Is the method of adjusted close calculation correct at Yahoo?

Is the method of adjusted close calculation correct at Yahoo?

Example: Adjusted Close Calculations
http://help.yahoo.com/l/us/yahoo/finance/quotes/quote-12.html

2/13/03 Close = 46.99
2/14/03 Close = 48.30
2/18/03 Split = 2:1
2/18/03 Close = 24.96
2/19/03 Cash Dividend = 0.08 (ex-date)
2/19/03 Close = 24.53

Split Multiplier = 0.5
Dividend Multiplier = 1 ∓ (0.08/24.96) = 0.9968

2/13/03 Adj. Close = 0.5 * 0.9968 * 46.99 = 23.42
2/14/03 Adj. Close = 0.5 * 0.9968 * 48.30 = 24.07
2/18/03 Adj. Close = 0.9968 * 24.96 = 24.88
2/19/03 Adj. Close = 24.53

But 24.53 / 24.88 - 1 = -0.014067 is not equal to (24.53 + 0.08) / 24.96 - 1 = -0.014022
Why do they use wrong method?

I think the pre-dividend data need to be multiplied by 1 / (1 + 0.08 / 24.53 ) in case of dividend distribution.