Cholesky decomposition of $A+kI$ given Cholesky decomposition of A

Question

Suppose I have the Cholesky decomposition for a symmetric matrix $A$:

$$ A = L L^T $$

I wish to compute the Cholesky decomposition for $A+kI$ where $I$ is the identity and $k$ is a scalar. Is there a way to obtain this using the decomposition for $A$ faster than recomputing the Cholesky decomposition from scratch?