21 th October 2008 Glasgow eprints Service

Transcription

1 Hirst, I. nd Dnbolt, J. nd Jones, E. (2008) Required rtes of return for corporte investment pprisl in the presence of growth opportunities. Europen Finncil Mngement 14(5):pp th October 2008 Glsgow eprints Service

2 Required Rtes of Return for Corporte Investment Apprisl in the Presence of Growth Opportunities In R. C. Hirst Deprtment of Accountncy nd Finnce, School of Mngement nd Lnguges, Heriot- Wtt University, Edinburgh, EH14 4AS, Scotlnd, UK e-mil: Jo Dnbolt Deprtment of Accounting nd Finnce, University of Glsgow, Glsgow, G12 8LE, Scotlnd, UK e-mil: Eddie Jones Mngement School nd Economics, University of Edinburgh, Edinburgh, EH8 9JY, Scotlnd, UK e-mil: Abstrct Trditionl methods of estimting required rtes of return overstte hurdle rtes in the presence of growth opportunities. We ttempt to quntify this effect by developing simple model which: (i) identifies those compnies tht hve vluble growth opportunities; (ii) splits the vlue of shres into ssets-in-plce nd growth opportunities ; nd (iii) splits the equity β into β for ssets-in-plce nd growth opportunities. We find growth opportunities for UK compnies over the period to verge 33% of equity vlue. Incorporting the effect of growth opportunities, the verge cost of cpitl for investment purposes flls by 1.1 percentge points. Keywords: Cost of cpitl, Bet, Growth opportunities, Assets-in-plce JEL Clssifiction: G31 Acknowledgements The uthors would like to thnk the nonymous referee, John Douks, Mrk Aleksnyn, Joe Hillier, Brin Nichols, Grhm Prtington, Antonios Signos nd prticipnts t the Finncil Mngement Assocition Annul Meeting (Sien, 2005), the Multintionl Finnce Society Annul Conference (Edinburgh, 2006), the Europen Finncil Mngement Assocition Annul Conference (Mdrid, 2006) nd seminrs t Glsgow Cledonin University nd Glsgow University for helpful comments on erlier versions of this pper. The norml cvet pplies.

3 1. Introduction This pper builds on n rgument tht ws first proposed by Myers nd Turnbull (1977). They note tht the mrket vlue of the firm is mde up of: (i) The present vlue of csh flows from ssets-in-plce, nd (ii) the present vlue of growth opportunities. They further note tht growth opportunities hve option-like chrcteristics, nd tht this hs implictions for rtes of return tht incorporte the mesurement of systemtic risk. They conclude: The risk (β) of n option is not the sme s the risk of the sset the option is written on. Usully it is greter. If so, the lrger the option vlue reltive to the vlue of ssets-in-plce, the greter is the systemtic risk of the firm s stock. Thus the systemtic risk of the firm s stock is n overestimte of the bet for tngible ssets, nd rte of return derived from common stock β s will be n overestimte of the pproprite hurdle rte for cpitl investment whenever firms hve vluble growth options. The prcticl nd theoreticl difficulties creted by this phenomenon re obvious. (Myers nd Turnbull, 1977, p. 332). This pper ttempts to tckle these prcticl nd theoreticl difficulties. Our min contribution is to develop simple model, bsed on stndrd pieces in the toolkit of finncil theory, to split the β of compny s shres into the two elements of ssets-inplce β nd growth opportunities β. We lso djust the cost of cpitl for the presence of growth opportunities, nd explore the properties of the model by pplying it to lrge smple of UK compnies over the period. Myers nd Turnbull s rgument, s well s our model, suggests growth opportunities should ffect required rtes of return whichever investment pprisl method is chosen. To illustrte the mgnitude of the growth opportunities effect, we look specificlly t the 2

4 chnge in the vlue of the weighted verge cost of cpitl (WACC) when growth is tken into ccount. In light of Myers nd Turnbull s nlysis, it cn be seen tht the trditionl method of clculting WACC for investment in new ssets is doubly flwed. Not only does it use the wrong β for equity committed to new ssets; it lso uses the wrong weights when combining the costs of debt nd equity. If debt is supported by ssets-in-plce, the weight given to equity should be bsed solely on the mrket vlue of equity derived from ssetsin-plce, omitting the mrket vlue of the compny s growth opportunities. From n initil smple of 5,059 firm-yer observtions, we re ble to estimte the vlue of growth opportunities for 3,715 cses. However, some of these cses yield negtive estimtes for the vlue of growth opportunities. Our model pplies to those cses in which compnies hve vluble growth opportunities. Assuming n equity risk premium of 6%, we identify vluble growth opportunities in 69% of the cses to which we cn pply the model (nd 51% of the whole dtset). For these 2,571 cses, we find tht growth opportunities ccount, on verge, for 33% of equity vlue. Adjusting WACC for the presence of vluble growth opportunities lowers the hurdle rte for new investments on verge by just over one percentge point. The djustment is lrger for compnies with higher levels of growth opportunities, rising to just over two percentge points for the decile of observtions with the highest levels of growth opportunities. The reminder of the pper is orgnised s follows: In section 2 we review relevnt prior work, while in section 3 we develop nd solve the set of equtions used in our model for splitting the equity bet. Section 4 develops the model for djusting the cost of cpitl for the presence of growth opportunities. In section 5 we pply the model to lrge smple 3

