Kennesaw State UniversityDigitalCommons@Kennesaw State University

Faculty Publications

Winter 2004

Drivers of the Value of the Firm: Profitability,Growth, and Capital IntensityTom W. MillerKennesaw State University

Richard E. MathisenKennesaw State University, rmathise@kennesaw.edu

Follow this and additional works at: http://digitalcommons.kennesaw.edu/facpubs

Part of the Business Administration, Management, and Operations Commons, CorporateFinance Commons, and the Marketing Commons

This Article is brought to you for free and open access by DigitalCommons@Kennesaw State University. It has been accepted for inclusion in FacultyPublications by an authorized administrator of DigitalCommons@Kennesaw State University. For more information, please contactdigitalcommons@kennesaw.edu.

Recommended CitationMiller, Tom W., and Richard E. Mathisen. "Drivers of the Value of the Firm: Profitability, Growth, and Capital Intensity." Journal ofAccounting & Finance Research 12.6 (2004): 70-9. Print.

DRIVERS OF THE VALUE OF THE FIRM:PROFITABILITY, GROWTH, AND CAPITAL INTENSITY

Tom W. Miller, Kennesaw State UniversityRichard £. Mathisen, Kennesaw State University

ABSTRACT

Value-based management systems focuson wealth and the wealth creation processand promote the generation of value for theshareholders. A valuation model for thefirm is extended analytically to focusexplicitly on profitability, growth, andcapital intensity as drivers of the value of thefirm. The extended model providesinformation about the sensitivities of thevalue of the firm to changes in the firm'sprofitability, growth, and capital intensity.These sensitivities are presented in terms ofchanges per dollar of sales and actual dollarchanges. The changes per dollar of salesshow the relative sensitivities of the changesin the value of the firm resulting fromchanges in the measures for profitability,growth, and capital intensity. Each dollaramount shows the total dollar changes in thevalue of the firm resulting from changes inthe profitability, growth, and capitalintensity measures. These sensitivities showthe impact of changes in the profitability,growth, and capital intensity measures onthe value of the firm. This information isvaluable in helping managers determine adesired course of action to improve thewealth generating ability of the firm bymanaging these value drivers moreeffectively.

INTRODUCTION

Value-based management systems focuson wealth and the wealth creation processand promote the generation of value for theshareholders (Fisher 1995; Lieber 1996;Walbert 1994). A valuation model for the

firm is extended analytically to focusexplicitly on profitability, growth, andcapital intensity as drivers of the value of thefirm. The extended model providesinformation about the sensitivities of thevalue of the firm to permanent changes inthe firm's profitability, growth, and capitalintensity. These sensitivities are presentedin terms of partial derivatives and dollarchanges. They show the impact of changesin the profitability, growth, and capitalintensity measures on the value of the firm.This information is valuable in helpingmanagers determine a desired course ofaction to improve the wealth generatingability of the firm by managing these valuedrivers more effectively (Lehn and Makhija1996). Value-based management is asystem that integrates valuation and action.A detailed analytical development of theextended valuation models used to producethe measures of sensitivities for profitability,growth, and capital intensity is presented.Profitability, growth, and capital intensityare shown to be important drivers of freecash flow, the value of the firm, and thevalue of the firm per dollar of sales. Therelationships of permanent changes inprofitability, growth, and capital intensity tofi-ee cash fiow, the value of the firm, and thevalue of the firm per dollar of sales arepresented. Expressions are developed forthe sensitivities of free cash flow, the valueof the firm, and the value of the firm perdollar of sales with respect to changes inprofitability, growth, and capital intensity inthe fifth section. Expressions for dollarchanges in the value of the firm per dollar ofsales and in the value of the firm forpermanent changes in profitability, growth.

Miller and Mathisen - Drivers of the Value of the Firm

and capital intensity are provided. Anillustrative example employing thesensitivity models is presented. Thisexample provides numerical values of thepartial derivatives and dollar changes for thevalue of the firm and the value of the firmper dollar of sales for permanent changes inprofitability, growth, and capital intensity.

