We Grow is going public with a perpetuity that offers 150% of the $100 face.

They will use an interest rate of 9% in the analysis. Managers anticipate that the recent slow-down in dot.com securities will be short-lived, so they think it might be less expensive to issue the security as a growing perpetuity with a constant annual growth of 4%. Are they right that issuing a growing perpetuity will be less expensive? What will happen if they issue the security as a 25-year growing annuity?