But if the stock price corrects itself to the pre bonus value, so will the company's share capital become the same it was before the bonus, the only difference being that there's now a hole in the cash reserves.
This is incorrect. Say there are 10 shares worth 10 ea. The total Shareholder's capital is 100. This [along with some other items] is classified as Tier 1 capital. Say after few years, the company has been making profit and has profit of 1000. This is classified as Retained Earnings. This is still an
Asset Liability; but not same as Tier 1 capital. Say the share price is x. This has no relevance. Total Asset Liability for simplicity is 100 [shareholders capital]+1000 [Retained earnings] = 1100
When a Bonus is issued; say 1:1. The number of shares now become 10. The company moves 100 from Retained Earnings to Shareholder's capital. So total Shareholder capital becomes 200; the retained earnings become 1000-100 = 900. Total
Asset Liability is still 200+900 = 1100. The share price would move to x/2.
In Stock Split, the 10 shares of value 10 are split into 20 shares of value 5. So the total Shareholder capital is still 100 and going by above, with retained earnings of 1000; total
Asset Liability = 1100. The share price would move to x/2
What's the point of a bonus issue? What advantage does it have over a stock split?
The shareholder capital has special significance from regulation [more so in case of Financial Institutions] as well as general health of a company. A large shareholder capital is always desired as these funds can never be called for ... unlike a debt / loan / bond / payable that companies issue and any untimely recalls can create cash flow issues. However Shareholder capital is due only when the company is wound down.
However for blue chip companies, this often doesn't matter to large extent. It is more of preference. Certain jurisdictions do offer different tax treatments and going one way over other helps.