5 of UK listed compnies, while in section 6 we explore some of the properties of the model. The finl section sets out our conclusions. 2. Literture nd theoreticl foundtions Recognition tht shre vlue is divided into ssets-in-plce nd growth opportunities dtes bck to Miller nd Modiglini (1961). 1 Kester (1984) demonstrtes prcticl method of decomposing shre prices into the vlue of ssets-in-plce nd growth opportunities, nd development of this model hs been given prominence in Breley nd Myers (1991 nd subsequent editions). On per shre bsis (where the vlue of one equity shre is P s ), the shre vlue due to ssets-in-plce (P ) is given by: P = EPS K s The ernings-per-shre (EPS), vlued in perpetuity, re ssumed to generte the vlue of the firm s ssets-in-plce. This csh flow strem is discounted t rte K s (the cost of equity cpitl), which is derived from CAPM (using the compny s equity β). The element of the shre price due to growth opportunities, P g, is then derived s: P g = P P s Both Kester (1984, 1986) nd Breley & Myers (2003) use this model to show (bsed on smples of eight to fifteen compnies) tht growth opportunities constitute lrge frction often bove one-hlf of shre vlue. Applying the Kester/Breley&Myers 1 Miller nd Modiglini present vrious methods of shre vlution, including the investment opportunities pproch, under which the worth of the enterprise to n investor will depend only on: () the norml rte of return he cn ern by investing his securities (i.e., the mrket rte of return); (b) the ernings power of the physicl ssets currently held by the firm; nd (c) the opportunities, if ny, tht the firm offers for mking dditionl investments in rel ssets tht will yield more thn the norml (mrket) rte of return. (p. 416). 4

6 model to lrger smples, Dnbolt et l. (2002) 2 find growth opportunities on verge to ccount for 56% of firm vlue bsed on smple of 2,010 firm-yers for lrge UK compnies, while Andrés-Alonso et l. (2006), pplying vrint of the Kester/Breley&Myers model to smple of 391 high-tech compnies listed in OECD mrkets, find the vlue of growth opportunities to verge more thn 75% of firm vlue. However, the Kester/Breley&Myers method, by vluing the ssets-in-plce t discount rte bsed on equity β, ignores the centrl insight of Myers nd Turnbull. Thus, while the method is well estblished technique for mesuring growth opportunities, it is not stisfctory for our purpose. To develop the Myers nd Turnbull nlysis, we require model which mesures not just vlues for ssets-in-plce nd growth opportunities, but lso genertes the β vlues ssocited with ech component. A number of ppers hve developed theoreticl models of the impct of growth options on shre bet nd the bet of ssets in plce (e.g., Miles, 1986; Pindyck, 1988; Chung nd Chroenwong, 1991; Chung nd Kim, 1997). However, these ppers rely on vribles tht re not redily observble, nd the models cnnot esily be pplied to rel firms. A pper by Ben-Horim nd Cllen (1989) is perhps closest in method to the present pper. They recommend the use of Tobin s Q to estimte future growth opportunities. 3 2 Dnbolt et l. (2002) lso provide criticl evlution of the Kester/Breley&Myers method. 3 A number of prior studies (e.g., Lng et l., (1989); Alexndrou nd Sudrsnm, (2001)) hve similrly used Tobin s Q, or the Mrket-to-Book rtio, s proxy for the level of growth opportunities. However, s these studies hve not ttempted to mesure the level of growth opportunities, nor commented on the impct of growth opportunities on the cost of cpitl, review of this strnd of literture is beyond the scope of this pper. 5

7 They use the dividend discount model, s we shll do, nd they demonstrte their model by pplying it to mjor US corportion. However, Ben-Horim nd Cllen do not use n sset-pricing model nd re concerned only to mesure the cost of equity cpitl defined s the return expected by investors in the shres. While prior studies hve ddressed the mesurement of growth opportunities, they do not with the exception of Chung nd Kim s (1997) theoreticl model ddress Myers nd Turnbull s (1977) centrl concern tht the trditionl method of clculting the cost of cpitl bsed on equity β provides n overestimte of the pproprite hurdle rte for compnies with vluble growth opportunities. In this pper, we im to ddress this gp in the literture. 3. A model for splitting the equity β The model is built on the following ssumptions: 1. The compny grows t constnt rte, g. This growth rte pplies to the book vlue of debt, equity nd ll ctegories of ssets nd libilities. It lso pplies to csh flows, ernings nd dividends. Growth is vlue creting, nd we ssume new projects, like existing projects, hve positive NPV s. Where do these vluble projects come from? We ssume, with Myers nd Turnbull, tht the cquisition of growth opportunities is independent of the cquisition of rel ssets. We do not model the cquisition of growth opportunities. We simply ssume tht the compny initilly holds set of future growth opportunities (with one opportunity for ech future yer) on which its future growth will be bsed. Investment is needed to generte csh-flows from growth opportunities, but growth opportunities themselves re not cquired through investment. 6

