General Meters is considering two mergers. The first is with Firm A in its own

volatile industry, the auto speedometer industry, while the second is a merger

with Firm B in an industry that moves in the opposite direction (and will tend to

level out performance due to negative correlation).

General Meters Merger

with Firm A

General Meters Merger

with Firm B

Possible

Earnings

(\( in millions) Probability

Possible

Earnings

(\) in millions) Probability

\(40 ........... 0.30 \)40 ........... 0.25

60 ........... 0.40 60 ........... 0.50

80 ........... 0.30 80 ........... 0.25

aCompute the mean, standard deviation, and coefficient of variation for both

investments (refer to Chapter 13 if necessary).

b.Assuming investors are risk-averse, which alternative can be expected to

bring the higher valuation?

Step by step solution

01

Definition of coefficient of variation

The coefficient variation means the ratio of standard deviation to the earnings per share.

02

Calculation of coefficient of variation

Firm A

X	P	XP	(X-D)2P
$40	0.30	12	120
$60	0.40	24	0
$80	0.30	24	120
		D= 60	(X-D)2P= 240

Mean (D)= 60

$\begin{array}{rcl}\mathbf{Standard}\mathbf{}\mathbf{Deviation}& \mathbf{=}& \sqrt{{\left(X-D\right)}^{\mathbf{2}}\mathbf{P}}\\ & \mathbf{=}& \sqrt{\mathbf{240}}\\ & \mathbf{=}& \mathbf{15}\mathbf{.}\mathbf{49}\end{array}$

Calculation of coefficient of varation:

$\begin{array}{rcl}\mathbf{Coefficient}\mathbf{}\mathbf{of}\mathbf{}\mathbf{Variation}& \mathbf{=}& \frac{\mathbf{Standard}\mathbf{}\mathbf{Deviation}}{\mathbf{Mean}}\\ & \mathbf{=}& \frac{\mathbf{15}\mathbf{.}\mathbf{49}}{\mathbf{60}}\mathbf{\times }\mathbf{100}\\ & \mathbf{=}& \mathbf{25}\mathbf{.}\mathbf{81}\mathbf{\%}\end{array}$

Firm B:

X	P	XP	(X-D)2P
$40	0.25	10	100
$60	0.50	30	0
$80	0.25	20	100
		D=60	(X-D)2P= 200

Mean (D)= 60

$\begin{array}{rcl}\mathbf{Standard}\mathbf{}\mathbf{Deviation}& \mathbf{=}& \sqrt{{\mathbf{(}\mathbf{X}\mathbf{-}\mathbf{D}\mathbf{)}}^{\mathbf{2}}\mathbf{P}}\\ & \mathbf{=}& \sqrt{\mathbf{200}}\\ & \mathbf{=}& \mathbf{14}\mathbf{.}\mathbf{14}\end{array}$

Calculation of coefficient of variation:

$\begin{array}{rcl}\mathbf{Coefficient}\mathbf{}\mathbf{of}\mathbf{}\mathbf{Variation}& \mathbf{=}& \frac{\mathbf{Standard}\mathbf{}\mathbf{Deviation}}{\mathbf{Mean}}\\ & \mathbf{=}& \frac{\mathbf{14}\mathbf{.}\mathbf{14}}{\mathbf{60}}\mathbf{\times }\mathbf{100}\\ & \mathbf{=}& \mathbf{23}\mathbf{.}\mathbf{57}\mathbf{\%}\end{array}$

03

Higher valuation

The second alternative gives a higher valuation because the second alternative has a low coefficient of variation.

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