DRIVING SHAREHOLDER VALUE

Management systems that focus ondriving shareholder value incorporatevaluation principles and are designed andimplemented in a way that promotes andrewards decisions that add market value toinvestor-supplied funds (Copeland, Koller,and Murrin 1995; Stem, Stewart, and Chew1995; Ehrbar 1998; Rappaport 1998;Stewart 1991). Such management systemsemphasizing value creation need valuationmodels that are expanded to includeconcepts from both the income statementand balance sheet. The value of the firmshould be related to income statement andbalance sheet items and financial metrics.The extended valuation models developed inthis paper incorporate items from the incomestatement and balance sheet as value drivers.The value drivers are designed so thatcomponents of the employees' work can beidentified and linked to the value drivers inthe extended valuation model. Performancetargets for the value drivers can beestablished and actual performance can bemeasured, evaluated, and rewarded in termsof the targets for value drivers. When thevalue drivers are identified properly, themeasurement system is designed properly,and actual performance is reinforcedappropriately, value-based managementsystems will produce business decisions thatincrease the value of the firm (Stem Stewart1992).

EXTENDING VALUATION MODELS

The cost of capital and measures offuture cash fiows and are used by generally

71

accepted valuation frameworks to providemeasures of the value of the firm. Thetiming, magnitude, and riskiness of futurecash flows, and the cost of capital determinethe value of the business. The two-phasevaluation model for free cash fiow shown inTable 1 as equation (1) is employed in thisstudy. When constant growth with g < roccurs after time T the two-phase valuationtakes the form shown by equations (2) and(3) in Table 1. The first T periods in thismodel, phase one, represent an explicitforecast (transition) period during whichvarying behavior is possible and theremaining periods (phase two) are acontinuing value (steady-state) period duringwhich growth is constant and parametershave steady-state values (Copeland, Koller,and Murrin 1995; Stewart 1991; Stewart1994). Free cash fiow, FCFt, is defined asequal to the net operating profit after taxes,NOPATi, less the required net investment,NINVt. Equation (4) in Table 1 is the modelfor free cash flow is that is used in thisstudy. Net operating profit after taxes isequal to eamings before interest and taxes,EBITt, after taxes. In this model, shown asEquation (5) in Table 1, x is the cash incometax rate. The required net investment is therequired change in invested capital, ICt -ICi-i. The model for net investment is givenby Equation (6) in Table 1. The retum oninvested capital, ROICt, which relates netoperating profit after taxes and investedcapital, ICt, is the measure of profitabilityused in this study. The definition employedfor the retum on invested capital is shown asEquation (7) in Table I. Capital intensity,cit, relates invested capital and salesrevenue. The model used for capitalintensity is shown as Equation (8) in Table1. These relationships provide a model fornet operating profit after taxes in terms ofthe retum on invested capital, capitalintensity, and sales revenue. This model ispresented in Table 1 as Equation (9). Themodel for invested capital in terms of capitalintensity and sales revenue shown asEquation (10) in Table 1 is provided by the

72 Journal of Accounting and Finance Research - Winter. 2004

TABLE 1Equations Employed in the Study

(1)

t=T+l (l + r)̂

F C F T . , 1

r-g r-g

asH->oo (2)

NOPATt = (I-T)-EBITt (5)

=ICt - I C t _ | (6)

( NOPATt "l

NOPATt =ROICi cit St (9)

ICt = c i f St (10)

- c i t - i St_| (H)

t_i (12)

+ g t ) S t - I - c i t -1 St-I =tcit (1+ gt ) - c i t _ i ] St_i (13)

cit St -[cii ( l + g i ) - c i t _ , ] S t _ i (14)

FCF]- ={ROICx c i j ( l + g j ) - [ c i x (l + g x ) - c i x _ i ] } Sy_i (15)

Miller and Mathisen - Drivers of the Value of the Firm 73

TABLE 2Equations Employed in the Study

i ( g t ) [ t ( g t ) t - i ] } S t - i V T+ IT (16)

1 = 1 (1 + r)' (1 + r)^[ROlCci (l + g ) - c i j g ] S x

Vj = (17)r - g

t - 1St-1 = n ( I + g n ) So (18)

T n o (19)

n = 1

0n ( l + gn) = l (20)

n = I

—, Uoj (21)

Tl R O l C c i ( l + g ) - c i x - g ] - n

(22)

oJ '•-g

+p (23)

g t + y (24)

c i t + 5 (25)

ROIC + p (26)

S + Y (27)

c! + 5 (28)

t-1p) (cit +5)-(l + gt +y)-[(cit +5) (1 + gt +Y)-(cit-i +6)]}- n ( l + gn +y) So (29)