8 New projects re funded with the sme mix of debt nd equity s existing projects nd this gering rtio remins constnt throughout project s life. The dividend nd ll vribles growing t rte g re mesured on per shre bsis. Growth is mesured in rel terms. The Gordon (1959) dividend-discount model cn therefore be used to vlue the firm s shres. These ssumptions crete simple nd trctble model whose limittions must be recognised. The compny is on fixed growth trck nd its growth opportunities re not trditionl growth options. They do not hve ll the chrcteristics tht would be predicted by stndrd option pricing model. Growth is expected to continue in perpetuity. Although the compny uses prt of its growth opportunities every yer, the vlue of its overll set of growth opportunities is not diminished becuse its future strem of profitble investments hs drwn closer nd hence become more vluble. Although compnies often hve long-term growth opportunities, we recognise tht perpetul growth is n extreme cse. 2. Asset prices re set using the stndrd cpitl sset pricing model (CAPM). 3. As the compny grows, its new investment projects hve the sme chrcteristics s its existing projects. We ssume tht newly cquired ssets hve the sme bet, β, s the stock of existing ssets. Thus the sset bet remins constnt when new ssets re cquired. Similrly, we ssume tht the β of the growth opportunity which is used in ny yer is the sme s the β of the remining portfolio of growth opportunities. Hence, the growth opportunities bet, β g, remins constnt when investment tkes plce. At the point when investment tkes plce, the growth opportunity plus the (book) vlue of the equity investment needed to implement it re put together to 7

9 become the new sset-in-plce. Hence the β of ssets-in-plce (β ) is the weighted verge of the β of the growth opportunity (β g ) nd the β of the csh investment (β c ). The β of csh is zero. 4. The compny s debt is risk free nd the book vlue of debt is equl to its mrket vlue. Our model is bsed on the proposition tht corporte debt cpcity derives from csh generting ssets. 4 Specificlly, we ssume tht ll debt is ssocited with ssets-in-plce nd tht growth opportunities support no debt. Given these ssumptions nd constnt debt-equity rtio, the level of debt plys no prt in the model for the derivtion of the two bets. However, corporte debt will be relevnt when using the β s to derive corporte required rtes of return. We use the following definitions. The vribles in bold re those we seek to estimte, while those in norml typefce re ssumed to be directly observble or mesurble: D 0 The nnul dividend per shre, ssumed to be pid just prior to the ccounting yer-end. (We obtin the dt for the empiricl nlysis from Dtstrem). D 1 The next nnul dividend per shre, due to be pid one yer from the current dte. P s P P g E K s The shre price s t the ccounting yer end. The component of the shre price ttributble to ssets-in-plce. The component of the shre price ttributble to growth opportunities. The ccounting yer end book vlue of equity (per shre). Investors required rte of return on the firm s shres. 4 This proposition hs some support in the stndrd finnce literture. See e.g., Breley nd Myers (2003): Normlly the firm s optiml debt level increses s its ssets expnd. (p. 552). 8

10 K Investors required rte of return on equity funds used in the firm s ssets-inplce. K f The risk free rte of interest. (We proxy this by the yield on long-term government bonds). K g Investors required rte of return on the component of the shre price justified by growth opportunities. K m The expected return on the mrket portfolio. (We tke the equity risk premium s given). β s The bet of the firm s shres. β The bet of the equity ssocited with the firm s ssets-in-plce. 5 β g The bet ssocited with the mrket vlue of the firm s future growth opportunities. Our objective is to show how, bsed on our ssumptions, the other vribles cn be clculted from the six observed vribles. Equtions linking the vribles re given below. From CAPM, we cn clculte the required rte of return on the firm s equity s follows: K = K + β K K ) (1) s f s ( m f The constnt growth, dividend discount model, gives vlue for the shre s: D1 P = (2) s K - g s 5 Note we re using the term bet of ssets-in-plce to refer to the bet of equity used (longside debt) to finnce ssets-in-plce. It is not n sset bet creted by ungering n equity bet. 9

11 Since the dividend grows in proportion to the other dimensions of the compny, next yer s dividend cn be estimted s: D 1 = D (1 + ) (3) 0 g The price of the shre is mde up of the ssets-in-plce nd the growth opportunities components: P = P + (4) s P g The firm could decide to bndon its growth opportunities. This would not be vlue mximising decision, but it is theoreticl possibility. The price of tking up the growth opportunities next yer is E*g (i.e., the compny grows its equity bse t rte g). If the growth opportunities were bndoned, the dividend would be incresed by this mount. The expecttion for this new level of dividend is tht it would remin constnt (subject to norml business risk) nd cn be vlued s level perpetuity discounted t the ssets-in-plce rte: P D + E * g 1 = (5) K Note tht the logic of this eqution only works when growth opportunities re nonnegtive. Growth opportunities hve option-like chrcteristics. They could, hypotheticlly, be bndoned nd the compny could crry on t its existing scle nd profitbility. If n equivlent contrction opportunity or contrction option existed it would never be exercised. The model is symmetric. It cn be pplied to corporte growth but it cnnot be pplied to firms tht re shrinking in scle. This symmetry is generl chrcteristic of the growth opportunities literture. Since Myers nd Turnbull s observtion reltes specificlly to compnies tht possess vluble growth opportunities, this feture of the model is not problem for our purpose. 10

12 The required rte of return for ssets-in-plce is derived, by wy of CAPM, from the bet of ssets-in-plce: K K + β K K ) (6) = f ( m f Given tht shre is effectively portfolio composed of the ssets-in-plce nd the growth opportunities, the shre bet will be weighted verge of the bets of the two components: P P g β s = β + β (7) g Ps Ps At the point in time when growth opportunity is converted into n sset in plce, the β of the pckge (the growth opportunity plus the equity funding (csh) needed for conversion) is equl to the β of the newly creted sset-in-plce. We tret the pckge s portfolio of two ssets, nd note tht the β of csh (β c ) is zero. The vlue of ssets-in-plce (P ) exceeds the book vlue of equity (E) by the NPV of current projects (the ssets-in-plce). From our ssumptions, the rtio of NPV (for the growth opportunity) to ssocited equity is the sme t the point of investment s throughout the rest of the project s life. In ddition, this rtio is the sme for ll the projects tht mke up the compny s ssets-in plce. We hve lredy rgued tht the β of ssets-in-plce (β ) will be the weighted verge of the β of growth opportunities (β g ) nd the β of the csh needed to relise the opportunities. Wht re the weights in this reltionship? When the investment tkes plce, the totl vlue of the new sset-in-plce is mde up of the mount of equity (csh) invested plus 11

