### Brief notes on partially franked dividends

On a recent trip to Brisbane I was having dinner with a group of old friends, and I realised that we had become incredibly boring people who talked about superannuation, the stock market, and so forth. In this post, I set out some notes on the taxation of partially franked dividends; I think it is relevant to at least two people, author included.

(I worked this algebra out today, not financial advice, may only apply to Australia, may not even be correct though I think it is, etc.)

You own shares in a company. The company pays out a dividend to its shareholders,

The more complicated case is if the company pays its company tax on the dividend before giving it to shareholders. If the company tax has been paid in full, then the dividend you get is

Algebra should make this clearer (if not, there are heaps of explanations on Google). Let t

(1 - t

More generally, the dividend may be only partially franked. Let f be the fraction of the dividend which is fully franked. Then

(1 - f*t

The total amount of tax the ATO wants is t

tax_owing = t

(If this quantity is negative, then the tax office owes you money, and this can either turn into a tax refund or offset some other tax.)

It is more useful to use (*) to work out how much tax you owe as a function of the dividend that you receive:

tax_owing = D

Plugging some numbers in: if the dividend is fully franked, then f=1. Say t

In the last couple of years, Vanguard's VHY fund has been giving distributions (which I gather is called a different term to 'dividend' because the distribution comprises lots of individual dividends from all the companies in the fund) around 70% franked. Plugging in f = 0.7, we get (37.5% - 0.7*30%) / (1 - 0.7*30%) = 20.9%. So about a fifth of the distribution you get will go to the tax office.

(This remains the case even if you set up an automatic re-investment plan; the ATO treats it as though you received the income in the form of partially franked dividends, then bought more shares with it. The income is taxed.)

We can use this to estimate the effective returns from a fund. From the above link, VHY's growth since inception has been an annualised average of 13% p.a., comprising 7.1% p.a. growth in the unit price and 5.9% p.a. in distributions. Since about a fifth of the latter is eaten up by tax, the effective return has been a bit under 12% p.a. rather than 13%.

My eyeballing of the table in that PDF file suggests that taking a percentage point off the returns is a decent rule of thumb for working this out, at least if you're in my tax bracket. The forecast growth is 8%, so I'll interpret that as around 7%. (And remember that as a 95% confidence interval, the forecast for a single year is more like (8 +/- 25)%.)

(I worked this algebra out today, not financial advice, may only apply to Australia, may not even be correct though I think it is, etc.)

You own shares in a company. The company pays out a dividend to its shareholders,

*without having paid company tax on it first*. In this case, we call the dividend*unfranked*, and you pay tax on it according to your marginal income tax rate (probably 32.5% or 37%). If your marginal income tax rate is t_{i}, and the dividend is D, then you'll owe the tax office t_{i}*D.The more complicated case is if the company pays its company tax on the dividend before giving it to shareholders. If the company tax has been paid in full, then the dividend you get is

*fully franked*. The key points are:- The ATO taxes, at your marginal income tax rate, the imputed full value of the dividend
*before the company tax was paid on it*(the grossed-up dividend). - You get credits for the tax that the company has already paid on the grossed-up dividend, so that the tax isn't paid twice.

Algebra should make this clearer (if not, there are heaps of explanations on Google). Let t

_{c}be the company tax rate (30%). Let D_{f}be the franked dividend, i.e., what you receive. Let D_{g}be the grossed-up dividend, i.e., what the tax is being imposed on. We have(1 - t

_{c})*D_{g}= D_{f}.More generally, the dividend may be only partially franked. Let f be the fraction of the dividend which is fully franked. Then

(1 - f*t

_{c})*D_{g}= D_{f}. (*)The total amount of tax the ATO wants is t

_{i}*D_{g}. The company's already paid f*t_{c}*D_{g}, so you owetax_owing = t

_{i}*D_{g}- f*t_{c}*D_{g}= D_{g}*(t_{i}- f*t_{c}).(If this quantity is negative, then the tax office owes you money, and this can either turn into a tax refund or offset some other tax.)

It is more useful to use (*) to work out how much tax you owe as a function of the dividend that you receive:

tax_owing = D

_{f}* (t_{i}- f*t_{c}) / (1 - f*t_{c}).Plugging some numbers in: if the dividend is fully franked, then f=1. Say t

_{i}= 37.5%, and t_{c}= 30%. Then you owe the ATO (37.5% - 30%) / (1 - 30%) = 10.7% of the dividend you receive.In the last couple of years, Vanguard's VHY fund has been giving distributions (which I gather is called a different term to 'dividend' because the distribution comprises lots of individual dividends from all the companies in the fund) around 70% franked. Plugging in f = 0.7, we get (37.5% - 0.7*30%) / (1 - 0.7*30%) = 20.9%. So about a fifth of the distribution you get will go to the tax office.

(This remains the case even if you set up an automatic re-investment plan; the ATO treats it as though you received the income in the form of partially franked dividends, then bought more shares with it. The income is taxed.)

We can use this to estimate the effective returns from a fund. From the above link, VHY's growth since inception has been an annualised average of 13% p.a., comprising 7.1% p.a. growth in the unit price and 5.9% p.a. in distributions. Since about a fifth of the latter is eaten up by tax, the effective return has been a bit under 12% p.a. rather than 13%.

My eyeballing of the table in that PDF file suggests that taking a percentage point off the returns is a decent rule of thumb for working this out, at least if you're in my tax bracket. The forecast growth is 8%, so I'll interpret that as around 7%. (And remember that as a 95% confidence interval, the forecast for a single year is more like (8 +/- 25)%.)