applied to paper rights such as the mortgage rather than to physical or human
capital itself.
Depreciation of those assets is not as simple as with the mortgage. Cash flow F and discount rate r are typically variables rather than constants. Depreciation theory avoids that complexity, much as accountants do, by treating each successive
investment in an asset as if it were a separate asset depreciating in itself.
(A2.5) through (A2.10) gave present value at time x of a differential foreseen
positive cash flow at future time z as dPV(x)= F (zje dz , (A8.1)
where the differential present value arose from a earlier or concurrent negative cash flow invested at time u<=x .It was shown that all of asset value PV(x) at any time x can be explained as a sum or integral of such differential increments
evolving with time alone from investment to eventual realization. Meanwhile all output within the differential increment of dPV is self invested. Growth dPV can be understood either as this self-invested output or equivalently
the shortening discount period, as each means growth at rate r. At interim moment t itis dPV’(t)=r(x)dPV(t)=F(z)je dt = EHO RG: , X<=t<z. (A8.2)
er la
Thus present value rises exponentially as long as the moment of cash flow is
deferred.
APPENDIX A: The Argument in Notation 3/7/16 17
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