13 the vlue of the opportunity (which is the investment s NPV). The proportion of the vlue tht comes from the opportunity is therefore: Vlue of new ssets in plce Vlue of equity investment Vlue of new ssets in plce From our ssumptions, this proportion remins the sme throughout the life of ny project nd is the sme for ll projects undertken by the firm. The proportion cn therefore be written s: Vlue of ll ssets in plce Vlue of Book vlue of ll compny equity investment ll ssets in plce Or, expressed on per shre bsis: P E P Hence P E E β = β g + P P β c Recognising tht β C is zero, this simplifies to: β g P = β P - E (8) This hs given us set of eight equtions, nd eight unknown vribles: P, P g, g, D 1, K s, K, β nd β g. The nture of the eight equtions is such tht the system cn be solved reltively simply by process of substitution. 12

14 4. Adjusting the cost of cpitl When compny invests in new ssets-in-plce, the pproprite required rte of return must s rgued by Myers nd Turnbull (1977) be bsed on the risk of ssets-in-plce. For the equity element of funding, this is mesured by the bet for ssets-in-plce (β ) nd not the bet for the shre (β s ). The set of equtions in the previous section provides mens of estimting β. With this, we use CAPM to djust the cost of equity cpitl from tht for the whole shre (K s ) to the cost of equity cpitl for ssets-in-plce (K ). The equity bet of ssets-in-plce would be useful whether project pprisl used the weighted verge cost of cpitl (WACC), djusted present vlue (APV) or projectspecific rtes. However, for illustrting the impct of djusting the required rte of return for corporte investment pprisl in the presence of growth opportunities, we will concentrte on the djustment to WACC. The trditionl WACC not only uses n inpproprite cost of equity cpitl (K s rther thn K ), but lso inpproprite weights of debt nd equity. In clculting the cost-ofcpitl for cquiring new ssets, these should be the proportions used for finncing new (nd existing) ssets. In our model these proportions re derived from the whole of the compny s debt nd the equity mrket vlue of ssets-in-plce (P rther thn P s ). It should be noted tht in the model for splitting the equity β outlined bove, ll growth rtes, interest rtes nd required returns re rel rtes. However, WACC is not only nominl rte by convention, but the fter tx djustment for the cost of debt logiclly reltes to the nominl cost of debt. We therefore move in the clcultions tht follow from rel to nominl interest rtes. The costs of equity for both conventionl nd djusted WACC simply rise by the level of forecst infltion i.e., we replce the rte on indexlinked gilts by the rte on nominl gilts in the CAPM clcultions. For the cost of debt we 13

15 use the nominl rte of return on n index of corporte bonds, s clculted by Dtstrem. 6 For the clcultion of WACC, dditionl informtion is required on the compny s gering nd tx rte. We collect dt on compnies libilities (including both long-term nd short-term), nd ssume corporte tx rte (t) of 30%. The trditionl weighted verge cost of cpitl formul (WACC s ), cn be stted s: Ps Debt WACC s = * K s + * K Debt *(1 0.30) (9) P + Debt P + Debt s s where Debt refers to the level of debt (on per shre bsis), nd K Debt to the pre-tx cost of debt. The djusted WACC cn be stted s: P Debt WACC = * K + * K Debt *(1 0.30) (10) P + Debt P + Debt We next explore the implictions of these djustments empiriclly, bsed on smple of UK compnies. We cknowledge, however, number of limittions of our model. The dividend discount vlution model is useful for compnies with stedy rte of prospective growth, nd which lso offer dividends s substntil element in shreholder return. We re unble to pply our model to compnies not pying dividends. 7 We recognise the substntil nd well-known limittions of the constnt- 6 For the risk free interest rte we use the redemption yields on British government index linked Gilts over 5 yers nd on (nominl) ten yer Gilts, respectively, while for compny interest rtes we use the yield on the Dtstrem index for corporte bonds. 7 This is reltively smll problem for the UK, where the vst mjority of compnies py 14

16 growth dividend discount model nd of ccounting mesurements of ssets nd equity in plce. 5. Applying the model To pply the model, we use dt for the UK Finncil Times All-Shre constituent compnies over fifteen-yer period from Jnury 1990 to December We re ble to obtin the ccounting nd mrket dt from Dtstrem, nd mtch this with bet estimtes from Dimson nd Mrsh s Risk Mesurement Service, for smple of 5,059 firm-yers. We obtin interest rte dt from Dtstrem. Our model ssumes knowledge of the equity risk premium, nd in the clcultions tht follow we ssume this to be 6%, which is towrds the middle of the estimtes put forwrd in the literture (Dimson et l., 2003). Since our model ssumes constnt rte of growth for ll the firm s bsic metrics, we hve to exclude cses with zero or negtive vlue of equity (143 cses), with zero dividends (571 cses), nd where the book vlue of equity exceeds the shre price (630 cses) 8, leving smple of 3,715 firm-yers for which we cn clculte the vlue of growth opportunities (Smple B), s detiled in Tble 1. Tble 1 bout here substntil dividends. In their study of dividend pyments in the UK during the 1990s, Renneboog nd Trojnowski (2005) found 85% of listed compnies to py dividends, with dividends verging 3.1% of mrket cpitlistion, or 20.3% of ernings before interest nd tx. Shre repurchses were reltively uncommon, on verge used by less thn 6% of UK compnies. These firms lso tended to py substntil dividends. Shre repurchses verged only 0.4% of mrket cpitlistion, or 2.3% of EBIT. 8 In the model, this would imply tht existing projects hve negtive NPV nd no compny would wnt to grow through scling-up under these circumstnces. 15

