Chapter 26, Problem 14QP

a)

Summary Introduction

To compute: The value of Publication IR to Company B.

Introduction:

Merger is the complete absorption of one company by another company. The acquiring company acquires all the assets and liabilities of the acquired firm and acquiring firm retains its name and identity. The acquired firm ceases to exist as a separate business entity after a merger.

Answer to Problem 14QP

The value of Publications I to Company B is $9,857,250.

Explanation of Solution

Given information:

“Company B” is analysing the purchase of “Publications I”. Company B expects that earnings and dividends of Publications I to grow at a constant rate of 5% every year. Because of synergy, Company B’s growth rate will increase to 7% each year.

The price earnings ratio of Company B and Publications I are 14.5% and 9.2% respectively. The outstanding shares of Company B and Publications I are $1,400,000 and $195,000 respectively. The earnings of Company B and Publications I are $4,300,000 and $705,000 respectively and the dividends of Company B and Publications I are $1,075,000 and $375,000 respectively.

Formula to calculate the value of Publications I to Company B:

${\text{EPS}}_{\text{I}}=\frac{\text{Value of dividends for company B}}{\text{Shares outstanding for Publications I }}$

Calculate the value of Publications I to Company B:

$\begin{array}{c}{\text{EPS}}_{\text{I}}=\frac{\text{Value of dividends for company B}}{\text{Shares outstanding for Publications I }}\\ =\frac{\$705,000}{195,000}\\ =\$3.61538\text{ per share}\end{array}$

Hence, the value of Publications I to Company B is $3.61538 per share.

Formula to calculate the share price of Target Company (I Publications):

${\text{P}}_{\text{I}}=\text{Price earning ratio of Publications I}\left({\text{EPS}}_{\text{I}}\right)$

Calculate the share price of Target Company (I Publications):

$\begin{array}{c}{\text{P}}_{\text{I}}=\text{Price earning ratio of Publications I}\left({\text{EPS}}_{\text{I}}\right)\\ =9.2\left(\$3.61538\right)\\ =\$33.261496\end{array}$

Hence, the share price of the target company is $33.261496.

Formula to calculate the dividend per share:

${\text{DPS}}_{\text{I}}=\frac{\text{Dividends of Publications I}}{\text{Outstanding share of Publications I}}$

Calculate the dividend per share:

$\begin{array}{c}{\text{DPS}}_{\text{I}}=\frac{\text{Dividends of Publications I}}{\text{Outstanding share of Publications I}}\\ =\frac{\$375,000}{195,000}\\ =\$1.923\end{array}$

Hence, the dividend of Publications I is $1.923.

Formula to calculate the required rate of return for the target company’ shareholders:

$\begin{array}{l}\text{Required rate of return }\\ \text{of }\text{?}\text{Publications I}\end{array}\}\text{ = }\frac{{\text{DPS}}_{\text{T}}\left(1+\text{growth rate}\right)}{\text{Share price}}+\text{Growth rate}$

Calculate the required rate of return for the target company’ shareholders:

$\begin{array}{c}\begin{array}{l}\text{Required rate of return }\\ \text{of }\text{?}\text{Publications I}\end{array}\}\text{ = }\frac{{\text{DPS}}_{\text{T}}\left(1+\text{growth rate}\right)}{\text{Share price}}+\text{Growth rate}\\ \text{= }\frac{\text{\$1}\text{.923}\left(1+\text{0}\text{.05}\right)}{\text{\$33}\text{.261496}}+0.05\\ =0.1107\\ =11.07\%\end{array}$

Hence, the required return of Publications I is 11.07%.

Formula to calculate the share price of the target company with new growth rate:

${\text{P}}_{\text{I}}=\frac{{\text{DPS}}_{\text{T}}\times \left(1+\text{New growth rate}\right)}{\left(\begin{array}{l}\text{Required rate of return of target }\\ \text{company}-\text{New growth rate}\end{array}\right)}$

Calculate the share price of the target company with new growth rate:

$\begin{array}{c}{\text{P}}_{\text{I}}=\frac{{\text{DPS}}_{\text{T}}\times \left(1+\text{New growth rate}\right)}{\left(\begin{array}{l}\text{Required rate of return of target }\\ \text{company}-\text{New growth rate}\end{array}\right)}\\ =\frac{\text{\$1}\text{.923}\times \left(1+\text{0}\text{.07}\right)}{\left(\text{0}\text{.1107}-\text{0}\text{.07}\right)}\\ =\frac{\text{\$}2.05761}{0.0407}\\ =\$50.55\end{array}$

Hence, the share price of the target company is $50.55.

