For a large corporation the cost of capital should only be what, 8-10%?  The floor now for projects is more around 15-20% ROI, AFAIK.  But I see no way on earth for corporate executives to be satisfied with 10% ROI when they've tasted 25%.
The cost of capital depends on the specific project/investment, not the investor/corporation.

However, if a corporation can realize returns of anything above their cost of capital they should be able to raise this from the market. Companies with access to returns above their cost of capital should not be capital constrained and hence can invest not only in the projects that return 25%, but those that return 24%, 23%, 22%, etc.

However, I dispute this statement "The floor now for projects is more around 15-20% ROI". No one in the world has access to a steady stream of projects with an expected return of 15 - 20% unless they are very risky.