17 However, this smple includes 1,144 cses of non-growth compnies for which the model does not generte positive vlue for growth opportunities. If the investment in new projects is optionl, investment opportunities should not hve negtive vlue. Furthermore, our model for djusting the cost of cpitl in the presence of growth opportunities is not pplicble to such compnies. We therefore remove these cses from the min prt of our nlysis, leving finl smple of 2,571 firm-yers (Smple A). We regrd Smple A s the most pproprite for our purposes, nd we focus on the results from this smple. However, we recognise tht growth opportunities will be mesured with n error. By discrding the negtive-growth cses, Smple A must incorporte, on verge, some element of upwrd bis. We therefore lso report results for Smple B, which is bis-free, but which includes, s explined bove, genuine non-growth compnies to which our model does not pply. Smple B thus provides lower bound to our estimtes. Note tht the 2,571 cses in Smple A re not drwn eqully from ech of the fifteen yers covered by our dt. Our smple period includes the new-technology bubble er (up to 2000) nd mjor fll in the UK mrket over the following three yers. Growth expecttions were much stronger during the bubble thn subsequently nd our nlysis will therefore identify more compnies s growth compnies in the erlier yers. For our purposes this does not pose problem, but we shll offer n nlysis of results by clendr yer lter in the pper. The results re reported in Tble 2. For the smple of firm-yers with non-negtive vlues of growth opportunities (Smple A), we find the verge proportion of equity vlue ccounted for by ssets-in-plce to be pproximtely 67%, with residul 33% ccounted for by the vlue of growth opportunities. Our model provides somewht lower estimtes for the vlue of growth opportunities thn hs generlly been suggested by prior 16

18 studies. Still, they ccount for significnt proportion of equity vlue for the mjority of compnies, suggesting tht the impct of djusting the cost of cpitl in the light of such growth opportunities my be non-trivil. Tble 2 bout here Our model requires djustment to both weights nd costs of equity in the WACC clcultion. The decomposition of the equity β gives us β for ssets-in-plce (β ) verging 0.82 compred to β s of The ppliction of our model lso results in reduced verge weighting for the equity component in the compny cpitl structure (from W s of 0.83 to W of 0.78), leding to reduction in the verge nominl cost of equity cpitl (from K s of 12.3% to K of 11.5%). The impct of these reclcultions is to move from n verge trditionl WACC of 11.1% to n djusted WACC of 10.0% reduction of lmost 1.1 percentge points when the cost of equity cpitl is clculted using our model. Our model hs ssumed tht compny investments convert pre-owned growth opportunity into profitble sset-in-plce. The djusted WACC is pproprite for this specific sitution. The tble, however, gives other informtion tht might be relevnt. If compny could purchse growth opportunities on their own ( possibility tht hs not formed prt of our model), the pproprite required return would be bsed on the risk of growth opportunities (β g ). In the specific cse where the compny ws mking corporte cquisition nd the trget compny s mix of growth opportunities nd ssets-inplce exctly mtched its own, then trditionl WACC would give the pproprite rte. As explined bove, the results for Smple A in Tble 2 contin some element of upwrd bis, nd we therefore lso report results for Smple B. The men vlue of growth 17

19 opportunities for Smple B is nturlly lower t 19% of firm vlue. So is the men djustment to the cost of cpitl t 0.4 percentge points. However, given tht our model, nd Myers nd Turnbull s insight, pply only to compnies with vluble growth opportunities, we cution ginst reding too much into the Smple B results. 6. Properties of the model nd sensitivity nlyses The results reported in Tble 2 re bsed on verges. We next explore: (i) the properties of growth opportunities over time; nd (ii) the sensitivity of the WACC djustment to the level of growth opportunities Time-Series Vritions in the Levels of Growth Opportunities. The pooled results suggest growth opportunities on verge ccount for 33% of shre vlue. However, our fifteen-yer smple period includes periods of very different economic climtes, nd we next explore the properties of our model estimtes over the smple period. As cn be seen from Figure 1, the vlue of growth opportunities hs vried significntly over time. As the UK recovered from recession in the erly 1990s, the vlue of growth opportunities incresed nd the proportion of firms with estimted negtive vlues of growth opportunities declined. However, the frequency of negtive vlues of growth opportunities once gin rose with the bursting of the new-technology bubble. For the compnies with vluble growth opportunities (Smple A), the verge level of growth opportunities incresed slowly during the 1990s, from 33% in 1990 to pek of 39% in 9 We hve lso tested the sensitivity of our model to the ssumed level of the equity risk premium. The number of firm-yers for which we identify positive growth opportunities increses with the risk premium, nd the djustments to the cost of cpitl would lso be somewht higher ssuming higher equity risk premium. With risk premium of 5% (7%), growth opportunities on verge ccount for 30% (34%) of firm vlue, compred to 33% bsed on n ssumed equity risk premium of 6%. While the men djustment to WACC mounts to 1.1 percentge points ssuming 6% equity risk premium (s reported in Tble 2), this flls to 0.8 percentge points ssuming 5% risk premium, or rise to 1.3 percentge points ssuming 7% equity risk premium. 18

