A firm has $1000 at time 0 that it can reinvest internally with return r_i or payout the cash to shareholders with a tax on the payout. If the firm pays out at time 0, the shareholders can reinvest the after-tax proceeds in an external opportunity and earn a return of r_x. At time 1, all money is paid out, whether from the firm or from the external investment, and shareholders pay a tax on this payout at time 1.

If the internal investment return was 5% and the external investment return was 12%, then for what range of tax rates would the shareholder prefer the firm pays out at time 0?