives. The first is mar%et value, which reflects what investors are willing to pay for a firm, which can be determined simply by multiplying the price per share by the number of shares shares outstanding. Financial Financial economists economists often argue that the stoc% mar%et is efficient, and therefore, the mar%et value of the firm should be the price the firm would bring if sold in the mar%et today. (lthough the stoc% mar%et as a whole is considered to be efficient, many financial analysts feel that individual stoc%s stoc% s and firms firms are seldom fairly valued. Therefore, Therefore , a second method, method , which is  based on the present value of epected cash flows, flows, or what we call intrin intrinsic sic financial financial value, has been been suggested. )nder effici efficient ent mar%et hyp hypothes othesis, is, we epect epect the mar%et mar%et value value to reflec reflectt the intrin intrinsi sicc financial value. *owever, *oweve r, in recent years, valuation of most firms firms in mergers mergers and ac$uisitions, have resulted in errors, and undervaluation of the companies. (s a result, these two values have not been the same, and the focus of this paper will be on the techni$ues of determining the intrinsic financial value. THE BASICS BASI CS OF INTRINSIC INTRI NSIC FINANCIAL FINAN CIAL VALUE + In finance, the intrinsic value of a firm is the present value of a firm#s epected free cash flows over a very long period in theory, to infini infinity. ty. "ince this is obviously impossibl impossible, e, there is a need to develop develop modifi modificati cations ons -or simpl simplif ific icati ations ons of this this model, model, in order to imple impleme ment nt it for  practical purposes purposes of valuation. valuation. This paper will discuss three simplifications of the free cash flow method of valuations that are, in fact, suitable for practical application. This simplification is based on the growth patterns of the companies. companies. In general, companies# growth patterns, patte rns, which can be identified identified from their industrial life cycle, may be classified as+ -/ supernormal or generally nonconstant growth, -0 normal or constant growth, and -1 !ero growth. The industrial life cycle is a representation of an industry#s life as it goes through four stages of growth, shown in (ppendi (, Figure /. The initial pioneering stage or supernormal growth stage, the superdecline, maturity or normal growth stage, and the last stage is a decline phase, where usually the companies face etinction. From Figure /, it is possible to determine the period of superior growth by ascertaining where the company of interest stands with respect to the cycle. *owever, a word of caution in respect to the life cycle theory+ it provides only a framewor%, and has some deficiencies. deficiencies. Firstly, the theory is a highly ideali!ed, and more or less a sub2ective point of view, of how companies or industries grow and mature. "econdly, there is no guarantee that a specific industry or a group of companies will systematically pass through these life cycles. Finally, there is nothing inherent in theory, that provides a way of identifying in advance when a company or an industry will pass from 1

one stage to another. *owever, it can be stated that the normal growth companies can be characteri!ed as those epected to grow at rates in line with the economy, while supernormal growth companies are characteri!ed as those that grow at superior rates. The distinction factors between the models are as follows. First, we epect super growth companies to have high retention rates and high profitability rates, as measured by rate of return on investment or some combination of the two. "econd, we epect normal growth companies to have low retention rates of profit and3or relatively lower profitability rates. 4orrespondingly, we epect compani companies es sustainin sustaining g high high growth rates to pay !ero or relati relativel vely y lower divide dividends, nds, and normal normal growth companies to pay higher dividends. VALUATION MODELS In theory, there are several valuation models. These models are Discounted 4ash Flow, 5ar%et36oo% 'alue, and 738 ratio, which could be used to estimate estimate the value of a firm. firm. The most commonly used approach to valuing a firm is the epected free cash flow -F4F method of valuation. The principles principles of valuation valuation of a company re$uires re$uires the following. following. First, the epected epected free free cash flows flows to all classe classess of the capital capital providers providers be calcul calculated ated according according to the economic setting of the company, its industry, and the economy as a whole, which determines the si!e and duration of the epected free cash flows. The second principle re$uires that the discount rate be consistent with the ris% of the epected free cash flows. The consistency between the valuation models, discount rates, and appropriate epected free cash flows is shown in Figure 0. VALUATION TECHNIQUES FOR A FIRM Discounted Cash Flo I! "ei#hted A$e%a#e Cost o& Ca'ital ("ACC) A''%oach* The 9eighted 9eighted (verage (verage 4ost of 4apital 4apital estimates estimates a company company:s :s value by discounti discounting ng its method re$uires unle$e%ed &%ee cash &los using a constant weighted average cost of capital. This method the calculation of four variables shown in e$uation -/+ + )nlevered free cash flows -)F4F , )nlevered terminal free cash flow -)TF4F - 8pected future growth rate -g . 9eighted (verage 4ost of 4apital, ; 9(44 9(44 