T5) ( ! + g + Y ) - [ ( c i + 6) ( l + g + Y ) - ( c i j + 5 ) ] } - n ( ! + g n +Y) S Q (30)

n - l

74

definition of capital intensity. Using themodel for invested capital gives the modelfor required net investment in terms ofcapital intensity and sales revenue given inEquation (11). The model for the period-to-period growth rate for sales revenue, gt,given in Equation (12) of Table 1 showshow sales revenue evolves over time. Netinvestment also depends on the period-to-period growth rate for sales revenue asshown in Equation (13) of Table 1. Usingthe models for net operating profit aftertaxes, required net investment, and salesrevenue growth, produces the models forfree cash flow shown in equations (14) and(15) of Table 1. Substituting the expressionfor free cash flow into the two-phasevaluation model shown in equations (!), (2),and (3) gives the valuation model shown inTable 2 as equations (16) and (17). Themodel for sales revenue can be expanded asshown in equations (18), (19), and (20) sothat each year's sales revenue depends on Soand tbe period-to-period growth rates fromtime 0 up to time t-1 and T. Substituting theexpanded model for sales into the model forthe value of the firm gives the extendedvaluation model for the value of the firm perdollar of saies shown in Table 2 as equations(21) and (22). The time subscripts areremoved from the symbols for retum oninvested capital, capital intensity, and salesrevenue growth after time T to emphasizethat steady-state values occur. This modelshows how the retum on invested capital,capital intensity, sales revenue growth, andcost of capital are drivers of the value of thefirm per dollar of sales.

THE IMPORTANCE OFPROFITABILITY, GROWTH, AND

CAPITAL INTENSITY

Profitability, growth, and capitalintensity are important drivers of free cashflow and the value of the firm in the modelspresented so far. The importance ofprofitability, growth, and capital intensity inthe value generation process can be

Journal of Accounting and Finance Research - Winter, 2004

examined more closely by looking at theireffects on free cash flow and the value of thefirm.

Perturbation Terms for the Value Drivers

The following notation that is used toexamine sensitivities for the measures ofprofitability, growth, and capital intensity ispresented in Table 2 in equations (23), (24),and (25) for the explicit forecast (transition)period and in equations (26), (27), and (28)for the for the continuing value (steady-state) period. In these models, rho, gammaand deit^ are perturbation terms whichnormally equal zero, but are set to positiveand negative values to measure sensitivitiesof the value of the firm with respect topermanent changes in these measures ofprofitability, growth, and capital intensity.

FCF in Terms of Profitability, Growth,and Capital Intensity IncludingPerturbation Terms

When the perturbations terms areintroduced into the expressions, therelationship between free cash flow and themeasures of profitability, growth, andcapital intensity are given in Table 2 byEquation (29) for the explicit forecast(transition) period and by Equation (30) forthe continuing value (steady-state) period.

Sensitivities of FCF with Respect toProfitability, Growth, and CapitalIntensity

The partial derivatives of free cash flowshow their sensitivities with respect toprofitability, growth, and capital intensity.The partial derivatives for free cash flowwith respect to permanent changes inprofltability, growth, and capital intensityare obtained from the models for free cashflow. For profitability, the partialderivatives of the free cash flow with respectto a permanent change in the rate of retumon invested capital are given in Table 3 by

Miller and Mathisen - Drivers of the Value of the Firm

TABLE 3Equations Employed in the Study

t - 1

= (ci + 5) • (I + g + y) • n (1 + gn + Y)

-(cit +6)]-

+p)-(cit +5)-(Ugt +y)-[(cit

n =

faFCFj + i'l

n =

{(R01C

^ U +y)-(gt

35 J

t=l

fdFCF

[ dp [ dp

t= l

as ast= l

T T2 n

h = l n = l

n ?i h

(31)

(32)

t - I t -1+y)-(cii_i +5)]}- I n (I + gn +y)-So

h = 1 n =1

(33)

(34)

(35)

(36)

(38)

(40)

Equation (31) for the explicit forecast The partial derivatives for free cash flow(transition) period and by Equation (32) for with respect to a permanent change inthe continuing value (steady-state) period. growth are given in Table 3 by Equation

76

(33) for the explicit forecast (transition)period and by Equation (34) for thecontinuing value (steady-state) period.Equations (35) and (36) in Table 3 are thepartial derivatives for free cash flow withrespect to a permanent change in capitalintensity for the explicit forecast (transition)period and for the continuing value (steady-state) period, respectively.

