If the majority of proposed projects fail to beat the cost of capital,
what can be said about their NPV? or IRR?

Dana --

If the majority of proposed projects fail to beat the cost of capital,
their net present value (NPV) is negative.  The result is that they
erode shareholders' equity, because when a firm is funded with debt
and equity, the cost of debt is virtually always lower (due to both
market and tax reasons).

QuickMBA has a complete description of valuation and the meaning and
use of NPV in its corporate finance section:
QuickMBA
"Corporate Finance" (undated)
http://www.quickmba.com/finance/cf/

The internal rate of return or IRR will be below the cost of capital
in these cases.  Thus, a corporation with a cost of capital of 12%,
might have projects returning 11%.  These would have a negative NPV
and an IRR of 11%.

For details on calculations of NPV and IRR, you may wish to see this Google Answer:
"Financial Accounting" (Omnivorous-GA, Feb. 3, 2003)
http://answers.google.com/answers/threadview?id=156829

Google search strategy:
"net present value" + finance
"internal rate of return" + finance

Best regards,

Omnivorous-GA

Thank you for explaining this question so clearly and for your quick
response. Also, thank you for the additional references.