$1.$ After completing its capital spending for the year, Carlson Manufacturing has $$1,000$ extra cash. Carlson$$s managers must choose between investing the cash in Treasury Bonds that yield $8$ percent or paying the cash out to investors who would invest in the bonds themselves.

a$)$ If the corporate tax rate is $35$ percent, what tax rate on ordinary income would make the investors equally willing to receive the dividend and to let Carlson invest the money?

b$)$ Is the answer to $($a$)$ reasonable? Why or why not?