Formula to calculate the value of Publications I to Company B:

${\text{V}}_{\text{I}}\text{*=Outstanding shares of Publications I }\left({\text{P}}_{\text{T}}\right)$

Calculate the value of Publications I to Company B:

$\begin{array}{c}{\text{V}}_{\text{I}}\text{*=Outstanding shares of Publications I }\left({\text{P}}_{\text{T}}\right)\\ =195,000\times \$50.55\\ =\$9,857,250\end{array}$

Hence, the value of Publications I to Company B is $9,857,250.

b)

Summary Introduction

To compute: The gain of Company B from the acquisition.

Introduction:

Merger is the complete absorption of one company by another company. The acquiring company acquires all the assets and liabilities of the acquired firm and acquiring firm retains its name and identity. The acquired firm ceases to exist as a separate business entity after a merger.

Answer to Problem 14QP

Company B’s gain from acquisition is $3,371,258.28.

Explanation of Solution

Given information:

“Company B” is analysing the purchase of “Publications I”. Company B expects that earnings and dividends of Publications I to grow at a constant rate of 5% every year. Because of synergy, Company B’s growth rate will increase to 7% each year.

The price earnings ratio of Company B and Publications I are 14.5% and 9.2% respectively. The outstanding shares of Company B and Publications I are $1,400,000 and $195,000 respectively. The earnings of Company B and Publications I are $4,300,000 and $705,000 respectively and the dividends of Company B and Publications I are $1,075,000 and $375,000 respectively.

Formula to calculate Company B’s gain from the acquisition:

$\text{Gain = }\left(\begin{array}{l}\text{Value of Publications I to Company B}-\\ \text{Outstanding share of Publications I}\times \text{Share price}\end{array}\right)$

Calculate Company B’s gain from the acquisition:

$\begin{array}{c}\text{Gain = }\left(\begin{array}{l}\text{Value of Publications I to Company B}-\\ \text{Outstanding share of Publications I}\times \text{Share price}\end{array}\right)\\ =\$9,857,250-195,000\times \$33.261496\\ =\$3,371,258.28\end{array}$

Hence, Company B’s gain from acquisition is $3,371,258.28.

c)

Summary Introduction

To compute: The NPV of the acquisition.

Introduction:

Merger is the complete absorption of one company by another company. The acquiring company acquires all the assets and liabilities of the acquired firm and acquiring firm retains its name and identity. The acquired firm ceases to exist as a separate business entity after a merger.

Answer to Problem 14QP

The NPV of the acquisition is $2,447,250.

Explanation of Solution

Given information:

“Company B” is analysing the purchase of “Publications I”. Company B expects that earnings and dividends of Publications I to grow at a constant rate of 5% every year. Because of synergy, Company B’s growth rate will increase to 7% each year.

The price earnings ratio of Company B and Publications I are 14.5% and 9.2% respectively. The outstanding shares of Company B and Publications I are $1,400,000 and $195,000 respectively. The earnings of Company B and Publications I are $4,300,000 and $705,000 respectively and the dividends of Company B and Publications I are $1,075,000 and $375,000 respectively.

Formula to calculate the NPV of the acquisition, if Company B offers $38 in cash for each share of Publications I:

${\text{NPV = V}}_{\text{I}}-\text{Outstanding share of Publications I}\left(\text{Offer price per share}\right)$

Calculate the NPV of the acquisition, if Company B offers $38 in cash for each share of Publications I.

$\begin{array}{c}{\text{NPV = V}}_{\text{I}}-\text{Outstanding share of Publications I}\left(\text{Offer price per share}\right)\\ =\$9,857,250-195,000\left(38\right)\\ =\$2,447,250\end{array}$

Hence, the NPV of the acquisition at $38 offer price is $2,447,250.

d)

Summary Introduction

To compute: The maximum bidding price that Company B will be willing to pay for Publications I.

