Some firms have been accused of using stock splits to manipulate their stock prices before being acquired by another firm. An article in Financial Management (Winter 2008) investigated the impact of stock splits on long-run stock performance for acquiring firms. A simplified version of the model fit by the researchers follows:
E(y) = β0 + β1x1, + β2x2 + β3x1x2,
where
y = Firm's 3-year buy-and-hold return rate (%)
x1 = {1 if stock split prior to acquisition, 0 if not}
x2 = {1 if firm's discretionary accrual is high, 0 if discretionary accrual is low}
a. In terms of the β's in the model, what is the mean buy-and-hold return rate (BAR) for a firm with no stock split and a high discretionary accrual (DA)?
b. In terms of the β's in the model, what is the mean BAR for a firm with no stock split and a low DA?
c. For firms with no stock split, find the difference between the mean BAR for firms with high and low DA.
d. Repeat part c for firms with a stock split.
e. Note that the differences, parts c and d, are not the same. Explain why this illustrates the notion of interaction between x1 and x2.
f. A test for H0: β3 = 0 yielded a p-value of .027. Using α = .05, interpret this result.
g. The researchers reported that the estimated values of both β2 and β3 are negative. Consequently, they conclude that "high-DA acquirers perform worse compared with low-DA acquirers. Moreover, the under performance is even greater if high-DA acquirers have a stock split before acquisition." Do you agree?