Why is grossing up a dividend not simply multiplying the dividend by 1.3?

This was a follow-up on the previous question in this section. The detailed question was:

Looking at the last Woolworths dividend of 65 cents the factor I use is 30% or 65x1.30.I use this because it tells me the actual cash plus credit this dividend is worth. I then compare this to my cost of the share to calculate the dividend percentage eg if I paid \$34 per share 65x130/3400=2.48%.Is this ok or not?

Facts:

Price paid\$34.00

Dividend per share \$0.65

Fully franked

The franking credit per share is = 0.65 ÷ 70 × 30 = \$0.2786 (rounded to 4 decimal places)

So, the grossed up dividend is = 0.65 + 0.2786 = \$0.9286

Thus, the grossed up yield on your purchase price is = 0.9286 ÷ 34 × 100 = 2.73%

You can cross-check this against the calculation I showed you last night:

The dividend yield on your purchase price is = 0.65 ÷ 34 × 100 = 1.9118%

Gross it up = 1.9118 ÷ 70 × 100 = 2.73%

You calculation is incorrect because you are trying to incorrectly apply the company tax rate of 30% that is used for franking  purposes to the dividend yield. To gross up the dividend yield  you have to calculate the pre-tax dividend assuming that tax rate. The franking credit is not 30% of the dividend. It is 30% of the profit notionally producing the dividend. So, if the profit is 100% and the tax rate 30%, the dividend is 70%. So if 65c is 70% of the pre-tax profit, you gross it up by dividing by 70 and multiplying by 100.

If you are still struggling with this very simple idea, get yourself ten coins and lay them out in a row. That is the pre-tax profit. Now, take three coins away. That is the tax. The remaining 7 coins are the after-tax profit from which dividends are paid.

So, every dividend amount you get is the seven coins. To get back to the pre-tax profit you have to add three coins back. Hence, you divide the dividend amount by 7 and then multiply it by 10. I used 70 and 100 in my explanation because it keeps the 30% tax rate clear, but in practice the last zeros can be dropped.

You use the same logic to gross up the yield percentage.

If you multiply the dividend by 1.30, you are calculating the franking credit as being 30% of the dividend instead of 30% of the pre-tax profit that notionally generated the dividend.

If the pre-tax profit was \$100, the tax for franking purposes is 30%, or \$30. The dividend in that case is the remaining 70% or \$70.

So, the dividend is \$70 and the franking credit is \$30. The grossed up dividend is \$100, which is the pre-tax profit.

On your calculation the grossed up dividend is \$70 × 1.3 = \$91. Thus, your calculation has the franking credit as = \$91 - \$70 = \$21 instead of the correct amount of \$30.

What you are doing in multiplying the dividend by 1.3 is not logical and as I have just shown gives an illogical answer.

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