Tax on capital gains vs franked dividends in Australia

Question

Consider two stocks "CG" and "DIV" that perform equally well, but the difference is:

• "CG" pays no dividends and all its performance comes from it raising its ticker price (capital gain);
• While "DIV" pays out all its gains as franked dividends while its ticker price remains constant

Which would be a better investment after tax, assuming we sell after 1 year?

^{Note: This is more than just an academic question, because there exist "accumulating" ETFs that convert underlying dividends into capital gains, but loses the franking credits. e.g., SAUS}

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Here's my attempt to answer this question

Let's define some variables first:

g_cg = capital gains on stock CG
g_div = dividends received on stock DIV

gat_cg = capital gains after tax on stock CG
gat_div = dividends after tax on stock DIV

r = marginal tax rate with medicare levy (e.g., 0.47 for top tax bracket)
f = ratio of dividend that's franked (can assume 1 for best-case scenario)
fr = 0.3 (company tax rate = withheld tax on franked dividend)

So we want to see whether gat_cg or gat_div is higher

gat_cg is trivial to calculate, since after holding the stock for 1 year, only half the capital gains are taxable (CGT discount):

gat_cg = g_cg - g_cg / 2 * r
       = g_cg * (1 - r / 2)

gat_div is more difficult, having to solve a system of equations:

gbt_div = taxable income ("before tax") from stock DIV
fc_div = franking credits from stock DIV's dividends

gbt_div = g_div + fc_div                 (taxable income includes franking credits)
fc_div / (f * g_div + fc_div) = fr       (franking credits should match the company tax rate)
gat_div = g_div - gbt_div * r + fc_div   (tax paid on the dividend is offset by franking credits)
        = g_div * (1 - r) * (1 - fr * (1 - f)) / (1 - fr)
        = g_div * (1 - r) * 10 / 7       (with fr = 0.3 and f = 1)

Using some common marginal tax rates with g_cg = g_div = 1:

r	gat_cg	gat_div (f = 100%)	gat_div (f = 80%)
18%	0.91	1.171	1.101
32%	0.84	0.971	0.913
39%	0.805	0.871	0.819
47%	0.765	0.757	0.712

From this, I can conclude that 100% franked dividends results in better return on investment after tax than capital gains at all except the highest marginal tax rate of 47%.
Is my calculation correct?