SENSITIVITIES OF VALUE PERDOLLAR OF SALES WITH RESPECTTO PROFITABILITY, GROWTH, AND

CAPITAL INTENSITY

The value of the firm per dollar of salesequals the present value of the future freecash flows divided by So and is given byEquation (37) in Table 3. The partialderivative of the value of the firm per dollarof sales with respect to permanent changesin profitability is equal to the expression inEquation (38) in Table 3. The partialderivative of the value of the firm per dollarof sales with respect to a permanent changein growth is equal to the expression inEquation (39) in Table 3. The partialderivative of the value of the firm per dollarof sales with respect to a permanent changein capital intensity is equal to the expressionin Equation (40) in Table 3.

TABLE 4Equations Employed in the Study

Journal of Accounting and Finance Research - Winter. 2004

DOLLAR CHANGES FORPROFITABILITY, GROWTH, AND

CAPITAL INTENSITY

Another way to measure tbesensitivities of value and value added tochanges in profitability, growth, and capitalintensity is the dollar change resulting froma permanent change in profitability, growth,and capital intensity. The dollar change fora permanent change in the measures ofprofitability, growth, and capital intensity isequal to the partial derivative of the value ofthe firm with respect to the respective valuedriver times the change in the value driver.The changes in the value of the firm aregiven by equations (41), (42), and (43) inTable 4 for a permanent change in each ofthe value drivers, profitability, growth, andcapital intensity.

ILLUSTRATIVE EXAMPLE

The models developed in this paper canbe used to generate information about thevalue of the firm per dollar of sales, thevalue of the firm per dollar of sales, and thesensitivities of the value of the firm perdollar of sales to profitability, growth, and

Miller and Mathisen - Drivers of the Value of the Firm 77

capital intensity. The models are used togenerate the information presented in tables5 through 8. In the tables, the explicitforecast (transition) period is five years anda continuing value (steady-state) periodoccurs after that. The different values ofROICt, gi, and cii shown in the four tablesare used to produce the different values ofthe partial derivatives of the value of thefirm per dollar of sales with respect to themeasures of profitability, growth, andcapital intensity. Table 5 uses an initialROIC of 25%, an initial growth rate of 20%,an initial capital intensity of 0.50, and a costof capital of 15%. Table 6 uses an initialROIC of 25%, an initial growth rate of 20%,a higher initial capital intensity of 1.00, anda cost of capital of 15%. Table 7 uses aninitial ROIC of 25%, an initial growth rateof 20%, an even higher initial capitalintensity of 1.50, and a cost of capital of15%. Table 8 uses a lower initial ROIC of20%, an initial growth rate of 20%, an initialcapital intensity of 1.00, and a cost of capitalof 15%. For the continuing value (steady-state) period, all four tables use an ROIC of15%, a growth rate of 5%, and a cost ofcapital of 15%. The capital intensity for the

continuing value (steady-state) period is0.50, 1.00, 1.50, and 1.00 for the four tables.For the parameters shown in the tables, apermanent change in ROIC has the largestimpact on tbe value of the firm per dollar ofsales and a permanent change in capitalintensity has the smallest impact on thevalue of the firm per dollar of sales. Apermanent change in growth has anintermediate impact on the value of the firmper dollar of sales for the parameters shown.The sensitivities of the value of the firm perdollar of sales to profitability, growth, andcapital intensity for other values of theparameters for the explicit forecast(transition) and continuing value (steady-state) periods can be generated using themodels developed in this paper. The valueof the partial derivative multiplied by theanticipated permanent changes in ROIC, g,or ci shows the magnitude of the anticipatedchange in the value of the firm per dollar ofsales resulting from the change in the valuedriver. Suppose there is a permanent changein ROIC equal to 1% when the relevantvalues for the parameters are shown in Table6. The value of the firm per dollar of saleswill increase by approximately 16.90277

