416 THE JOURNAL OF BUSINESS proach amounts to defining the value of investments in real assets that will yield the firm as more than the"normal"(market)rate of return. The latter opportunities, fre V(0)= 2(1+p) quently termed the“ good will’ of the (10) business, may arise, in practice, from any [(-0(4)1+①+p(T), of a number of circumstances (ranging all the way from special locational advan where R()represents the stream of cash tages to patents or other monopolistic outlays, or, abbreviating, as above, to To see how these opportunities affect the value of the business assume that in some future period t the firm invests I() v(0)f-0(1+p)i* [R(-0(01(11) dollars. Suppose, further, for simplicity, that starting in the period immediately But we also know, by definition, that following the investment of the funds [X(o-I(D]=[R(-0(0] since, X( the projects produce net profits at a con differs from R( and I( differs from stant rate of p*() per cent of I( )in each (and also by the depreciation expense if worth as of t of the (perpetual) stream of rather than gross profits and invest- the "good will "of the projects(i.e, the ment). Hence(11)is formally equivalent difference between worth and cost)will to(9), and the discounted cash flow ap- be proach is thus seen to be an implication I(PD-1(0)=I([P*(D) of the valuation principle for perfect The investment opportunities approach. ture"good will", as of now of this fu- markets given by equation(1) The present worth -Consider next the approach to valua- tion which would seem most natural I() (1+p)-(+), from the standpoint of an investor pro- posing to buy out and operate some al- and the present value of all such future ready-going concern. In estimating how opportunities is simply the sum much it would be worthwhile to pay for the privilege of operating the firm, the I() (1+p)-(+) to be paid is clearly not relevant, since the new owner can, Adding in the present value of the(uni- within wide limits, make the future divi- form perpetual)earnings, X(O), on the as dend stream whatever he pleases. For him the worth of the enterprise, as such The assumption that I() yields a uni is not restrictive in the present o will depend only on:(a) the"normal since it is always possible by rate of return he can earn by investing his capital in securities (i. e, the market the time shape of its actual ety p note also that the physical assets currently held by the the firm are behaving rationally, they will, o cogens rate of return); (b)the earning power of p"( is the auerage rate of return. If the i their cut-off criterion(cf. below p. 418) firm; and( ) the opportunities, if any, in this event we would that the firm offers for making additional mulas remain valid, however, even where"0<e his content downloaded from 202.. 18.13 on Wed, 1 1 Sep 2013 02: 04: 42 AM All use subject to JSTOR Terms and Conditions416 THE JOURNAL OF BUSINESS proach amounts to defining the value of the firm as T-1 V(O) = E t=O (0 P) (10) X [E (t-co() +(+p Tv (T), where IR(t) represents the stream of cash receipts and ()(t) of cash outlays, or, abbreviating, as above, to co v ( ?) = E 1+p teRW [st-(t I . ( 1 1) ,_O (1+p),+'(11 But we also know, by definition, that [X(t) -I(t)] = [IR(t) -()(t)] since, X(t) differs from IR(t) and 1(t) differs from CO(t) merely by the "cost of goods sold" (and also by the depreciation expense if we wish to interpret X(t) and I(t) as net rather than gross profits and invest￾ment). Hence (11) is formally equivalent to (9), and the discounted cash flow ap￾proach is thus seen to be an implication of the valuation principle for perfect markets given by equation (1). The investment opportunities approach. -Consider next the approach to valua￾tion which would seem most natural from the standpoint of an investor pro￾posing to buy out and operate some al￾ready-going concern. In estimating how much it would be worthwhile to pay for the privilege of operating the firm, the amount of dividends to be paid is clearly not relevant, since the new owner can, within wide limits, make the future divi￾dend stream whatever he pleases. For him the worth of the enterprise, as such, will depend only on: (a) the "normal" rate of return he can earn by investing his capital in securities (i.e., the market rate of return); (b) the earning power of the physical assets currently held by the firm; and (c) the opportunities, if any, that the firm offers for making additional investments in real assets that will yield more than the "normal" (market) rate of return. The latter opportunities, fre￾quently termed the "good will" of the business, may arise, in practice, from any of a number of circumstances (ranging all the way from special locational advan￾tages to patents or other monopolistic advantages). To see how these opportunities affect the value of the business assume that in some future period I the firm invests 1(t) dollars. Suppose, further, for simplicity, that starting in the period immediately following the investment of the funds, the projects produce net profits at a con￾stant rate of p*(t) per cent of I (t) in each period thereafter.6 Then the present worth as of t of the (perpetual) stream of profits generated will be I(t) p*(t)/p, and the "good will" of the projects (i.e., the difference between worth and cost) will be I(t)fP-22)-I(t) P* =1(t) [P (t) P P* The present worth as of now of this fu￾ture "good will" is It P* ( ) p] (1 + p)-+ and the present value of all such future opportunities is simply the sum to P Adding in the present value of the (uni￾form perpetual) earnings, X(O), on the as- 8 The assumption that I(t) yields a uniform per￾petuity is not restrictive in the present certainty context since it is always possible by means of simple, present-value calculations to find an equiva￾lent uniform perpetuity for any project, whatever the time shape of its actual returns. Note also that p*(t) is the average rate of return. If the managers of the firm are behaving rationally, they will, of course, use p as their cut-off criterion (cf. below p. 418). In this event we would have p*(t) > p. The for￾mulas remain valid, however, even where p*(t) < p. 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