the cost of equity, the c.a.p.m. and management

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THE COST OF EQU ITY, TH E C.A.P.M. AN D M AN AG EM ENTOBJECTIVES UNDER UN CER TAIN TY

JOHN R. GRINYER"

INTRODUCTION

This paper considers the choice of a cost of equ ity capital rate, for use in capitalbudgeting, under the uncertainty typically prevailing in the stock market. Itsuggests that the maximisation of shareholders' wealth is likely to be achievedmore by luck than judgement, given that the shareholders' opportun ity costprobably differs from the market's required rate of return and is unknow n. Theauthor therefore contends that the shareholders' wealth maximisation objectiveis not operationally sensible as a proxy for shareholder satisficing in the multiple-

objective environment of m odern business. He suggests tha t a shareholdersatisficing objective be explicitly specified for capital budgeting decisions, and heconsiders how the Capital Asset Pricing Model (C.A.P.M.) could then be usedto estimate the rate of return required from the investment of equity funds,using a multi-period analysis recognising the term structure of interest rates.

Appraisal of capital projects presupposes the recognition of an objective function .Many people now accept tha t the m anagement of private industry has responsi-bilities to a variety of interest groups, e.g. employees, creditors, customers,

shareholders and the local and national cum munities. The Trueblood Report (and the Corporate Report (2) provide evidence of such thinking in the U.S.A.and in the U.K., respectively, for in specifying the need for the corporation toreport to a number of groups, they implicitly recognise tha t management hasresponsibilities to those groups. As these seem likely to have different, andfrequently conflicting, interests, it initially seems reasonable t o suggest that asingie financial objective based on the requirements of only one subset of thepeople to whom management is accountable will be inadequate for decisionpurposes. In contrast t o such thinking, the literature of financial management

usually assumes the single objective of the m aximisation of current shareprice.' Such an approach may, however, be sensible because perceived successor failure in meeting the requirements of shareholders could, via the capitalmarkets, affect the future availability of funds and the continued control ofthe business by its existing management. Failure t o satisfy shareholders cantherefore reduce the likelihood of achievement of other management objectives,

*The author wishes to acknowledge the helpful comm ents received from prof:

R.A , Brealey, h o t M. Bromwich and Mr. F. Fishwick, on early dra fts of thispaper. Errors o f omission andcom mission are, however, his. The author isProfessor of Accountancy at Dundee L'niversity. (Paper received July 19 75 ,revised August 19 7 6 )

Journal o f Business Finance & Accounting, 3,4(1976) 101



so tha t such satisfaction may be considered to be a dominant constraint andan appropriate choice of objective function. Clearly other aims feature in theanalysis of capital projects, bu t can be considered as constraints and excludedfrom the definition of that function. H.A. imon (4) discussed this type ofapproach.

We therefore assume, initially, that the sole aim of management is t o maximisethe welfare of the f m ’ s shareholders,as a means of satisfying them, but wemodify thisobjective at an appropriate point in the analysis. Further assumptions,adopted throughout the paper to limit the analysis t o a comprehensible volume,are as follows:

1. Firms are considered to be financed entirely by the funds of existing equityholders, and are not sufficiently large to be able to affect the market price for

money.

2. Taxation does not affect the analyses.

3. If the f m oes not invest shareholders’ funds, their alternative investmentis in the national equity markets.

4. On the introduction of uncertainty, the expectations of management andinvestors are nonhomogeneous.

We commence our analysis, however, by assuming markets whjch ‘correctly’ priceshares,in the Sense tha t securities sell for sums which adequately reflect the cashto be derived from holding them and the rate of return expected by the market.

SHAREHOLDER WEALTH M AXIM ISAT ION W ITH ’CORRECTLY’PRICED SHARES

Consider a world in which there were no transaction costs and there was certaintyconcerning the cash flows associated with all investment opportunities. Given the

relevant assumptions outlined earlier, the utility of shareholders’ consumptionwould be maximised if management accepted all capital projects yielding returnsgreater than or equal t o the single riskless rate of interest which would prevail.Such a policy would also maximise current share price, which would be thepresent value of the cash flows to be derived from owning the share, whendiscounted at the riskless rate. When transactions costs are included in theanalysis, the criterion rate is found to vary depending on whether the ahareholderis a lender (investor) or borrower (seller of shares).? It is ansumed, throughoutthispaper, that he is a lender for the entire period of the project’, lifetime: m

the appropriate rate is found by reference to his alternative invmtmentopportunity, and we maximise theutility of the shareholder’s consumption by

102 John R . Grinyer



maximising his terminal wealth. Figure 1 illustrates the position assuming a twoperiod world and initial funds of (1-0). Curve 111 shows the cash available to the

shareholder, in periods 0 and 1,with different amounts of investment in thephysical assets available to the fm .Theslope of the curve at any point reflectsthe rate of return on the marginal project at that point. Instead of investing in

physical assets the shareholder could invest in monetary claims, e.g. shares, andthe lines LLl and IL, show possible combinations of consum ption available byinvesting(L-0) and (1-0) respectively in thisway. The slope of these linesrefleets the market’s risk free rate of return after adjusting for transaction costs.Adoption of the maximisation of terminal wealth objective implies tha t the fmshould enable the shareholder to reach the highest position possible on the y axis,

and that can be done by investing (I-F) in physical assets and the balance (F-0)in monetary assets - enabling the owner t o reach point L1 n period 1. Thus, inthese circumstances, the cut off rate for physical investment should be the

market’s required risk-free rate of re turn, for the shareholder has always theopportunity to invest to earn that rate elsewhere.

