Question

Assume the Knight Corporation is considering the acquisition of Day Inc. The expected earnings per share for the Knight Corporation will be $3 with or without the merger. However, the standard deviation of the earnings will go from $1.92 to $1.26 with the merger because the two firms are negatively correlated.

a. Compute the coefficient of variation for the Knight Corporation before and after the merger. (Do not round intermediate calculations and round your answers to 2 decimal places.) Coefficient of Variation Pre-merger Post-merger
b. Comment on the possible impact on Knight's postmerger P/E ratio, assuming investors are risk-averse. Risk-averse investors are being offered risk and may assign a P/E ratio to postmerger earnings.

Answer 1

The coefficient of variation pre-merger for Knight Corporation is 0.64, and post-merger, it is 0.42, indicating more stable earnings after the merger. For risk-averse investors, the lower post-merger earnings variability could increase the P/E ratio, as they may be willing to pay more for perceived stability in earnings.

Step-by-step explanation:

To calculate the coefficient of variation for Knight Corporation before and after the merger, we use the formula: CV = Standard Deviation / Mean (Earnings Per Share). Pre-merger, the coefficient of variation is calculated as $1.92 / $3, which equals 0.64. Post-merger, it is calculated as $1.26 / $3, which equals 0.42. This indicates that post-merger, the earnings per share have a lower relative variability, implying that the earnings are more stable relative to their mean after the merger.

Considering the possible impact on Knight's post-merger P/E ratio, assuming investors are risk-averse, we can expect that the decrease in the standard deviation of the earnings (due to the negative correlation between the firms) might make the stock more attractive to conservative investors. Risk-averse investors prefer stability and predictability in earnings, and therefore a lower coefficient of variation post-merger could lead to a higher P/E ratio. The lower perceived risk may result in these investors being willing to pay more for each dollar of earnings, hence increasing the P/E ratio.