risk tolerance now. She discounts each expected future flow not by her foreseen time preference rate then, but by her time preference rate today. It seems to me that the appropriate discount rate r in (A2.4) is r(x). She will provide for anticipated
changes in her time preference rate by factoring costs of trading the asset if tradeable, or modifying it if modifiable, into her evaluations of future value F (z)dz,
and so from present value too. I consequently interpret (A2.4) to mean
dPV(x)= F (ze dz and =F (z)dz= APV(x)e 0), (A2.5)
The value of the whole asset V(x) at time x will be the sum or integral of present values of all foreseen cash flows both negative and positive over (x, w ), where w
(omega) is the foreseen end point of flows. w may be infinity oo . Thus V(xXJ=PV(x)=["F(zje" dz, xx<=z<=0. (A2.6)
The terms value and total capital are interchangeable, as are their notations V and
K
7 Present cost PC(x) evaluates V(x) as the sum or integral of earlier negative cash
flows compounded at rate r since moment of investment u, and not yet
decapitalized in positive cash flow. The counterpart to (A2.1) becomes diC(u)=F (ujdu and = dPC(x)=dV(x)=dPV{(x), (A2.7) where IC is what I call “investment cost”. The counterparts to (A2.2) and (A2.3) are
dV(x)=F (uje“*du sands F (ujdu=dV(xJe™™ . (A2.8)
APPENDIX A: The Argument in Notation 3/7/16 6
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