FIGURE 1

Y

Amount availablein Period 1.

Ll

in

Period 0

We now introduce uncertainty, but retain the assumption that the market

‘correctly’ prices shares. The opportunity cost of investment in the fm’s projectsmust now be represented by the rate of return expected by the market onalternative equities of equivalent risk to the projects, since, by assumption, such

returns equal the actual returns to be earned on those equities? so that that rate

must be the required project cut-off rate. A model which enables the calculationof the rate of return expected by the market therefore becomes necessary as soonas we introduce uncertainty into the analysis. Such a model is to be found in the

The cost of equity , the W M nd management object ives 103



Sharpe, Lh tn er et a1 Capital Asset Pricing Model (CAPM): the simplest formof which can be defined as fallows:

Rjt it + Bjt (Rmt - it) (1)

where

a weighting relating the prem ium for systematic risk on share j during period tto the system atic risk premium for the m arket as a whole.

R, is the expected retu rn from investing in the market as a whole for period 1

Rjt is the expected return on share j during period t .

it is the “risk free” rate for period t, i.e. the rate available on single-periodrisk-free lending.

(R, - it ) is the m arket premium for system atic risk, which is the risk whichcannot be diversified away.

Empirical work6 has suggested that the simple CAPM outlined above is not acomplete description of the way in which the market values capital assets. It isalso recognised that the model is based on somewhat unrealistic assumptions.’Despite these shortcom ings, the CAPM is probably the most developedempirically-tested theory of security valuation which we currently have, and ithas gained wide academic acceptance and offers a practical approach t o th e

estimation of required discount rates. On these grounds it seems acceptable, as a

model of market behaviour, for use in estimating rates of return required byinvestors. Clearly, ‘correctly’ priced shares are unlikely generally to exist, so we

now remove that assumption.

SHAREHOLDER WEALTH MA XIMISATION WITH ‘INCOR RECT LYPRICED SHARES

Analysis usually considers an ex ante position when, as risk prem iums areexpectgd compensation for additional uncertainty perceived at the time of takinga decision, it is reasonable to expect that equivalent return be required forequivalent risk, i.e. that the required return should be selected by reference tothe investment’s risk class. We are looking at the stock market aa an alternative

investment to the capital projects under consideration. When a fm invedrshareholders’ funds, within thefm,he latter are asmuned to lose I -am of

104 John R.Grinyer



cash which would otherwise be generated externally, and to forego the actual andnot an estimated flow - lthough it is obviously impossible to know the actualflow at the time of the decision. It is the actual flow which is the opportun itycost and, if shares are not ‘correctly’ priced, the CAPM derived rate may be aninadequate surrogate for that cost. This concept is central to be subsequentanalysis, so it seems worthwhile to consider it in greater detail. The followingexample illustrates the thinking involved.

EXAMPLE

At a point in time, the equity market operates with a required (expected) rate ofreturn (R,) of lo%, and the risk free rate of interest (i) is 6%.The risk premiumfor investing in the va rk et iis therefore 4%, and it is that rate which is required byinvestors as a whole to com pensate them for the disutility of risk-taking. For

ease of understanding, we will assume that cash flows derived from shareholdingsare in the form of perpetuities, so, for every €100 invested in the market,investors expect to receive a perpetuity of €10 (including €4 compensation forrisk-taking). Their expectations are wrong, and they will actualb receive aperpetuity of €15 , providing a return of 15% instead of the 10% hey anticipate.In this case, we can reason that the opportun ity cost of market investment iseither -

(a)

returns in excess of requirements (15%-

o%), i.e. 11% or

(b)plus the excess return (1 5% - 10%) equals 15%. Note that the differencebetween these rates is the risk premium of 4%. The opportun ity cost is, inboth approaches, based on actual returns -which are, of course, unknownat the time of taking the decision to invest. We proceed by using the rateincluding compensation for risk-taking (i.e. ‘b’ above).

a risk-adjusted rate equal t o the required risk-free rate 6% , plus the

a rate including compensationfor risk-taking of the required return 10%

Of course the impossibility of knowing the opportunity cost ex ante makes it oflittle practical value, but use of the concept with ex post information enables usto consider the likelihood of conventional approaches achieving their statedobjectives. Further understanding of the concept may be obtained by consideringFigure 2, which is Figure 1 altered by the addition of a further line CC l ,whichshows the actual amount which wi l l be obtained in period 1 by investment in thestock market of (C-0) in period 0. The slope of LLl still reflects the returnexpected by the market, but now differs from the actual return. Assuming hatthe disutility of perceived risk is fully compensated for by the risk premiumincluded in the expected return, management could, by increasing the cut-off

rate to the actual opportunity cost (reflected by CCI) and allowing theshareholders personally to invest more on the share market, have obtained for

105he cost of equity, the CAPM and management objectives



shareholders a larger amount in period 1 without altering the disutility ofrisk-taking. Ideally, it would invest (I-Fl) in physical assets and leave (F, -0)

for shareholders to invest, which is a different solution to one wing the market'sexpected rate of return as criterion rate.

