Chapter 31, Problem 10PS

a)

Summary Introduction

To determine: The gain from merger

Explanation of Solution

The pre-merger values of Company C and Company D:

$\begin{array}{c}{\text{PV}}_C=\text{1million}\times \text{\$9}0\\ =\text{\$9}0\text{million}\end{array}$

$\begin{array}{c}{\text{PV}}_D=\text{600,000}\times \text{\$2}0\\ =\text{\$12million}\end{array}$

Compute r to determine ${\text{ PV}}_{CD}$,

$\begin{array}{c}\frac{\text{\$0}\text{.80}}{\text{(r}-0.\text{06)}}=\text{\$20}\\ \text{r}=0.10,\text{or }10\%\end{array}$

Compute pre-merger values:

$\begin{array}{c}{\text{PV}}_{CD}={\text{PV}}_{C\text{ pre-merger}}+{\text{PV}}_{D\text{ post-merger}}\\ =\text{\$90million}+\text{600,000}\times \left(\frac{\text{\$0}\text{.80}}{\left(\text{0}\text{.10}–0.\text{08}\right)}\right)\\ =\text{\$114 million}\end{array}$

Compute acquisition gain:

$\begin{array}{c}\text{Acquisition gain}={\text{PV}}_{CD}-({\text{PV}}_C+{\text{PV}}_D)\\ =\text{\$114million}–\text{(\$90million}+\$\text{12million)}\\ =\text{\$12 million}\end{array}$

Hence, the acquisition gain is $12 million.

b)

Summary Introduction

To determine: Cost of acquisition.

Explanation of Solution

Compute cost of acquisition:

$\begin{array}{c}\text{Cash acquisition cost}=\text{Cash paid}-{\text{PV}}_C\\ =\left(\text{\$25}\times \text{600,000}\right)-\text{\$12million}\\ =\text{\$3 million}\end{array}$

Hence, Cost of acquisition is $3 million.

c)

Summary Introduction

To determine: Cost of acquisition if Company D offers 1 share of Company D for 3 shares of Company D.

Explanation of Solution

Compute cost of acquisition:

$\begin{array}{c}{\text{Shares}}_{CD}={\text{Old shares}}_C+\text{New shares}\\ =\text{1million}+\left(\frac{\text{600,000}}{\text{3}}\right)\\ =\text{\$1}\text{.2 million}\end{array}$

$\begin{array}{c}{\text{Share price}}_{CD}=\frac{{\text{PV}}_{CD}}{{\text{Shares}}_{CD}}\\ =\frac{\text{\$114million}}{1.2\text{million}}\\ =\text{\$95}\end{array}$

$\begin{array}{c}\text{ Stock acquisition cost}=\left(\text{New shares}\times {\text{Price}}_{CD}\right)–{\text{PV}}_D\\ =\left[\left(\frac{\text{600,000}}{\text{3}}\right)\times \text{\$95}\right]-\text{\$12million}\\ =\text{\$7 million}\end{array}$

Hence, cost of acquisition is $7 million.

d)

Summary Introduction

To determine: Cost of acquisition.

Explanation of Solution

Compute cost of acquisition:

$\begin{array}{c}\text{Cash acquisition cost}=\text{cash paid}-{\text{PV}}_D\\ =\left(\text{\$25}\times \text{600,000}\right)-\text{\$12million}\\ =\text{\$3 million}\end{array}$

Hence, Cost of acquisition is $3 million.

e)

Summary Introduction

To determine: Stock acquisition cost

Explanation of Solution

The stock acquisition cost is dependent on the rate of growth.

$\begin{array}{c}{\text{PV}}_{CD}={\text{PV}}_{C\text{ pre-merger}}+{\text{PV}}_{D\text{ post-merger}}\\ =\text{\$90million}+\text{600,000}\times \left(\frac{\text{\$0}\text{.80}}{\left(\text{0}\text{.10}-0.\text{06}\right)}\right)\\ =\text{\$102 million}\end{array}$

$\begin{array}{c}{\text{Share price}}_{DC}=\frac{{\text{PV}}_{DC}}{{\text{Shares}}_{DC}}\\ =\frac{\text{\$102million}}{1.2\text{million}}\\ =\text{\$85million}\end{array}$

$\begin{array}{c}\text{ Stock acquisition cost}=\left(\text{New shares}\times {\text{Price}}_{CD}\right)-{\text{PV}}_D\\ =\left[\left(\frac{\text{600,000}}{\text{3}}\right)\times \text{\$85million}\right]-\text{\$12million}\\ =\text{\$5 million}\end{array}$

Hence, the stock acquisition is $5 million.