Abstract

Investment
in new capacities is most often based on a Weighted Average Cost of Capital
where the cost of equities is derived from the Capital Asset Pricing Model
(the cost of debt following a different logic). While a single corporate
discount rate was most often used in the past, differentiated discount rates
reflecting elements such as technology and country risks are now more used.
These introduce undesirable arbitrage phenomena in standard capacity
expansion model interpreted as market simulation models. We discuss three
types of differentiated discounting namely the standard (often based on CAPM )
exogenous discount rate, the more general stochastic discount rate and the
endogenous discount rate derived from risk functions possibly with hedging
instruments. The three approaches are cast in a unifying risk premium
equilibrium formulationwhere arbitrage phenomena are eliminated. The
models are of the complementarity form and can be handled through splitting
algorithms. We report numerical results for medium size problems adequate for
industrial use. Convergence is based on an(often implicit)
assumption of monotonicity that is not necessarily satisfied for endogenous
discount rates. We briefly discuss the different equilibrium that can arise
when this assumption is not satisfied.