FIGURE 2

Y

Amount availablein Period 1

X

0 F F l I C L Amount availableinperiod 0

Even casual observation implies .that, during some periods, investors' expectationschange so dramatically that the general levels of market prices often cannot evenbe approxiinations of the actual cash flows discounted at the market's requiredrates of return. Consider the behaviour of prices on the New York and Londonstock exchanges during the period January 1973 to June 1975. During the years1973 and 1974 prices fell by almost 50% in New York and by about 70% inLondon, then in November 1974 and the first four months of 1975 they rose by50% in New York and 130% in London. Such major changes in a short periodcould only derive from very significant revisions of formerly-held expectations.The percentages are calculated in money terms but the changes are so markedthat inferences drawn from them would also seem valid in real terms.

The practical implications of the concept of the investors' opportunity cost,advanced above, can be illustrated using a hypothetical stock and the changesobserved on the London market in 1975. Assume that ownership of a share of XLimited will actually provide a perpertuity of €0.6,and, at January 1st 1975, the

share price stood at €1 SO (presumably because investors then expected a muchlower figure of income than will actually be derived from owning the share). By




early June 1975, he share price had risen to €3.50 n line with the F.T.Industrial Ordinary Index. At €3.50,n investor would buy virtually the sameactual stream of income as he could have purchased for €1.50 ix months earlier.The long-term return available from investment in X Ltd. was 40% in January1975, nd 17% in June 1975. f X Ltd. represented the shareholders’ alternative

investment, it is this variation which has occurred in the opportunity “cost ofequity capital” during the six-month period, for the rates 40% and 17% representapportunities alternative to the firm’s investments. Depending o n one’sassumptions concerning investors’ holding periods, and the pattern of cash flowsto be derived from investing, widely different figures of alternative cost could becalculated - .g. at one extreme the investment yields 130% return for a holdingperiod of six months. These available returns seem likely t o be dissimilar to therate expected by the market at any time during the period.

Adoption of the objective of maximisation of future share price would, under anassumption that fuhtre share prices will adequately reflect the underlying cashflow from the firm, yield a similar analysis. This can be illustrated by elaboratingon the example of X Ltd. as follows.

Assume that

(1)return of 17% from investing in X Ltd.

(2)

throughout the period January to June 1975 he market expected a

the company had l,OOO,OOO ssued shares at 1st January 1975.

(3)€7 0,000.

on 2nd January it issued a further 500,000 hares for net proceeds of

(4)this being greater than the expected rate of 17%.

the €750,000 raised under (3) was invested to yield 20% in perpetuity,

The stock market price per share in June could then be calculated as follows:

(a) (b)Without transactions With transactions

3&4 3&4

Total Value EOOOs

Business existing 1st Jan.6

.17(- x 1,000,000)

New business

(”or

3,530 approx) 3,530 approx)

880 ”-3,530 4,410

The cost o f equity, the CAPM and management objectives 107



(a) (b)Number of issued sharesin June 1,000,000 1,500,000

Average price per share €3.5 €2.9

So the adoption of the expected rate of return as a criterion rate, reducedfutu re share price below th e level which would otherwise have applied, evenwhen the investments yielded returns in excess of tha t rate. The reader canwork out for himself that the firm would have had t o invest the €750 ,000 toyield at least 40% (the equity opportunity rate previously identified) to avoida fall in share price. Clearly, if it were possible, the adoption of the shareholderopportun ity cost approach could serve, over time, t o maximise individualshare prices - which is exactly wha t one would have anticipated .

It is possible that the above illustrations are atypical because they are based onan exceptional period. Merrett and Sykes’ (8) 1966 study implies otherwise.Their results are summarised by the data in Appendix A and provide evidenceof continuing and large fluctuations in returns available from investment inU.K. equities at d ifferent times. A different study by Barr (9) appears tosupport rather than refu te these conclusions so far as the U.K. is concerned.Evidence concerning the annual monetary return to be obtained by investingin the Standard and Poor’s Composite Index for all years from 1929 to 1972is provided by Sharpe (10). He found a mean return of 10.64% with a standard

deviation of 21.06% and sizeable fluctua tions in annual return occurredthroughout the period tested, so his data implies the existence of frequentand marked revision of expectations by the U.S.A. market. It seems mostlikely th at very of ten th e markets provide prices which are poor approxima-tions of the actua l future cash flows discounted at the rate of re turnrequired by the market. The CAPM helps us to estim ate the latter rate, andconventional wisdom tells us that its use in capital budgeting will maximiseshareholders’ wealth.* This paper argues tha t such an ou tcome will only beachieved if share prices,are adequate reflections of actual future cash flowsand expected rates of return , and that that is unlikely under the uncertaintytypically existing in practice. So it seems that the use of ma rket expectationsderived figures of equity cost are unlikely to maximise shareholders’ terminalwealth.

