Question

# Assume the Knight Corporation is considering the acquisition of Day Inc. The expected earnings per share...

Assume the Knight Corporation is considering the acquisition of Day Inc. The expected earnings per share for the Knight Corporation will be \$8 with or without the merger. However, the standard deviation of the earnings will go from \$1.92 to \$1.36 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.)

b. Comment on the possible impact on Knight’s postmerger P/E ratio, assuming investors are risk-averse.

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a.

Coefficient of variation = Standard deviation / mean

the mean earning in our case = expected earning = 8

Standard deviation Pre-merger = 1.92

Standard deviation Post-merger = 1.36

Coefficient of variation Pre-merger = 1.92 / 2 = .96

Coefficient of variation Post-merger = 1.36/2 = .68

b.

A reduced coefficient of variation represents reduced risk, it means there will be lesser variance in earnings now and that makes the stock less risk.

Risk averse investors are being offered lesser risk and may assign a higher P/E ratio to post-merger earnings.

Because investors are taking less risk for same earning levels they will be willing to pay more for the shares.

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