Can a project meet the after tax required rate of return and not meet the pretax required rate of return?

If yes, wouldn't that immediately lower the pretax rate of return?

Consider a country that has just changed from 0% tax to 50% tax, and shareholders meet all of the burden.  As is said in one of the practice problems, the pretax rate of return stays the same. 

Say a project returns 9% before taxes and 5.5% after taxes.  The required rates of return are 10% pretax and 5% posttax (for firms with 50%-50% debt to equity).

(This can happen if a project is 50% debt- 50% equity, has a 4% borrowing interest rate, and a 50% corporate tax rate, invests 100 to get back 109 at the end of the year.  A $1 tax credit is given for interest paid (.5*4%*50), and a $4.5 tax debt is incurred, so aftertax the project nets $105.5.)

It seems obvious from this that the posttax rate cannot be 5% when the pretax rate is 10%.  If the pretax rate was 10%, the posttax required rate would have to be more than 5.5%.

[NEAS: The incidence of corporate taxes is complex. If you are interested in this subject, start with the textbook by Scholes et al.: Taxes & Business Strategy (4th Edition) by Myron S. Scholes, Mark A. Wolfson, Merle M. Erickson, and Edward L. Maydew (Jul 19, 2008). This is the standard textbook now used in all business schools. The literature on the incidence of tax rates is enormous; this is a hot political subject.]