Under assumptions of perfec t, frictionless, markets and homogeneousexpectations on the part of all market participants - ncluding management -it can be argued that current wealth in the form of share price can bepaximised by accepting all projects with positive net present values whendiscounted at the market’s required rate for the sys tematic risk class involved.

Such an outcome would free the analysis from the restrictive assumptionConcerning homogeneous consumption preferences, identified in note 3, fora l l shareholders could then choose either to hold or sell the investment




represented by the pro ject. A well kno wn presen tation of this type of approach

is to be foun d in Fama and Miller (12). This paper is based on the assumptionthat expectations are not hom ogeneous so far as management and t he m arket areconcerne d, because delays occur in th e communica tion of managements’forecasts to the marke t and in the market’s acceptance of them (even if they are

correct). P.S.Albin (13) discusses this problem more fully. Markets are not,therefore, assumed to be perfect in the manner described above, although theycan be “efficient” (in the sense that share prices reflect all publicly availableinformation) and encompass homogeneou s investor expectations withou taffecting the analysis. Failure of the m arket price pro mp tly to reflect manage-ment’s expecta tions seems sufficient t o invalidate th e current wealth-basedapproach so the adoption of the “ oppo rtunity cost” basis outlin ed in this papermerits serious consideration.

MAN AGE MEN T OBJECTIVES UNDER UNC ERTA INTY

There is n o evidence to suggest that managements are usually exp ert a t predictingthe futu re movements in general share prices, and i t seems likely th at in suchmatters their judgement is inferior t o that of professional investors.’ In practice,then, operating under equivalent or greater uncertainty th an the market, it maybe unwise for managements to assume that the m arket do es not provide anadequate measure of the worth of shares in general. If the decisionmaker wishesto rnaximise shareholders’ wealth and has t o assume that share prices are ‘correct’,it is probable th at he cannot d o bette r th an estimate the re turn anticipated by

the marke t when investing in equivalent risk equities, and use t ha t as th e cost ofequ ity capital. Our discussion has identified, however, th at the cost of equityfigure so derived may not only be wrong because of th e failure of the analyst tocorrectly estimate the market’s required rate of return , but also (probably to amuch greater extent) because of the m arket’s failure to adequa tely forecastfuture cash flows to be derived fro m holding shares.

Appendix B shows tha t, even if management could adequately estimate theshareholders’ opportunity costs, it would still have to accept highly unrealistic

assumptions in capital project appraisals using maximisation of existing share-holders’ wealth as the objective fun ctio n. In prac tice, neither management no rthe marke t seems likely t o be able consistently to estimate that o ppo rtunity costwithin an acceptable range of accuracy. Sizeable error m ay , there fore, exist a ttwo stages in the analysis and it seems likely that shareholders’ wealth willusually be maximised m ore by luck than b y judgement. This is an unsatisfactoryposition. At the commen cement of this paper, it was suggested that man agementprobably wishes to satisfice so far as shareholders’ intere sts are concern ed and, asthe adoption of the maximisation of shareholders’ wealth proxy for such anobjective appears to fail, it seems sensible for management to resta te its satisficingrequirement more directly in a form amenable t o analysis witho ut the difficulties

l’Xe cost of equ ity, the CAPM and tnanagement objectives 109



identified above. There are a number of grounds for selecting the provision toshareholders of the market’s currently required rate of retum as the satisficingcriterion, e.g.

(a) It is presumably the rate which has been used in investor decisions

concerning investment in alternative markets, after taking account of requiredcompensation for the disutility of d ifferential risk - nd therefore probablyreflects opportunity costs in nonequity markets.

(b) One can argue that it should equal the marginal rate of time preference,after compensation for risk-taking, of investors and therefore the firms’shareholders (under the assumption that they are a l l currently investors ratherthan borrowers). It should, therefore, help them to maximise the u tility oftheir consumption decisions over time if the rate is adopted.

(c)holders reasonably satisfied and failure to provide it might create dissatis-faction.

As it is the rate which they expect, provision of it should leave share-

Following the above reasoning, we now define the objective of the firm as “themaximisation of specified objectives, subject to providing shareholders with thereturn which they would have required, at the date of expenditure of their funds,from investments of equivalent risk”. This definition is compatible with a varietyof objectives, such as maximising the size of the firm, which can be viewed as

proxies for nonquantifiab1e.satisfactions o be derived by participants in thefirm. A purpose of the project appraisal must now be to estimate the extent towhich considered projects meet the shareholders’ required return constraint. Ifshare prices were always good approximations of future cash flows and the rateof return currently expected by shareholders from investments in the appropriaterisk class, the shareholder could sell his shares at any time to realise his expectedreturn. (Subject, of course, to the distorting effects of transaction costs.) In thatunlikely event, the market’s required return could be used with the satisficingobjective in capital budgeting without further assumptions. The real world

conditions of significant variability in share prices require, however, an additionalassumption to validate capital project appraisal techniques. Such an assumption,now generally adopted in this paper, is that the firm’s existing shareholders willhold their shares until the terminal date of the project, so that the firm coulddistribute the total project net cash inflows to them. This relieves the analysis ofthe problems deriving from ‘incorrectly’ priced shares. Within this framework,the familiar discounted cash flow techniques can be used, subject only to theirwell known limitations concerning reinvestment rates, with the selected criterionrate.