20 2000, before flling to low of 24% in Figure 1 bout here As result of the flling interest rtes, there hve been lrge reductions in both the trditionl nd djusted verge weighted verge cost of cpitl over the smple period. However, s cn be seen from Figure 2, the men djustment to the cost of cpitl in the presence of growth opportunities hs remined reltively stble over the economic cycle, rnging from low of 0.9 percentge points during the recession in 1990 to high of 1.3 percentge points t the pek of the new economy boom in Figure 2 bout here 6.2. The Level of Growth Opportunities. The results in Tble 2 suggest the pproprite djustment to the cost of cpitl for our smple of compnies with positive growth opportunities verge 1.1 percentge points. However, the djustment to WACC will be lrger for compnies with high levels of growth opportunities thn for compnies where growth opportunities ccount for only smll proportion of firm vlue. To explore the reltionship between the WACC djustment nd the level of growth opportunities, we could split the smple bsed on the level of growth opportunities. However, s growth opportunities re mesured with n element of error, such n pproch my introduce bis 10. Insted, we split the smple into deciles bsed on the level of dividend yield. Low dividend yield cn be tken s proxy to identify compnies with high growth opportunities 11 nd, of course, dividend yields re mesured without 10 Splitting the smple bsed on the levels of growth opportunities, rther thn on the level of dividend yield, yield similr results to those reported. 11 The correltion between the level of dividend yield nd the percentge of vlue 19

21 sttisticl error. For completeness, the nlysis is bsed on Smple B, but we wrn gin tht we do not regrd the model s meningful when pplied to compnies with high dividend yields (which we ssocite with n bsence of vluble growth opportunities). The results re reported in Tble 3. Tble 3 bout here Tble 3 suggests there is monotonic inverse reltionship between the dividend yield nd the level of growth opportunities. For the decile of compnies with the lowest dividend yield, growth opportunities on verge ccount for 56% of equity vlue. For the seventh decile, they ccount for 10%. Deciles 8, 9 nd 10 contin non-growth compnies, which fll outside the scope of our model. The djustment to the weighted verge cost of cpitl rises with the level of growth opportunities, from low of 0.1 percentge points for decile 7 (where dividend yield verge 4.1% nd growth opportunities on verge ccount for 10% of equity vlue), to high of 2.1 percentge points for the decile of firmyers with the highest levels of growth opportunities (the lowest dividend yield, t 0.8%). We find there to be little vrition in the equity β between the deciles of compnies with vluble growth opportunities. However, consistent with the theories of Jensen nd Mekling (1976) nd Myers (1977), nd empiricl evidence by e.g., Titmn nd Wessels (1988) nd Rjn nd Zingles (1995), we find high growth (low dividend) compnies to hve lower gering thn compnies with lower levels of growth opportunities. W s (the proportion of equity in the blnce sheet) rises from 77% for compnies in decile 7 with low levels of growth opportunities, to 89% for the decile of compnies with the highest levels of growth opportunities. ccounted for by growth opportunities is (bsed on Smple B). 20

22 In Tble 3, conventionlly mesured WACC (WACC s ) ppers similr for compnies with vluble growth opportunities nd firms with few or no growth opportunities. These numbers, however, re potentilly misleding. The highest growth observtions in our dt set tend to come from the yers prior to 2000 when interest rtes were high. Our low growth observtions tend to come from the finl yers of our dt, when interest rtes were substntilly lower. To remove the influence of vrying interest rtes, the tble lso shows the WACC premium the vlue of WACC less the nominl risk free interest rte both for conventionl clcultion nd fter Myers-Turnbull djustment. Our discussion will focus on this mesure. The conventionl picture shows tht high growth compnies hve higher cost of cpitl (mesured by the WACC premium). They use more equity in their cpitl mix (78% t decile 7 compred to 89% t decile 1), but their equity is still just s risky. Equity β is similr cross the deciles (0.94 for decile 7 nd 0.98 for decile 1). The result is tht the conventionl WACC premium rises from 4.1% for decile 7 to 5.1% for decile 1. After Myers-Turnbull djustment nd with 100% equity finnce for growth opportunities the picture looks very different. For finncing ssets-in-plce we find no tendency for higher growth compnies to use less gering. This is notble observtion. The tendency for growth compnies to use low levels of gering is widely recognised in the empiricl literture, with Pecking order nd gency theories being offered s explntions. Our results suggest n lterntive possible explntion. The vribility in overll gering cn be fully explined by the proposition tht growth opportunities re 100% equity finnced. High growth nd lower growth compnies pper in our nlysis to use lmost exctly the sme level of gering in finncing ssets-in-plce (77% t decile 7 nd 79% t decile 1). 21