T  UTFCF  UFCF t t  V = ∑ +  Equation (1) t  T  t =1 (1+ R WACC  ) (1+ R WACC  ) 8$uation / can also be stated as+ V =

UTFCF  UFCF  N  UFCF 1 UFCF 2  + + + + T  T  (1 + R WACC  ) (1 + R WACC  )2 (1 + R WACC  ) (1 + R WACC  )

Where UTFCF =

UFCF (T +1)  R WACC  - g 

Which UFCF (T +1) = UFCF T (1 + g)  Equation (2)

2

 !   and the cost of capital is e$ual to+  R = (1 - t)(   )r + (   )r  Equation (3) #  " WACC  V  V  +! Unle$e%ed F%ee Cash Flos (UFCF)* The unlevered free cash flow which is defined as net operating profit after ta -N> defines the concept of the free cash flow as, &cash flow in ecess of that re$uired to fund all pro2ects that have positive net present values when discounted at the relevant cost of capital&. The basic measurement of unlevered free cash flow -)F4F is as follows+ 86IT ?ess+ 4ash Taes on 86IT 7lus+ Depreciation and (morti!ation O'e%atin# Cash Flo (OCF) ?ess+ Increase in Net 9or%ing 4apital -a ?ess+ Increase in 4apital 8penditures -a ?ess+ Increase in other operating (ssets -b reduced by increase in other noninterest bearing liabilities Unle$e%ed F%ee Cash Flo (UFCF)

The )F4F reflects the firm:s true operating cash flow after all re$uired investments. The )F4F is not affected by the company:s capital structure. The capital structure will affect the discount rate, hence value. -a Increase in net wor%ing capital and capital ependiture+ Investment in net wor%ing capital is often estimated by finding the relationship of net wor%ing capital to sales. Increase in wor%ing capital e$uals net wor%ing capital at the end of the year less net wor%ing capital at the beginning of the year. @enerally, ca'ital e/'enditu%e  could be the summation of capital ependiture re$uired, net of replacement of eiting capacity. The formula for these two items is+ Ca'ital In$est0ents 1 CE 2

N"C

where 48 is capital ependiture in fied assets. 9ith identified components of free cash flows, we can epress the )nlevered free cash flow as follows/+ UFCF 1 OCF 3 ( CE 2 N"C) (4) Increase in other operating assets reduced by increase in other noninterest bearing liabilities sweeps up any other assets or noninterest bearing liabilities that are related to the operations of the  business. These would eclude any current assets or ad2ustment or special investments 0. ,! Te%0inal F%ee Cash Flos* )nless there are specific plans or reasons for terminating the business in the nearterm, the 3

assumption of &ongoing concern& will re$uire estimating the value of the unlevered free cash flows for an indefinite period. In practice, one ma%es a detailed pro2ection of free cash flow for a period of years, usually A/B years, and then estimates the present value of the free cash flow beyond that  period by calculating the terminal free cash flow. The calculation of the )F4F and )TF4F, in general, depends on the assumption of the epected future growth rate. The valuation of the business is usually sensitive to the estimate of the terminal free cash flows -TF4F. There are several approaches for arriving at that value. / 6oo% 'alue+ ( simple approach for estimating terminal value would be the summation of the net fied asset and net wor%ing capital at the end of terminal year, T. 0 5ar%et 'alue to 6oo% 'alue ;atio+ This method re$uires calculation of the mar%et value3boo% value ratio -5'36', which is multiplied by the Cend of the period cash flow -F4FT+ TF4FE -5'36'-F4FT 1 Discounted Terminal Free 4ash Flows+ This method assumes that the pro2ected cash flow continues beyond the forecast period -T forever. 8$uation 0 shows the estimation of the terminal free cash flow beyond the forecast period, as long as the growth rate is less than the discount rate. (ssuming that free cash flow is increasing at a constant growth rate -gT after T period, and so long as the growth rate is less than the cost of capital, the terminal free cash flow is estimated by e$uation -0. FORECASTIN5 CASH FLO" The pro2ection of Free 4ash Flows begins with a pro2ection of sales. This pro2ection should ta%e into consideration+ • (n assessment of the company:s recent historical finance performance. (n ad2ustment of historical financial performance for nonrecurring and non • operating income and epense items. 4ertain assumptions regarding the company:s prospects for the future. • In case of a ta%e over, the forecast of future cash flows should reflect the epected results of the target company assuming that it is managed by the ac$uirer. Therefore, we must ta%e into account+ 8pected overhead reductions • "everance payments • • "hut downs costs • 8conomies of scale or synergies 4hanges in business strategy -different pricing policy, different level of service, and • mar%eting strategy  Net proceeds from divestitures • It would be important to note that a great deal of guesswor% would be involved in estimating epected F4F for the above mentioned methods. 5any factors might enter the 4