TABLE 5

t

ROICt

gtcitr

Explicit Forecast (Transition) Period0

0.250.200.500.15

10.250.200.500.15

2

0.250.200.500.15

30.250.200.500.15

4

0.250.200.500.15

50.150.050.500.15

SteadyState0.150.050.500.15

PartialDerivative

8.451392.306271.64568

times 0.01 equals 0.1690277. In addition,assume that the firm's sales are $1 billion.The value of the firm will increase byapproximately 16.90277 times 0.01 times $1billion equals $0.1690277 biUion. Theeffects of permanent changes in the growthrate and capital intensity can also beanalyzed using this approach. This example

shows how the models provide quantitativemeasures of the effects of permanentchanges in profitability, growth, and capitalintensity on the value of the firm per dollarof sales and on the value of the firm. Othercombinations of profitability, growth, capitalintensity, and cost of capital for explicitforecast (transition) period and a continuing

78 Journal of Accounting and Finance Research - Winter, 2004

TABLE 6

tROICt

gi

citr

Explicit Forecast (Transition) Period0

0.250.201.000.15

10.250.20

1.000.15

20.250.201.000.15

30.250.20

1.000.15

40.250.201.000.15

50.150.051.000.15

SteadyState0.150.051.000.15

PartialDerivative16.902774.612531.64568

TABLE 7

t

ROICt

gi

citr

Explicit Forecast (Transition) Period0

0.250.201.500.15

10.250.201.500.15

20.250.201.500.15

30.250.201.500.15

40.250.201.500.15

50.150.051.500.15

SteadyState0.150.051.500.15

PartialDerivative25.354156.918801.64568

TABLE 8

tROICt

gt

citr

Explicit Forecast (Transition) Period0

0.20

0.201.000.15

10.20

0.201.000.15

20.20

0.201.000.15

30.20

0.201.000.15

40.20

0.201.000.15

50.150.051.000.15

SteadyState

0.150.051.000.15

PartialDerivative16.902774.138691.42298

value (steady-state) period can be examinedin similar fashion. Such results areinterpreted as discussed in this example andcan be used to develop a more completeunderstanding to the response surface for thevaiue of the firm.

SUMMARY AND CONCLUSIONS

This research extends two-stagevaluation models so that they includeexplicit treatment of profitability, growth,and capital intensity. Extended valuationmodels are presented which show therelationships between these three valuedrivers and the value of the firm and thevalue of the firm per dollar of sales. Partialderivatives for the extended valuation

models are used to provide expressions forthe sensitivities of the value of the firm perdollar of sales and the value of the firm withrespect to profitability, growth, and capitalintensity. The partial derivatives are used toproduce expressions for dollar changes inthe value of the firm associated withpermanent changes in profitability, growth,and capital intensity. The partial derivativesand dollar changes are measures of thesensitivities of the value of the firm withrespect to changes in these value drivers.An illustration example demonstrates theusefulness of the valuation models andsensitivities models developed. Thesensitivity measures show the relativeimportance of permanent changes inprofitability, growth, and capital intensity.

Miller and Mathisen - Drivers of the Value of the Finn

This information can be used by value-basedmanagement systems in designing programsto enhance the value of the firm.

REFERENCES

Copeland, T., T. Koller, and J. Murrin.1995. Valuation: Measuring andManaging the Value of Companies, 2ndedition. New York: John Wiley & Sons,Inc.

Ehrbar, A. 1998. EVA: The Real Key toCreating Wealth. New York: JohnWiley & Sons, Inc.

Fisher, A. B. 1995. Creating ShareholderWealth. Fortune (December 11).

Lehn, K, and A. K. Makhija. 1996. EVA andMVA as Performance Measures andSignals for Strategic Change. Strategyand Leadership 3 (May/June).

Lieber, R. B. 1996. Who are the RealWealth Creators? Fortune (December9).

Marshall, A. 1997. Principles of Economics.Amherst, New York: PrometheusBooks.

79

Rappaport, A. 1998. Creating ShareholderValue, revised and updated edition.New York: The Free Press.

Stem Stewart. 1992. Roundtable onManagement Incentive Compensationand Shareholder Value. Journal ofApplied Corporate Finance 2(Summer).

Stem, J. M., G. B. Stewart III, and D. H.Chew. 1995. The EVA FinancialManagement System. Journal ofApplied Corporate Finance 2(Summer).

Stewart III, G. B. 1991. The Quest forValue. New York: HarperCollinsPublishers Inc.

. 1994. EVA: Fact and Fantasy.Journal of Applied Corporate Finance2 (Summer).

Walbert, L. 1994. The 1994 Stem StewartPerformance 1000. Journal of AppliedCorporate Finance 4 (Winter).