23 Tble 3 lso shows tht the ssets-in-plce equity β is lower for compnies with higher growth prospects (0.94 for decile 7 nd 0.70 for decile 1). The combined effect of the lower β nd the unchnged gering is tht the djusted WACC premium is ctully lower for compnies with higher growth potentil. It flls from 4.0% for decile 7 to 3.1% for decile 1. Without djustment it rises from 4.1% to 5.1%. The djusted numbers hve some intuitive ppel. Why should the hurdle rte be higher for sset investments by high-growth compny thn for low-growth compny? We might hypothesise tht, other fctors equl, there is less risk in incresing compny s stock of ssets when the business hs n underlying tendency to grow thn when it does not. The lower risk would led to lower required return. After Myers-Turnbull djustment the numbers re consistent with this rgument. 7. Conclusions This pper is bsed on the well-estblished division of shre vlue into growth opportunities nd ssets-in-plce. It hs built on the insight of Myers nd Turnbull (1977) who showed tht, in the presence of growth opportunities, the risk level of the compny s ssets will differ from the risk level of its shres. The required rte of return for sset investment should be djusted ccordingly. We hve constructed model, bsed on stndrd elements in finnce theory, which splits the equity β of compny into growth opportunities element nd n ssets-in-plce element, nd pplied this model to smple of 2,571 firm-yer cses for UK compnies over the period. Our results suggest (ssuming n equity risk premium of 6 percentge points) tht ssets in plce on verge ccount for 67% of equity vlue, leving residul 33% ttributble to growth opportunities. Splitting the equity bet (β s, which verges 0.97), we find the bet for ssets-in-plce (β ) to verge 0.82 nd the 22

24 bet of growth opportunities (β g ) to be Using the trditionl method for clculting hurdle rtes, we find the cost of cpitl to be generlly higher for compnies with high levels of growth opportunities. This finding is closely linked to the lower gering levels ssocited with high growth. However, fter mking Myers-Turnbull djustment nd ssuming growth opportunities re 100% equity finnced, we find tht compnies cross the growth spectrum use very similr proportions of debt nd equity to finnce ssets-in-plce, nd tht high growth compnies hve lower required returns for sset investments. The result follows from the observtion tht the risk (β) ssocited with equity investment in new ssets is lower for high growth compnies. Controlling for the effect of growth opportunities lowers the cost of cpitl for investment pprisl by n verge of 1.1 percentge points. The djustments increse with the level of growth opportunities, rising from low of 0.1 percentge points for the decile of firms with the lowest positive vlues of growth opportunities, to 2.1 percentge points for the decile with the highest levels of growth opportunities. Anlysis of the time-series properties of our model suggests both the level of growth opportunities nd the cost of cpitl hs vried over the economic cycle. However, our nlysis suggests the djustment to the cost of cpitl to tke ccount of the effect of growth opportunities hs remined reltively stble over the smple period. When they first recognised tht growth opportunities hd significnt implictions for the required rtes of return, Myers nd Turnbull (1977) referred to the prcticl nd theoreticl difficulties of mking pproprite djustments. Growth opportunities re 23

25 difficult to mesure ccurtely, nd the dividend discount model used here, like other methods, hs substntil limittions. Our nlysis is, we believe, the first to try nd quntify the implictions of Myers nd Turnbull s observtions bout growth opportunities, nd we hve demonstrted tht, for compnies with lrge growth opportunities, these implictions re on scle tht hs prcticl significnce. 24

26 References Alexndrou, G., nd Sudrsnm, S., (2001), Shreholder Welth Effects of Corporte Selloffs: Impct on Growth Opportunities, Economic Cycle nd Brgining Power, Europen Finncil Mngement, Vol. 7, No. 2, pp Andrés-Alonso, P., Azofr-Plenzuel, V., nd Fuente-Herrero, G., (2006), The Rel Options Component of Firm Vlue: The Cse of the Technologicl Corportion, Journl of Business Finnce & Accounting, Vol. 33, No. 1&2, pp Ben-Horim, M., nd Cllen, J.L., (1989), The Cost of Cpitl, Mculy's Durtion, nd Tobin s q, Journl of Finncil Reserch, Vol. 12, No. 2, Summer, pp Breley, R.A., nd Myers, S.C., (1991), Principles of Corporte Finnce, Fourth Edition, McGrw-Hill. Breley, R.A., nd Myers, S.C., (2003), Principles of Corporte Finnce, Seventh Edition, McGrw-Hill. Chung, K.H., nd Chroenwong, C., (1991), Investment Options, Assets in Plce, nd the Risk of Stocks, Finncil Mngement, Vol. 20, No. 3, Autumn, pp Chung, K.H., nd Kim, K.H., (1997), Growth Opportunities nd Investment Decisions: A New Perspective on the Cost of Cpitl, Journl of Business Finnce & Accounting, Vol. 24, No. 3&4, pp Dnbolt, J., Hirst, I., nd Jones, E., (2002), Mesuring Growth Opportunities, Applied Finncil Economics, Vol. 12, No. 3, pp Dimson, E., nd Mrch, P., (Eds.), Risk Mesurement Service, London Business School, Institute of Finnce nd Accounting. Dimson, E., Mrch, P., nd Stunton, M., (2003), Globl Evidence on the Equity Risk Premium, Journl of Applied Corporte Finnce, Vol. 15, No. 4, pp Gordon, M.J., (1959), Dividends, Ernings nd Stock Prices, Review of Economics nd Sttistics, Vol. 41, My, pp