estimation of the cash flows, nontheless the F4F model represents a fairly accurate position of the company#s future financial prospects. Techni$ues used to forecast free cash flows and terminal free cash flow vary widely in degree of sophistication. The simplest method is to loo% at the historical rate of growth and etrapolate this growth into the future. For eample, if sales have been growing at a certain rate in recent years, then the future sales figure could be pro2ected by that rate. If we assume that the various items of the balance sheet and income statement, such as direct costs, general and administrative costs will continue to maintain their historical relationship to sales, then based on pro forma financial statements, free cash flows can be pro2ected annually. It is important that we understand clearly what is meant by the term growth rate when used in the contet of valuing a company. To value a company, we need to %now how the F4F and TF4F are going to be estimated. In general, the growth of free cash flows and terminal free cash flow are based on the  profitability of the business operation and epected growth of the free cash flows. ( company#s free cash flows can grow in a variety of ways. It can grow by borrowing money, issuing common stoc%s, retention of epected profits or merging with another company. In all of these cases the firm#s free cash flows is growing and this &growth& potential has important implication in valuing the company. "ince growth epectations are unobservable, one needs to resort to proies to assess the sort of growth, that an analyst epects a company or a group of companies to have. There are several growth models that will be discussed in subse$uent sections1. Conclusion* The techni$ue of using a constant weighted average cost of capital for valuation is widely applied in practice. The usual capital budgeting approach re$uires that prospective investments offer a return in ecess of some Churdle rate. 9hat is often overloo%ed is that the 9(44 will be constant onl6 if the firm maintains a constant debt to capital - or debt3e$uity ratio in mar%et value terms, and the ris% of the investments remains constant. There are a number of situations in which a firm does not intend to maintain a fied debttovalue structure. In these cases, the 9(44 changes over time. 8ach year:s cash flow could have a different 9(44G For eample, in a levered buyout, a firm:s owners begin with a heavy debt load, but are epected to pay off outstanding principal according to a specific timetable, and often very rapidly. The firm:s debt3e$uity ratio declines each year. )nder these circumstances, Ad7usted 8%esent Value  is the most practical method to value cash flows. II! AD9USTED 8RESENT VALUE + This is another techni$ue of valuing a company. The (7' and 9(44 use the same form of cash flows. 9ith this method the value of the company is simply the summation of the present value of epected unlevered free cash flows to e$uity holders, and the present value of the ta  benefit due to the amount of debt in the capital structure of the company. The value of the company using (d2usted 7resent 'alue -(7' can be epressed asH+  7resent value of the side effects (7' E 7resent value of all e$uity finance Investment

associated with the financing.

T  UFCF  UTFCF  T   &  %( T   )  &  %( T   ) t  + t  C  + T  C   Equation ($) T  + V = ∑ ∑ t  T  t  T  t =1 (1+ R u"  ) (1+ R u"  ) t =1 (1+ R #  )  R # (1+ R #  ) where )F4F is the unlevered free cash flows to the e$uity holders and r su is the unlevered cost of 5

e$uity (d2usted present value is very fleible and accommodates any particular pattern of cash flows and debt financing with its associated ta shields. 9ith this method, we can specify the structure of debt financing and calculate the present value of the interest ta shields, and add it to the present value of epected unlevered cash flows to the e$uity holders. *owever, this process can be tedious if a large number of periods are involved. If we assume that debt is epected to be a constant  proportion of the value of the firm, and that the income ta rate is constant, we can simplify the calculation to a certain degree. There are two different approaches to (7' if the debt ratio is constant over time. 9ith the first approach, the present value of interest ta shields is calculated using the cost of debtA. 9ith the second approach, because the debt ratio is epected to be constant, the interest ta shields are tied to the value of the firm and therefore are uncertain. 4onse$uently, the unlevered cost of e$uity should be used to calculate the present value of the ta shields .-this model is not presented here III! VALUATION OF EQUIT:* In addition to valuing an entire company, the e$uity portion of a firm can also be valued by setting the second term in e$uation A to !ero. That is+

T   FCF  t  +  FCF T +1  Equation (') V = ∑ t  T  t = 1 (1 + R u"  ) (1 + R u"  ) This model is good only for a total e$uity financed company. If the company has debt in its capital structure, the $alue o& e;uit6 is 4ased on le$e%ed &%ee cash &los and le$e%ed cost o& e;uit6 . That is+

T   FCF  t  +  FCF T + /  Equation () V = ∑ t  T  t =1 (1 + R   ) (1 + R   )

