Let's consider the firm has a cashflow of 1 and a discount rate of 10% (for everything)
Before anything happens, the equity is:
\(E = \frac{1}{0.1}=10\)
If we have 10 shares (just to simplify), each of them is worth 1
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Let's assume the project requires an initial investment of 1 and provides a constant flow of 0.2 (NPV=1)
As soon as debt holders arrive, they give 1 to equity holders (leveraged recap), and there are only 9 shares
After the project's implementation, we know that debtholders receive 2; for instance, they might receive 0.2 forever.
Then the current equityholders will receive
\(E = \frac{1+0.2-0.2}{0.1}=10\)
since we have 9 shares, the share price is 1.11