Mutual funds report total returns assuming reinvestment of dividend and capital gain distributions. Support for purchasing fractional shares and automatic dividend reinvestment was introduced in December 2019. Some companies have dividend reinvestment plans, or DRIPs, not to be confused with scrips. The tax treatment of a dividend income varies considerably between jurisdictions. A franking credit is a nominal unit of tax paid by companies using dividend imputation. After this date the shares becomes "ex dividend". Estimates of future dividend yields are by definition uncertain. Alaska also requires registration to receive an Alaska Permanent Fund dividend. This was for a dividend based on profitability. Its reciprocal is the Price/Dividend ratio. This refund is a form of dividend. Any dividend divided by zero is undefined. Such a division can be formally expressed as where "a" is the dividend (numerator). It is a type of cap and dividend program. An explicit formula for the dividend is given by formula 11.