JEAN-PAUL PAQUIN, ANNICK LAMBERT AND ALAIN CHARBONNEAU 285a distinctive legal entity prevents such a substitution but generates its own
types of risk. To the increased overhead costs and underinvestment moral
hazard problem, one must consider the increased financial cost generated
by the increased financial risk that must be supported by the incorporated
project (Flannery, Houston and Venkataraman, 1993).
Contrary to what the MM paradigm asserts, the cost of total risk depends
also on how the firm is financed. Debt financing improves the profitability
of the firm by confering tax benefits and thus lowering its cost of capital,
but makes the probability of financial distress and bankruptcy more likely.
A highly levered firm must therefore assess the impact on the firm’s total
risk. Debt financing has a cost, so has equity financing. Otherwise, as Stulz
(1999) remarks, all firms would be all-equity financed with no probability
of financial distress. Agency costs and asymmetrical information explains
why equity financing is costly since there are few all-equity firms. The cost
of equity financing is, at the margin, equal to the cost of total risk (Stulz,
1999). When total risk matters, the appropriate measure of risk is obviously
not an equity return volatility index. A firm can increase at no additional
cost its total risk when the probability of financial distress is unaffected by
a risky project:
However, any increase in risk that increases the probability of distress is costly
and should be accounted for when evaluating the costs and benefits of a project.
Because the risk that is costly is the risk associated with large losses, the appro-
priate measures of risk are lower-tail measures of risk such as Value-at-Risk or
Cash-flow-at-Risk rather than measures such as volatility of stock returns or
volatility of cash-flows. (Stulz, 1999: 9)In other words, one needs to know the probability distribution of risky
investment projects.
15.4 THE NPV PROBABILITY DISTRIBUTION AND THE CLT:
THEORETICAL RESULTS
Hillier (1963) invoked the Central Limit Theorem (CLT) to explain why the
NPV probability distribution should be Normal. His conclusion rests on the
argument that when the discounted cash flows are
mutually independent random variables, with finite means and variances,
which are either identically distributed or uniformly bounded, then (by the
Lindeberg Theorem) the Central Limit Theorem will hold and the sum of these
random variables will be approximately normal if n is large. If this holds, the
probability distribution of the measures of the merit of an investment will
be approximately normal, regardless of whether theXjrandom variables are
normal or not. (Hillier, 1963: 446)However, Hillier (1964) would later on modify such a statement by pointing
out that since the net present value equation is not the direct sum of random