The difference between e$uation - and -> is due to the amount of debt in the capital structure of the company. The free cash flows to the e$uity investors must account for not only operating cash flow but also for any net return of principal -new debt issues  principal repayments to debt holders. The ?F4F is a measure of what a firm can afford to pay out as dividends. 6elow is the estimation of ?F4F. 86IT ?ess+ ?ess+ 7lus+ ?ess+ ?ess+ ?ess+ ?ess+

Interest payment 4ash Taes on 86IT Depreciation and (morti!ation O'e%atin# Cash Flo (OCF) Increase in Net 9or%ing 4apital Increase in 4apital 8penditures new debt issues minus debt repayments -ND8 Increase in other operating (ssets reduced by increase in other noninterest  bearing liabilities 6

?evered Free 4ash Flow -?F4F LFCF 1 OCF 3 ( CE 2

N"C+ND8)

-! Esti0ation o& 5%oth Rates and Valuation Models = to MH1B million in /==H. The following table shows the growth in net income for (mgen from /=>= to /==H, in both percentage and dollar terms. Illust%ation = M /=./B /==B /==/ /==0 /==1 /==H

 5%oth Rate

Net Inco0e

>.1B />.1B 1B.B 1AH.=B H1B.BB

1A/.1/ //./1 H.1 /A.0 0/./

M ./B /BB./B /0B.HB H>.0B A./B

@eometric (verage @rowth ;ate E >.H0 (ssuming that this growth rate continues for the net five years+ :ea% Net Inco0e /==A

 5%oth Rate

Net Inco0e M >B/.B M1/.B /,H=H.10 0,>A. /,0=/.1A A,/=0.=> 0,HB.1/ =,>B.1 H,H>.A

/== /== /==> /===

>.H0 >.H0 >.H0

=0.0

>.H0 >.H0

The dollar increase in net income needed each year to sustain an >.H0 growth rate  becomes larger and larger and rises to MH.H> billion by /===. 8ven if (mgen remains a wellrun and successful firm, it will become progressively more difficult over time to deliver theses high growth rates. -! C6clicalit6 in Econo06 + *istorical growth rates for cyclical firms are strongly influenced by where in the business cycle the economy is at the time of the estimation. If historical growth rates for cyclical firms are estimated in the middle of a recession, the growth rates are li%ely to be very negative. The reverse is generally true if the estimation of historical growth is done at an economic 12

 pea%. These growth rates are of little value. *owever, in predicting future growth, it would be more useful to estimate growth across two or more economic cycles for these firms. .! Chan#es in &unda0entals*   The observed growth rate is the result of fundamental decisions made by the firm on business mi, pro2ect choice, capital structure, and dividend policy. If a firm changes in any or all of these dimensions, the historical growth rate may not be a reliable indicator for future growth. For instance, the restructuring of a firm often changes both its asset and its liability mi, and ma%es past growth rates fairly meaningless in predicting future growth. The other problem with using past growth rates arises when the business in which the firm is operating changes, either as a result of mar%et forces or government regulation. These changes in fundamentals may cause a shift upward or downward in growth for all companies in that business and have to be factored into predictions. For instance, pharmaceutical companies at the end of /==0 had en2oyed a decade of high growth as medical technology advanced and health care costs surged. ?oo%ing into the future, however, mar%et forces and the potential for health care reform ma%e it unli%ely that these growth rates would continue. @! Qualit6 o& ea%nin#s*  (ll earnings growth is not e$ual. 8arnings growth created by changes in accounting policy or ac$uisitions is inherently less reliable than growth created by increasing units sold, and should be weighted less in forecasting future growth. B! The Dete%0inants o& Ea%nin#s 5%oth 9hile growth in a firm may be measured using history or analyst forecast, it is determined  by fundamental decision that a firm ma%es on product lines, profit margin, financial leverage and dividend policy. Sustaina4le 5%oth? Retention Rate and Retu%n On E;uit6 It is a fairly direct and ob2ective measure of the growth prospect of a company, although it suffers from the usual deficiencies associated with accounting data. *owever, it reveals the interdependence among financial policies when firms pursue a policy of a constant debt ratio and does not sell new stoc%. )nder the assumption of no eternal e$uity financing, the assets of the firm can grow only as fast as it retains earnings -*iggins /=. The simplest relationship is+

# 1 RR / ROE In this relationship, growth in earnings is an increasing function of both the retention rate and the return on e$uity. This relationship is also referred to as sustainable growth rate. (lternative specification of sustainable growth that is consistent with the above e$uation is+  g u"taina, e =

 RR%- R*E . 1 - RR%- R*E .

Inte%nal 5%oth Rate  It is the maimum possible growth rate for a firm that relies only on internal

financing.  g  &nterna,  =

 RR%- R*A. 1 - RR%- R*A.

;EROA 3 R d(+ 3 TC)

where D38 rd TC 6'

;