ESTIMATIN G TH E R E W I R E D RA TE

Even if management adopts the satisficing objective, it has still tO estimate thereturn required by investors from inves tments of th e project’s risk class. Suchestimates require a mod el of market behaviour an d, as discussed above , the

CAPM seems likely to be the most appropria te choice given the ex isting state ofknowledge. The la tter , however, defines return s by reference t o a single period.(In practice “B’s” have usually been calculated for relatively short periods, e.g.of one month’s duration.) Attempts t o adapt the model t o a multi-period setting”often seem complex, requiring the input of data which is unlikely to be readilyestimated by m anagem ent, ye t not fully to utilise the information implicit incurrent market data. Some improvement may be possible by simplifying theprocedure and recognising in the analysis the existen ce of a term-struc ture ofinterest rates. The most casual observation reveals such a struc ture which, at any

point in time, yields different rates of interest for loans of different maturity. Thispaper will not discuss the theories suggested to explain this phenomenon : it issufficient tha t it exists and has interesting implications for the use of the CAF’M,

e.g.

(a)assumed that it does) and

a different ‘riskless’ rate may exist fo r each term (in this paper it is

(b)rate can only be calculated under estimates of reinvestment rates during theperiod; bu t such estimates are themselves presumably based o n probabilitydistribu tions such that the rate is not ‘riskless’ aft er all!

for a long period, including a number of receipts of int ere st, the risk-less

Comment ‘b’ might be challenged on the basis that the interest rate iscontractually determined, so that it must be riskless. Such reasoning couldproceed by defining the rate as iI T in equa tion 3 .

where i is the interest payable as a proportion of the amount borrowed,

B is the amou nt borrowed,itT is the compound interest rate actually received by the investor for a loan

of T periods,M is the amount paid to the investor on maturity, andT is the period at the end of which the ioan is repaid.

As all other terms are contractually agreed, i I T is also contractually agreed andcan be viewed as risk free. The CAPM is a single-period model, however, so the

111he cost of equ ity, the CAPM and nianagenient o bjectiv es



T-period ‘risk-free’rate must surely require forward contracts for onward lendingof future returns, i.e. i t is i 2 ~n equation 4.

T TZ iB ( I1 (1 + i j n , ) + M

o= n = t = n + -B (4)1 t i 2 T

where i3nt is the reinvestment rate in period t for the cash inflow in period n,

noting that the investor may face a different term structure of rates in eachperiod n.i 2 ~s the single period rate which solves the equation and other terms are aspreviously defined.T

t = n + 1I1 means multiplying the following expression (T-n) times, with the

variables taking on the assigned values.

Only if i3,,t was contractually set at the outset of a transaction, could it beregarded as riskless, so a riskless rate fo r a multi-period term seems unlikely toexist. Nevertheless, the CAPM seems likely to be useful for estimating requiredreturns, so further analysis is necessary to identify the assumptions implied by itsuse for that purpose. If we substitute (1 + i 2 ~ 0 ) ~n Equation 4, where i 2 ~ 0sthe periodic rate such that 1 t i 2 ~(1 + i ~ ~ o ) ~ ,nd assume that ij n t equalsi 2 p for all periods, we find that Equatioq 4 converts to the form of Equation 3,

such that i 2 ~ 0 iIT. We are unlikely t o be able adequately to forecast ij n t, so wemight just as well assume that i t equals iIT and use the la tter equation, which hasthe advantage that it seems more com patible with accepted thinking andevaluation methods. This step is, however, based on judgement and convenienceand many alternatives may be defended on the same grounds.

Assuming that i jn t equals iIT, we can define the single-period “riskless’ rate of

return for a T-period term, h ~ ,s

Insertion of this in equation 1 then gives a required return (over the T-periodterm for a project of system atic risk class j) of

%If = i4T BjT(RmT - hT) (6 )

where B ~ Ts the B for systematic risk j and a T-period term,R,,,T is the expected market return for a term of T-periods

% jT is the single-period return expected for a T-period term and systematic

112 John R.Grinyer



risk class j, and o ther symbols are as previously defined.

The reader wi l l not that our analysis is still in the form of a single-period model.Now defme R * 4 ~ js the periodic rate of return such that

Projects would meet the estimated required rate of return, defmed in equation 6,if

which can be shown as

where I is the amount of the investment in the project,C, is the project cash flow in period n

rnt is the return in period t of investments (at equivalent systematic risk) inperiod n, and other terms are as previously defined.

If we assume that r n t = R*4T j for d eriods, equation 9 converts to

which is the ”V calculation.

