Hi there and thank you for your question,
There is no tax that is payable by you when purchasing shares in a privately held company.
The shares are purely an asset in the seller's name, and you're simply purchasing that asset.
When you SELL the shares however, you may find that you're liable for CGT on the increase in value of the shares, but that's a story for the future.
The only cost that you will need to pay is the purchase price of the shares to the current owner, and also possibly for a sale of shares agreement to be drawn up by a lawyer to cover you.
You may need to submit a CoR39 to CIPC, but that could only cost a few hundred rands.
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Please note: This answer does not create an attorney-client relationship. Please consult a local attorney in person for legal advice. This information is being provided so you can better discuss legal matters with your attorney.