Solution Found!
Manipulating rates of return with stock splits. Some
Chapter 12, Problem 80E(choose chapter or problem)
Manipulating rates of return with stock splits. 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 of acquiring firms. A simplified version of the model fit by the researchers follows:
\(E(y)=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{1} x_{2} \text {, }\)
where
y = Firm’s 3-year buy-and-hold return rate (%)
\(x_1\) = {1 if stock split prior to acquisition, 0 if not}
\(x_2\) = {1 if firm’s discretionary accrual is high, 0 if discretionary accrual is low}
a. In terms of the \(\beta\)’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 \(\beta\)’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. (Hint:Use your answers to parts a and b.)
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 \(x_1\) and \(x_2\).
f. A test for \(H_0:\ \beta_3\ =\ 0\) yielded a p-value of .027. Using \(\alpha\ =\ .05\), interpret this result.
g. The researchers reported that the estimated values of both \(\beta_2\) and \(\beta_3\) are negative. Consequently, they conclude that “high-DA acquirers perform worse compared with low-DA acquirers. Moreover, the underperformance is even greater if high-DA acquirers have a stock split before acquisition.” Do you agree?
Questions & Answers
QUESTION:
Manipulating rates of return with stock splits. 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 of acquiring firms. A simplified version of the model fit by the researchers follows:
\(E(y)=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{1} x_{2} \text {, }\)
where
y = Firm’s 3-year buy-and-hold return rate (%)
\(x_1\) = {1 if stock split prior to acquisition, 0 if not}
\(x_2\) = {1 if firm’s discretionary accrual is high, 0 if discretionary accrual is low}
a. In terms of the \(\beta\)’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 \(\beta\)’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. (Hint:Use your answers to parts a and b.)
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 \(x_1\) and \(x_2\).
f. A test for \(H_0:\ \beta_3\ =\ 0\) yielded a p-value of .027. Using \(\alpha\ =\ .05\), interpret this result.
g. The researchers reported that the estimated values of both \(\beta_2\) and \(\beta_3\) are negative. Consequently, they conclude that “high-DA acquirers perform worse compared with low-DA acquirers. Moreover, the underperformance is even greater if high-DA acquirers have a stock split before acquisition.” Do you agree?
ANSWER:Step 1 of 10
The model fit by the researcher is 
Where
Y = Firm’s 3-year buy-and-hold return (BAR) rate (%)
