THE VALUATION OF SHARE 413 ications of this principle for our prob- able information as to what that future lem of dividend policy can be seen some- dividend policy would be. The first possi what more easily if equation (2)is re- bility being the relevant one from the stated in terms of the value of the enter- standpoint of assessing the effects of divi- prise as a whole rather than in terms of dend policy, it will clarify matters to as- the value of an individual share. Drop- sume, provisionally, that the future divi ping the firm subscript i since this will dend policy of the firm is known and ad to no ambiguity in the present con- given for t+ 1 and all subsequent peri text and letting ods and is independent of the actual divi- n(= the number of shares of record dend decision in 4. Then V(+ 1) will at the start of t also be independent of the current divi- m(t+ 1)=the number of new shares(if dend decision, though it may very well any) sold during t at the ex be affected by D(t+1)and all subse- dividend closing price p(+ 1), quent distributions. Finally, current div idends can influence v through the v(2=n(0)p(t)= the total third term, -m(t+1)p(t+1), the val the enterprise and ue of new shares sold to outsiders during D(=n(ed(o= the total the period. For the higher the dividend id during t to hold ord at the start of t, rout in capital that must be raised from external we can rewrite(2) sources to maintain any desired level of investment 1+p() D()+#()(+1)] The fact that the dividend decision effects price not in one but in these two 1+p(4)[D()+v(4+1) conflicting ways-directly via D()and inversely via -me)p(t-+ 1)-is, of m(L+1)P(L+1)].(3)course, precisely why one speaks of there being a dividend policy problem. If the The advantage of restating the funda- firm raises its dividend in t, given its in- mental rule in this form is that it brings vestment decision, will the increasein the into sharper focus the three possible cash payments to the current holders be routes by which current dividends might more or less than enough to offset their affect the current market value of the lower share of the terminal value? Which firm V(), or equivalently the price of its is the better strategy for the firm in individual shares, P. Current divi- financing the investment: to reduce divi- dends will clearly affect v(o via the first dends and rely on retained earnings or to term in the bracket, D(. In principle, raise dividends but float more new current dividends might also affect v shares? indirectly via the second term, V(E+ 1), In our ideal world at least these and the new ex dividend market value. since related questions can be simply and v(t+1)must depend only on future mediately answered: the two dividend and not on past events, such could be the effects must always exactly cancel out so case, however, only if both(a)v(+ 1)that the payout policy to be followed in t were a function of future dividend policy will have no effect on the price at t. and(b)the current distribution D() We need only express m(+1). P(t+1) served to convey some otherwise unavail- in terms of d( to show that such must his content downloaded from 202.. 18.13 on Wed, 1 1 Sep 2013 02: 04: 42 AM All use subject to JSTOR Terms and ConditionsTHE VALUATION OF SHARES 413 plications of this principle for our prob￾lem of dividend policy can be seen some￾what more easily if equation (2) is re￾stated in terms of the value of the enter￾prise as a whole rather than in terms of the value of an individual share. Drop￾ping the firm subscript j since this will lead to no ambiguity in the present con￾text and letting n(t) = the number of shares of record at the start of t m(t + 1) = the number of new shares (if any) sold during t at the ex dividend closing price p(t + 1), so that n(t + 1) = n(t) + m(t + 1) V(t) = n(t) p(t) = the total value of the enterprise and D(t) = n(t) d(t) = the total dividends paid during t to holders of rec￾ord at the start of t, we can rewrite (2) V(t l +,) 1[D(t)+n(t)p(t+1) I 1+0 -1+ (t) [ D(t) + V(t+ 1) -m (t+ 1) p (t+ 1)I. (3) The advantage of restating the funda￾mental rule in this form is that it brings into sharper focus the three possible routes by which current dividends might affect the current market value of the firm V(t), or equivalently the price of its individual shares, p(t). Current divi￾dends will clearly affect V(t) via the first term in the bracket, D(t). In principle, current dividends might also affect V(t) indirectly via the second term, V(t + 1), the new ex dividend market value. Since V(t + 1) must depend only on future and not on past events, such could be the case, however, only if both (a) V(t + 1) were a function of future dividend policy and (b) the current distribution D(t) served to convey some otherwise unavail￾able information as to what that future dividend policy would be. The first possi￾bility being the relevant one from the standpoint of assessing the effects of divi￾dend policy, it will clarify matters to as￾sume, provisionally, that the future divi￾dend policy of the firm is known and given for t + 1 and all subsequent peri￾ods and is independent of the actual divi￾dend decision in t. Then V(t + 1) will also be independent of the current divi￾dend decision, though it may very well be affected by D(t + 1) and all subse￾quent distributions. Finally, current div￾idends can influence V(t) through the third term, -m(t + 1) p(t + 1), the val￾ue of new shares sold to outsiders during the period. For the higher the dividend payout in any period the more the new capital that must be raised from external sources to maintain any desired level of investment. The fact that the dividend decision effects price not in one but in these two conflicting ways-directly via D(t) and inversely via -m(t) p(t + 1)-is, of course, precisely why one speaks of there being a dividend policy problem. If the firm raises its dividend in t, given its in￾vestment decision, will the increase in the cash payments to the current holders be more or less than enough to offset their lower share of the terminal value? Which is the better strategy for the firm in financing the investment: to reduce divi￾dends and rely on retained earnings or to raise dividends but float more new shares? In our ideal world at least these and related questions can be simply and im￾mediately answered: the two dividend effects must always exactly cancel out so that the payout policy to be followed in t will have no effect on the price at t. We need only express m(t+l) 1 p(t+1) in terms of D(t) to show that such must This content downloaded from 202.115.118.13 on Wed, 11 Sep 2013 02:04:42 AM All use subject to JSTOR Terms and Conditions