** **

The basic idea expressed in this course is that, if benefits are greater than costs, do it. Hence, investments appear to resolve to a simple matter of maximizing NPV. We note, however, that when firms are faced with risky choices (i.e., actions or investments that have uncertain outcomes) they often use hurdle rates to evaluate risky choices that greatly exceed anything that can be justified by CAP-M -- or any other portfolio model for that matter. One possible reason is project selection bias (i.e., where outcomes are risky, the likelihood that project selection will be biased in favor of projects for which costs have been underestimated and benefits over estimated).

There is another possible reason: as we have seen, experience,
history, time can reduce uncertainty and therefore project risk. We
know that information has a measurable value. If time will provide
information, it follows that delay can have value as well. It is a
mistake to ignore the value of delay in analysis. High hurdle rates
can be a proxy for the cost of not delaying, although not a very good
one. Recently, finance scholars have come up with a new approach to
the evaluation of risky choices based on a better understanding of
financial engineering - the theory of real options. This theory
provides an evaluative method that is conceptually and practically
superior to the alternative of ignoring project risk or subjecting
all risky projects to evaluation using very high hurdle rates.

SOME UNSTATED ASSUMPTIONS of NPV:

- The investment is reversible (i.e., there are no sunk costs --
if benefits are less than anticipated or costs turn out to be
higher, the investment can be undone and costs fully recovered);
**OR** - If the investment is irreversible, it is a now or never proposition (i.e., it cannot be delayed without a substantial loss)

**THE ABILITY TO DELAY AN IRREVERSIBLE
INVESTMENT UNDERMINES THE SIMPLE NPV RULE. **

WHY? Holding an investment opportunity that can be postponed is analogous to holding a call option; it gives you the right but not the obligation to exercise it at a future time. When an entity makes an irreversible investment, it "kills" its option to invest. That means that it sacrifices the possibility that waiting would provide information that would affect the desirability or timing of the investment. This "opportunity cost" (lost option value) should be included as part of the cost of the investment. Hence, where investments are both irreversible and can be postponed, the NPV rule should be amended to read:

**BENEFITS MUST EXCEED COSTS BY AN AMOUNT
EQUAL TO KEEPING THE INVESTMENT OPTION ALIVE.**

LET'S SAY WE HAVE TO DECIDE WHETHER OR NOT WE WANT TO BUY 2000 F-22s @ $100M/PER ($200B). (these would replace existing planes, consequently they would have no effect on operating and maintenance costs). q = .5. Benefits are PVs at .05)

If we buy now we get an NPV of $50 B.

If we delay for ten years it will cost $400 B in current dollars to buy the equivalent of 200 F-22s (@ $200 M/PER), hence the PV cost = $246 M. However, in ten years we will buy the F-22 only if the more dangerous SON eventuates.

Hence EV = .5 (0) + .5 (500 -246) = $127 B

Note, if we could get our money back we would invest today; if it
were now or never, we would buy 200 F-22s. But neither situation
obtains. The value of the option to wait is, in this case, = $77 B.
Another way of putting it: HOW HIGH WOULD PRICES HAVE TO GROW ON THE
200 F-22s BETWEEN NOW AND THEN TO JUSTIFY BUYING NOW? ANS = $651.5 =
PV 651 = 400; .5 (0) + .5 (500 - 400) = $50 B.

**IN OTHER WORDS, BUYING 200 F-22s NOW OR ONLY
NOW AT A COST OF $200 B IS THE SAME AS BUY NOW OR LATER AT A COST OF
$651 BILLION.**

(by the by, if the alternative to buying the 200 F-22s now is maintaining a richer force structure, the pv cost could easily exceed $400 B; also if the the industrial capacity to build F-22s will not exist in 10 years if we don't build them now, this may in reality be a now or never decision).