Please make sure it's unique and not copy$-$paste from AI or elsewhere.

RBE owns $70\%$ of the ordinary share capital of DCA. The total group equity as at $31$ December $20$X$1$ was $$4,000,000,$ which included $$650,000$ attributable to non$-$controlling interest.

RBE purchased a further $20\%$ of the ordinary share capital of DCA on $1$ October $20$X$2$ for $$540,000.$ During the year to $31$ December $20$X$2,$ RBE issued $2$ million $$1$ ordinary shares, fully paid, at $$1\mathrm{.}30$ per share.

Dividends were paid by both group entities in April $20$X$2.$ The dividends paid by RBE and DCA were $$200,000$ and $$100,000,$ respectively.

Total comprehensive income for the year ended $31$ December $20$X$2$ for RBE was $$900,000$ and for DCA was $$600,000.$ Income is assumed to accrue evenly throughout the year.

Required $($a$)$ Explain the impact of the additional $20\%$ purchase of DCA's ordinary share capital by RBE on the equity of the RBE Group.

$($b$)$ Prepare the consolidated statement of changes in equity for the year ended $31$ December $20$X$2$ for the RBE Group, showing the total equity attributable to the parent and to the non$-$controlling interest.