The above analysis was made using a guaranteed rate of 5% for the entire duration. If the winner wants to try for a higher rate of return he/she could try riskier investments, the lottery commission can’t take that chance.
The advantage of taking it earlier is in case the lottery goes bankrupt or the government raises the tax rates later on.
The advantage of going for the annuity is if the interest rates drop to .1% or something and the winner is still getting paid as if it’s 5%.