Question

Time in bankruptcy. Refer to the Financial Management (Spring 1995) study of pre-packaged bankruptcy filings, Exercise 2.32 (p. 86). Recall that each of 49 firms that negotiated a reorganization plan with its creditors prior to filing for bankruptcy was classified in one of three categories: joint exchange offers with prepack, prepack solicitation only, and no prefiling vote held. Consider the quantitative variable length of time in bankruptcy (months) saved in the accompanying file. Is it reasonable to use a single number (e.g., mean or median) to describe the center of the time-in-bankruptcy distributions? Or should three "centers" be calculated, one for each of the three categories of prepack firms? Explain

Short answer

The mean is 2.6546, or the median is 1.5

Step-by-step solution

Reasonable to use a single number of mean or median

As a result, three sorts of plans were investigated:

That is, a "joint" exchange offer accompanied by a pre-packaged bankruptcy request.

"Prepack" refers to solely pre-packaged bankruptcy solicitation.

"None" means there was no pre-filing vote. The information for the 49 businesses is shown in the table below.

\(\begin{aligned}{\rm{Mean for joint}} &= \frac{{\sum\limits_{i = 1}^n {{x_i}} }}{n}\\ &= \frac{{29.2}}{{11}}\\ &= 2.6546\end{aligned}\)

First, they must arrange the data in ascending order.

\({\rm{ }}\;1.2,{\rm{ }}1.2,1.4,{\rm{ }}1.4,{\rm{ }}1.4,{\rm{ }}1.5,{\rm{ }}2.1,{\rm{ }}3.9,{\rm{ }}4.5,{\rm{ }}5.2,{\rm{ }}5.4.\)

\(\begin{aligned}{\rm{\;Median}} &= {\rm{The middle value\; \; \; \; \; \; \; }}\\ &= 1.5\end{aligned}\)

The mean time for “Joint exchange offers with pre-pack” enterprises is 2.6545 months, while the median duration is 1.5 months. Therefore, the average duration spent in bankruptcy for “joint” enterprises is 2.6545 months, whereas half of the businesses are in bankruptcy for 1.5 months or less.

Three categories of pre-pack firms

a) Those who have not pre-registered to vote.

b) Those who vote for a collaborative solution.

c) Those who voted for pre-packaged food