We have, then, identified that we can validly use the multi-period rate R * 4 ~ jnNw alculations under the assumptions

(a)securities is constant and equals the geometric mean of the single-periodreturn (after reinvestment) less one - .e. that

i 3 n t = ( I + iz T ) T - 1 for allyears

that the reinvestment rate on periodic payments on ‘riskless’ T-term

I-

- so that the ‘riskless’ T-term rate is fully defined by contractual flows, and

The cost of equity, the CAPM and management objectives 113



(b)j , of cash flows generated by projects o f that risk class, is the same as theselected discount rate - .e. tha t rnt = R * 4 ~ jor all periods.

that the rate of return available on reinvestment in systema tic risk class

These assumptions are unrealistic, but may provide as plausible a set of values as

can be produced by management forecasts. If that is the case they would appearto be acceptable as a basis for practical decisions, when the NPV criterion ratecan be estima ted using equa tions 6 and 7 , i.e. it is

1

i 4 T F - 1

Obviously the estim ates of many of the variables in the equation are likely to bewrong - bu t this may still be the best approach available! The variables 4~ andR m ~an be estimated from data concerning present and past market transactions.

B ~ Ts more difficult t o estimate because it is observed tha t the B applied by themarket to a firm’s shares changes over time. (W.F. Sharpe and G.M. Cooper haveprovided an interesting paper on this topic , (16).) A natural starting point forestimating B for a capital project may be the B’s calculated as applying t o thefirm in the past. Management could then determine some rules t o enable it toadjust B, for project assessment, by reference to t he perceived project risk class(e.g. a replacement project in the firm’s major line of business might be assignedthe firm’s B). This procedure seems crude, but an even less satisfactory approachhas usually applied in the past, when no specific recognition has typically been

given t o systematic risk. Adoption of the assu mptions specified earlier wouldthen allow the derived discount rate t o be validly used in the fu rtherance of theshareholder satisficing objective.

CONCLUSIONS

This paper claims that in the oncertain market environment the maximisation ofshareholders’ wealth is likely to be only achievable by luck and not by judgment,because highly unrealistic assumptions, concerning both the market and th e

individual shareholder’s alternative investment, are then necessary to the validuse of the expec ted marke t rate of return with discounting models. Themaximising objective conventionally advanced in the literature of financialmanagement, th erefo re seems inappropriate as a proxy for the satisficing ofshareholders’ interests. An alternative, directly satisficing, aim is to provideshareholders with the return which they require at the date of the investment,i.e. the market’s expected rate of return . Such an approach seems fully consistentwith the concep t of multiple corporate objectives and to require less unrealisticassumptions than th e wealth maximisation model when using capital projectevaluation methods. The analysis of the paper suggests a capital budgetingapplication of the con cepts of the CAPM w h c h recognises the term-structure ofinterest rates when estimating the required rate of return for multi-period projects.

114 John R.Grinyer



Almost inevitably this paper poses more problem s than it solves. I t has, however,developed a line of analysis which may prove relevant to the cur ren t businessenvironment and lead t o new directions for the development of theo ry: forexam ple, it seems likely tha t an original and relevant depar ture from receivedwisdom WIIIesult from the application of the satisficing model in a geared firm.

NOTES

E.g. see Bogue and Roll (3).

The conclusions of the paragraph are supported by extensive analysis, whichwill not be outlined here bu t can be found elsewhere, e.g. in Grinyer ( 5 ) .

This implies homogeneity of shareholders’ consumption preferences, to the

extent that they are all assumed to prefer consumption on or after the terminaldate of the pro ject, which is clearly unrealistic. I t appears that any approachto analysis in this area requires the ad opt ion of dubious assumptions, and inthe end choice between alternatives depends upon the reader’s judgemen t asto which assumptions are most acceptable.

This is a potentially confusing point, because we are including risk premiumsin a world of certain returns. Redefine the slope of lines such as LLI as themarket’s expected rate of return, then, under an assumption of ‘correctly’priced shares, the lines in figure 1 are correct in the sense that they correctlypredict the consumption possible in period 1 by present investment inmonetary assets. But under uncertainty investors would not know that, and,assuming tha t th ey are risk averse, they would require compensa tion by wayof a risk premium for the disutility of risk bearing. O n this basis risk premiumscan be perceived as the price paid for the acceptance of such d isutility, whichconcept must surely be reasonable since we would on a conventiona l analysisei pec t an investor who was indifferent to risk, to discount the expe cted valuesof fKture cash flows at the riskless rate o f interest, for the acceptance of riskcreates no disutility for him.

A summary of the basic literature on the CAPM s to be found in Jensen (6).

See Jensen (6) for a summary of the early work.

See Rubinstein (7) for a discussion of the assumptions.

See Van Horne (1 1) for a well known exposition of this view.

As they appear to consider that the timing of issues of equity is imp orta nt,however, it appears that in practice managements do act on th e assumption

The cost of equi ty , th e CAPM and management objectives 115



tha t they know bette r than the market. There is, of course, strong academicbacking for the hypothesis tha t the markets are efficient in the sense that theypromptly reflect available information, see Fama (14) for a summary, whichsupports the view that managers are unlikely to be bette r predictors of generalmovements, than is the market.

lo E.g. See Bogue and Roll (3) and Bieman and Smidt (15) for discussions on theapplication of the CAPM to multi-period capital project appraisal.

