How do you gross up a fully franked dividend yield?

The detailed question was:

I was looking at your stock investment journal for Woolworths and I noticed you had a dividend of 3.76% and 100% franking and a grossed up dividend yield of 5.37%. I think a franking credit is 30% so can you please tell me how you obtained the 5.37%?

To gross up a fully franked (100% franked) dividend yield you take the dividend and divide it by 70 and multiply by 100.

So, for the Woolworths fully franked dividend = 3.76 ÷ 70 × 100 = 5.37%

This is because the dividend is paid out of after tax earnings, that are notionally taxed at 30% for franking credit purposes. Franking gives you a dividend on a pre-tax basis. So, the dividend represents 70% of the pre-tax profit from which it was paid. To gross it up, you work out what the pre-tax dividend would have been.

The way I did it above  is the ideal because it is always better to round the final answer, not the intermediate factors. However, you can simplify the calculation by multiplying the fully franked dividend by 1.42857 and you will be close enough.

If the dividend is partly franked, you must gross up the franked portion of the dividend and add that to the unfranked portion of the dividend before calculating the yield.

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