$$\begin{array} { l r r }
&\underline{ \text { Company A }} &\underline{ \text { Company B }} \
\text { Total earnings } & \$ 2,000,000 & \$ 1,000,000 \
\text { Number of shares outstanding } & 400,000 & 100,000 \
\text { Earnings per share } & \$ 5.00 & \$ 10.00 \
\text { Price/earnings } & 6 \mathrm { X } & 3 \mathrm { X } \
\text { Market price/share } & 30.00 & \$ 30.00
\end{array}$$
-Company A has a growth rate in EPS of 14%.Company B's growth rate in EPS is 10%.What is the post-merger growth rate assuming the facts as previously stated? (Assume no Synergy.)
A) 13.20%
B) 10.88%
C) 12.00%
D) 12.67%

Question

$$\begin{array} { l r r } 
&\underline{ \text { Company A }} &\underline{ \text { Company B }} \
\text { Total earnings } & \$ 2,000,000 & \$ 1,000,000 \
\text { Number of shares outstanding }  & 400,000 & 100,000 \
\text { Earnings per share } & \$ 5.00 & \$ 10.00 \
\text { Price/earnings } & 6 \mathrm { X } & 3 \mathrm { X } \
\text { Market price/share } & 30.00 & \$ 30.00
\end{array}$$
-Company A has a growth rate in EPS of 14%.Company B's growth rate in EPS is 10%.What is the post-merger growth rate assuming the facts as previously stated? (Assume no Synergy.)
A) 13.20%
B) 10.88%
C) 12.00%
D) 12.67%

Quizplus · Accepted Answer

Firstly, let us calculate the current earnings per share of both companies: 
- Company A: \$2,000,000 ÷ 400,000 = \$5.00 eps
- Company B: \$1,000,000 ÷ 100,000 = \$10.00 eps

Next, we can calculate the current market price per share of Company A using the price/earnings ratio:
- Price/earnings ratio = Market price per share ÷ Earnings per share
- 6 = Market price per share ÷ \$5.00 eps
- Market price per share = 6 x \$5.00 eps = \$30.00 per share

Since Company B already has a market price per share of \$30.00, we can skip this step for Company B.

Now, let's calculate the post-merger earnings per share for both companies:
- Company A: \$5.00 eps x 1.14 (growth rate) = \$5.70 eps
- Company B: \$10.00 eps x 1.10 (growth rate) = \$11.00 eps

To calculate the post-merger earnings per share, we need to add the total earnings of both companies and divide by the total number of shares outstanding:
- Total earnings = \$2,000,000 + \$1,000,000 = \$3,000,000
- Total shares outstanding = 400,000 + 100,000 = 500,000
- Post-merger earnings per share = \$3,000,000 ÷ 500,000 = \$6.00 eps

Finally, we can calculate the post-merger price/earnings ratio for both companies:
- Company A: \$30.00 (market price per share) ÷ \$5.70 eps (post-merger eps) = 5.263 X
- Company B: \$30.00 (market price per share) ÷ \$11.00 eps (post-merger eps) = 2.727 X

To calculate the post-merger growth rate, we need to use a weighted average formula:
Post-merger growth rate = (Company A's weighted growth rate + Company B's weighted growth rate) ÷ Total market value
- Company A's weighted growth rate = (\$5.70 eps - \$5.00 eps) ÷ \$5.70 eps = 0.1228 or 12.28%
- Company B's weighted growth rate = (\$11.00 eps - \$10.00 eps) ÷ \$11.00 eps = 0.0909 or 9.09%
- Total market value = Company A's market value + Company B's market value = (\$30.00 x 400,000) + (\$30.00 x 100,000) = \$12,000,000
- Post-merger growth rate = (0.1228 x \$6,000,000 + 0.0909 x \$6,000,000) ÷ \$12,000,000 = 0.1267 or 12.67%

Therefore, the answer is D, 12.67%.

-Company a Has a Growth Rate in EPS of 14