REFERENCES

REPORT OF THE STUDY GROUP ON THE OBJECTIVES O FFINANCIAL STATEMENTS, New York, A.I.C.P.A., 1973.

THE CORPORATE REPORT, a discussion paper published by the U.K.Accounting Standards Steering Committee, August 1975.

M.C. Bogue and R. Roll, ‘Capital Budgeting of Risky Projects with“Imperfect” markets for Physical Capital’, JOURNAL OF FINANCE, 29,May 1974.

H.A. Simon “On he concept of Organisational Goal”, ADMINISTRATIVESCIENCE QUARTERLY, 1964.

J.R. Grinyer, “An Extension of Fisher’s Model” JOURNAL OF BUSINESSFINANCE, Spring 1973.

M.C. Jensen, “Capital Markets Theory and Evidence”. In STUP IES INTHE THEORY O F CAPITAL MARKETS, Praeger Publishers, 1972.

M.E.Rubinstein, “A Mean-variance Synthesis of Corporate FinancialTheory”, JOURNAL OF FINANCE, March 1973.

A J . Merrett and A. Sykes, “Return on equities and fured interestsecurities: 1919-1966”, DISTRICT BANK REVIEW, No.158, 1966.

N. Barr, “Real Rates of Return to Financial Assets since the War”, THETHREE BANKS REVIEW, September 1975.

W.F. Sharpe, “Likely Gains from Market Timing”, FINANCIALANALYSTS JOURNAL, MUch-April 1975,

J.C. Van Horne, FINANCIAL MANAGEMENT AND POLICY, 3rd edition,1974.Prentice Hall Inc.




(12) E.F. Fama and M.H. Miller, THE THEORY O F FINANCE, Holt Rinehart

and Winston, 1972.

(1 3) P.S.Albin, “Information Exchange in Securities Markets and the Assump-tion of Homogeneous Beliefs”, JOURNAL OF FINANCE, 29, September1974.

(14) E.F. Fama, “Efficient Capital Market: A review of Theory and EmpiricalWork”, JOURNAL O F FINANCE, March 1973.

(15) H. Bierman and S. Smidt “A pplication of the Capital Asset Pricing modelto M ulti-period Investments”, JOURNA L O F BUSINESS FINANCE AND

ACCOUNTING, Autumn 1975.

(16) W.F. Sharpe and G.M. Cooper, “Risk-Return Classes on New York StockExchange Comm on Stocks, 18 31-1967”, FINANCIAL ANALYSTSJOURNAL, March-April 1972.

APPENDIX A

Returns from investment of lump sums in a U.K. stock exchange index in eachof years 1919-1956 , each investment being held for ten years.

YEARS

Mean return

Standard devia-tion of return

Range of return

Greatest differ-ence in returnfrom invest-ments in

succeeding years

Proportionatechange in returnrepresented by(d) above - .e .

’d’/precedingyear’s rate

MC

1919-29

8.8%

2.8%

2.9%to

13.2%

5.4%

0.4

:Y TEI

130-45

5.5%

2.8%

3 O%

to0.5%

4.4%

0.7

IS

946-56

10.4%

3.9%

4.4%to

14.6%

5.5%

0 .6

RE

9 19-2s

11.4%

4.0%

3.6%to

17.2%

6.3%

0.6

The cost of equity, the CAPM and management objectives

L T E N

9 3 0 4

1.3%

2.9%

- 1.9%to

7.9%

3.3%

0.4

1

1946-56

6.2%

4.4%

-0.7%to

11.3%

5.5%

1.3

117



SourceObservations taken from data listed in AJ.Merrett 8c A. Sykes, “Return

on equities and fixed interest securities: 1919-1966”. District BonkReview. No. 15 8 (1966)

An increase in the volatility of the measured retu rn could be expected t o appearas the no tional holding period was shortened from 10 years, and Merrett andSykes’s analysis of the results for a one-year holding period confirmed thatexpectation, with real and money returns fluctuating dramatically from below- 10% n 1956 to over +40% in 1957.

APPENDIX B

MAXIMISING SHAREHOLDER WEALTH WITH KNOWN RATESOF

RETURN TO ALTERNATIVE INVESTMENT

This appendix identifies assumptions under which the use of net present valuetechniques to maximise shareholders’ wealth , would be valid if managementoperated under certainty concerning the rate of return , to shareholders, frominvestment alternative to that available in the firm. We proceed b y assuming:-

1) That existing equity holders will immediately invest elsewhere on thenational equity markets, in shares of comparable risk, if their fu nds are notinvested in the firm in which they cu rrently hold shares and tha t managementknows the rates of return which will actually be realised on such investments.

2) That the term of the shareholders’ alternative equity investment will be thesame as tha t of the project under consideration by t he firm, and th at th ey willreinvest intermediate cash flows prior to the terminal date.

3) That reinvestment rates available t o the shareholder and the firm are thesame.

4) That there are no transaction costs.

5 ) That all cash flows occur at the end of the periods involved.