27 Jensen, M., nd Mekling, W., (1976), Theory of the Firm: Mngeril Behvior, Agency Costs nd Cpitl Structure, Journl of Finncil Economics, Vol. 3, pp Kester, W.C., (1984), Tody's Options for Tomorrow's Growth, Hrvrd Business Review, Mrch/April, pp Kester, W.C., (1986), An Options Approch to Corporte Finnce, in Altmn, E.I., (Ed.), Hndbook of Corporte Finnce, Chpter 5, John Wiley & Sons. Lng, L., Stulz, R., nd Wlkling, R., (1989), Mngeril Performnce, Tobin s Q, nd the Gins from Successful Tender Offers, Journl of Finncil Economics, Vol. 24, pp Miles, J.A., (1986), Growth Options nd the Rel Determinnts of Systemtic Risk, Journl of Business Finnce nd Accounting, Vol. 13, No. 1, Spring, pp Miller, M.H., nd Modiglini, F., (1961), Dividend Policy, Growth nd the Vlution of Shres, Journl of Business, Vol. 34, October, Myers, S.C., (1977), Determinnts of Corporte Borrowing, Journl of Finncil Economics, Vol. 5, pp Myers, S.C., nd Turnbull, S.M., (1977), Cpitl Budgeting nd the Cpitl Asset Pricing Model: Good News nd Bd News, Journl of Finnce, Vol. 32, No. 2, My, pp Pindyck, R.S., (1988), Irreversible Investment, Cpcity Choice, nd the Vlue of the Firm, Americn Economic Review, Vol. 78, December, pp Rjn, R.G., nd Zingles, L., (1995), Wht Do We Know About Cpitl Structure? Some Evidence From Interntionl Dt, Journl of Finnce, Vol. 50, No. 5, pp Renneboog, L., nd Trojnowski, G., (2005), Ptterns in Pyout Policy nd Pyout Chnnel Choice of UK Firms in the 1990s, Finnce Working Pper No 70/2005, Europen Corporte Governnce Institute, nd SSRN working pper

28 Titmn, S., nd Wessels, R., (1988), The Determinnts of Cpitl Structure Choice, Journl of Finnce, Vol. 42, No. 1, pp

29 Tble 1 Smple The nlysis is bsed on finncil informtion for Finncil Times All-Shre constituent compnies with ccounting yer-ends between 1 Jnury 1990 nd 31 December As the model incorportes the dividend discount model, compnies with zero dividends re removed. Our model is unsuitble for compnies with negtive or zero book vlues or where the book vlue exceeds the mrket vlue of equity. Similrly, if compnies hve discretion in whether or not to exercise their growth options, growth opportunities should not hve negtive vlue. Firm-yers for which ccounting, mrket vlue nd bet dt is vilble: 5,059 Less: - Zero dividends Zero or negtive vlue for book equity (E) Book vlue of equity exceeding shre price (E>P s ) 630 Smple B 3,715 - Clculted vlue of growth opportunities (P g ) negtive 1,144 Smple A 2,571

30 Tble 2 Growth Opportunities, Bet Coefficients nd Cost of Cpitl The tble is bsed on n ssumed equity mrket risk premium of 6%. %P refers to the percentge of shre price ttributble to ssets-in-plce, nd %P g to the percentge ttributble to growth opportunities. g is the estimted rel rte of growth. W refers to the proportion of equity in the weighted verge cost of cpitl (WACC), bsed either on the trditionl WACC clcultion (W s ) or on the revised (W ) model. K s nd K refer to the overll cost of equity nd the cost of equity for ssets-inplce, respectively. β s, β nd β g re the bet coefficients for the shre (equity), for ssets-in-plce, nd for growth opportunities, respectively. Finlly, we clculte the WACC bsed on the trditionl model, nd on our revised model. N Men Medin Std. Dev. Min. Mx. Q1 Q3 Smple A Non-negtive growth opportunities %P 2, %P g 2, G 2, W s 2, W 2, K s (%) 2, K (%) 2, β s 2, β 2, β g 2, WACC s (%) 2, WACC (%) 2, Adj to WACC 2, Smple B Including negtive growth opportunities %P 3, %P g 3, g 3, W s 3, W 3, K s (%) 3, K (%) 3, β s 3, β 3, β g 3, WACC s (%) 3, WACC (%) 3, Adj to WACC 3,

31 Tble 3 Sensitivity to the Level of Dividend Yield WACC Adj to The tble reports men vlues, for deciles bsed on the level of dividend yield (%DY). The nlysis is bsed on Smple B (3,715 firm-yer observtions), including negtive estimtes of the vlue of growth opportunities. %P g refers to the percentge ttributble to growth opportunities, β s to the bet coefficient for the shre, β to the bet for ssets in plce, W s to the proportion of equity finnce in the trditionl weighted verge cost of cpitl clcultion, nd W to the proportion of equity finnce in the djusted weighted verge cost of cpitl clcultion, K s to the trditionl cost of equity cpitl, K to the cost of equity for ssets-in-plce, WACC s to the weighted verge cost of cpitl bsed on the trditionl eqution nd WACC to the weighted verge cost of cpitl corrected to tke into ccount the presence of growth opportunities. R f refers to the nominl risk free interest rte. Equtions re s specified in the pper. %DY %P g β s β W s W K s K WACC s WACC R f WACC s - R f - R f WACC Deciles

32 Smple Yer Smple A Smple B % Negtive Pg Fig. 1. Percentge Growth Opportunities Notes: The figure shows the time-series vrition in the estimted men percentge of shre prices ccounted for by growth opportunities. Smple A refers to the smple of 2,571 firm-yers with non-negtive estimted vlues of growth opportunities (P g ), while Smple B refers to the full smple of 3,715 firm-yers, including negtive P g. %Negtive P g shows the time-vrition in the percentge proportion of the smple with negtive estimted vlues for P g. The estimtions re bsed on n ssumed equity risk premium of 6%, s in Tble 2.

33 Smple Yer WACCs WACC Fig. 2. Percentge Weighted Averge Cost of Cpitl Notes: The figure shows the time-series vrition in the men vlues of the weighted verge cost of cpitl, estimted using the trditionl (WACC s, s in eqution 9) nd the djusted (WACC, s in eqution 10) model, s discussed in the text. The nlysis is bsed on Smple A (2,571 cses).