LE, You're very close I think.
You are correct the company earned $142,857, paid 30% tax and passed on $100,000 to you as a dividend. You get $100k plus a franking credit of $42,857.
Your taxable income is your dividend plus your franking credit, so you are taxed on $142,857. This is easy to work out on the tax tables, from http://www.ato.gov.au/youth/content.asp?doc=/Content/40811.htm this is $18,000 plus 40% for every $ over $80,000. So you rtax is:
$18,000 + 0.4 x (142,857 - 80,000) = $43,142.80.
BUT, you subtract once again your franking credit. The tax you have to pay is:
$43,142.80 - $42,857 = $285.80
Have to board a flight - sorry to be quick. Hope this helps. BB
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