6) That managers have the sole objective of maximising existing shareholders’wealth at the terminal date of the projec t, and tha t existing holders willretain their shares until that time.

Under these assumptions the rate of return which the shareholder would obtain

on the investment alternative to a capital project would be “r” in equation 2below




nwhere , I1

(n- t) times with i taking th e value fo r period j

n is the terminal period of the capital projectPo is the present share price of the alternativeAt is the cash flow at time t derived from the investmentand ij is the ra te of interest during period j.

means multiply the following expressionJ=t+1

This equation defines the shareholder’s average annual retu rn f rom th e alternativeinvestment as the discount rate which equate s the terminal value of the cash flow

associated with that investment with its present price. It will be noted that thesize of the rate “r” depends on th e fu ture rates of interest available, th e size ofthe cash flows (including present share price) and also the timing of those flows.

The average annual return actually obtainable from holding the alternativeinvestment is ‘r l ’ in the Equation A2.

where m is the period of sale of the shareP, is the price obtained on the sale and othe r terms are as defined inEquation A1 .

Thu s the shareholders’ opp ortun ity cost is a func tion of the stream of cash flowsactually resulting from holding the alternative investment, and its present share

price.

The rate ‘r , ’ will only be constant for all shareholders if they all sell the identicalalternative investment at a com mon d ate , unless share prices are always anadequa te reflection of the future cash flows to be derived from holding theshares and the futu re interest rates. They are unlikely to be such a reflection, soa model which is based on an acceptance of share sale at different da tes requiresassumptions which are as unreahstic as that of sale of shares at a comm on date ,and the latte r seems tenable as th e basis for analysis. This paper assumes tha t th ealternative investment would be sold at the terminal da te of the capita lexpenditure project, so that P, becomes A, and equations A1 and A2 areequivalent. We co ntin ue on the basis of A l .

The cost of equity, the CAPM and management objec tives 119



The use of the opportun ity cost rate 'r' to derive Net Present Values ("Vs) willonly generally be correct, in the absence of furth er assumptions, if th e periodreinvestment rate 'ij' equals 'r' fo r all periods. This can be seen from th e following:

let ij = r for a l l periods, then A1 converts to

Po =- E At (1 t r ) n - t(1 t r)" t = 1

a capital project will appear to be acceptable w hen evaluated at discoun t rate '?if

where I is the immediate outlay on th e projec t (which is assumed to be equal

Ct is the flow associated with the project in period t and o ther terms are aspreviously defined.

to Po)

Equation A4 could be rewritten as:

But I=Po, so it can be shown as

i.e.

Therefore, if the Net Present Value of a project is positive or zero, at discountrate 'r', and the reinvestment rate is also 'r', its terminal value wi l l exceed or equalthat of the alternative investments and the project is acceptable on financialgrounds under the assumptions of this analysis. Conversely, if the N et PresentValue is negative the project is no t acceptable.

As he required assumption o f constant reinvestment rates is inappropria te to therealistic situation of changing interest rates, alternative analyses shou ld be

120 John R . Crinyer



considered. For example, a possible approach is to assume, in add ition toassumptions 1 to 6 above, that the potterns of the future cash flows o f the

project and the shareholders’ alternative investment are identical (although theflows can naturally differ in size) and th at all future flows will be non-negative.The discount ra te t o be used in capita l budgeting as a reflection of shareholders’

oppo rtunity cost can the n be defined as the rate which discoun ts the cash flowsassociated with the shareholders’ alternative investment to the initial outlay onthat investment, i.e. it is ‘d’ in Equat ion A6.

” AtP 0 = C-= l (1 t d)t

Use of ‘d’ would signal acceptance of the capital project if

But Po equals I , so that on the stated assumptions At <Ct in each period if theproject has a positive or zero net present value at the discount rate ‘d’. In thatcase, the terminal value of the project must be greater than, or equal to, that ofthe shareholders’ alternative investment, regardless of the reinvestment ratesavailable, which are assumed to be identical for the shareholder and firm.Similarly, a negative net present value will indica te tha t the project has a lower

net terminal value than the alternative, regardless of the reinvestment rates.Although a correc t accept/reject decision would emerge the NPV is no tnecessarily a meaningful figure, however.

The above analysis highlights a number of points apparently over looked in muchof the literature. Even under the unrealistic assumptions 1 to 6 above, to useNPV analyses to maximise shareholders’ terminal wealth, management mustfurther assume that either (1) reinvestment rates will not change and will equalthe equity holders’ present opportunity cost or (2) the alternative investments

will generate identical patterns of cash flows, t o identical terminal dates, tothose of the capital projects. Under (2) reinvestment rates becom e irrelevant t othe accept/reject signal i f those rates are identical for the firm and the share-holder, but the NPV figures derived may n ot be meaningful stateme nts of value.I t appears that the adoption of a shareholder wealth-maximisation objectiverequires some highly unrealistic assumptions, even if management is certain aboutthe alternative shareholder investment opportu nity costs!

The cost of eq ui ty, the CAPM and management ob jectives 121

the cost of equity, the c.a.p.m. and management

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