STOCHASTIC

that new riskless debt is available in unlimited
amounts at a fixed rate r*) insures that all projects
will either be accepted or rejected in toto.
All a,-° will be either o or i, and the troublesome
problems associated with fractional projects or
recourse to integer (non-linear) programming
do not arise.
Consider now the set of accepted projects, and
denote this subset with asterisks. We then have
all a,-.° = akt°= i; the corresponding MJ»°=J«»°
= o; and for any project j*, the corresponding
7i,-.°> o (i.e. strictly positive), 1 ' and the number
i),-*° is the "dual evaluator" or "shadow price"
registering the net gain to the company and its
shareholders of accepting the project. Rewriting
the corresponding equation from (360), we have"
(37) Vi.'=Bl.'"-r*Hi."l- y IH,,,,
Several important features and implications
of these results should be emphasized. First of
all, note that we have shown that even when
uncertainty is admitted in only this highly
simplified way, and when any effect of changes
in capital budgets on the covariances between
returns on different companies' stocks is ignored,
the minimum expected return (in dollars of expected
present value /?,•." *) required to justify
the allocation of funds to a given risky project
costing a given sum Hj,