Introduction:

Merger is the complete absorption of one company by another company. The acquiring company acquires all the assets and liabilities of the acquired firm and acquiring firm retains its name and identity. The acquired firm ceases to exist as a separate business entity after a merger.

Answer to Problem 14QP

The maximum bid price is $50.55.

Explanation of Solution

Given information:

“Company B” is analysing the purchase of “Publications I”. Company B expects that earnings and dividends of Publications I to grow at a constant rate of 5% every year. Because of synergy, Company B’s growth rate will increase to 7% each year.

The price earnings ratio of Company B and Publications I are 14.5% and 9.2% respectively. The outstanding shares of Company B and Publications I are $1,400,000 and $195,000 respectively. The earnings of Company B and Publications I are $4,300,000 and $705,000 respectively and the dividends of Company B and Publications I are $1,075,000 and $375,000 respectively.

Formula to calculate the maximum bid price:

$\text{Maximum bid price = }\left[\begin{array}{l}\text{Offer price per share+}\\ \left(\frac{\text{NPV}}{\text{Outstanding share of Publications I}}\right)\end{array}\right]$

$\begin{array}{c}\text{Maximum bid price = }\left[\begin{array}{l}\text{Offer price per share+}\\ \left(\frac{\text{NPV}}{\text{Outstanding share of Publications I}}\right)\end{array}\right]\\ =\$38+\left(\frac{\$2,447,250}{195,000}\right)\\ =\$50.55\end{array}$

Hence, Company B’s maximum bid price is $50.55.

e)

Summary Introduction

To compute: The NPV of the acquisition, if Company B was offered $205,000 of its shares for the stock outstanding of Publications I.

Introduction:

Merger is the complete absorption of one company by another company. The acquiring company acquires all the assets and liabilities of the acquired firm and acquiring firm retains its name and identity. The acquired firm ceases to exist as a separate business entity after a merger.

Answer to Problem 14QP

The NPV is $634,300.

Explanation of Solution

Given information:

“Company B” is analysing the purchase of “Publications I”. Company B expects that earnings and dividends of Publications I to grow at a constant rate of 5% every year. Because of synergy, Company B’s growth rate will increase to 7% each year.

The price earnings ratio of Company B and Publications I are 14.5% and 9.2% respectively. The outstanding shares of Company B and Publications I are $1,400,000 and $195,000 respectively. The earnings of Company B and Publications I are $4,300,000 and $705,000 respectively and the dividends of Company B and Publications I are $1,075,000 and $375,000 respectively.

Formula to compute the EPS of Company B:

${\text{EPS}}_{\text{B}}=\frac{\text{Earnings of Company B}}{\text{Outstanding shares of Company B}}$

Calculate the EPS of Company B:.

$\begin{array}{c}{\text{EPS}}_{\text{B}}=\frac{\text{Earnings of Company B}}{\text{Outstanding shares of Company B}}\\ =\frac{\$4,300,000}{1,400,000}\\ =\$3.07143\end{array}$

Hence, the EPS of Company B is $3.07143.

Formula to calculate the share price of Company B:

${\text{P}}_{\text{B}}=\text{Price earning ratio of Company B}\left({\text{EPS}}_{\text{B}}\right)$

Calculate the share price of Company B:

$\begin{array}{c}{\text{P}}_{\text{B}}=\text{Price earning ratio of Company B}\left({\text{EPS}}_{\text{B}}\right)\\ =14.5\left(\$3.07143\right)\\ =\$44.5357\end{array}$

Hence, the share price of Company B is $44.5357.

Formula to calculate the market value of Company B:

${\text{V}}_{\text{B}}=\text{Outstanding shares of Company B}\left({\text{P}}_{\text{B}}\right)$

Calculate the market value of Company B:

$\begin{array}{c}{\text{V}}_{\text{B}}=\text{Outstanding shares of Company B}\left({\text{P}}_{\text{B}}\right)\\ =1,400,000\left(\$44.5357\right)\\ =\$62,349,980\end{array}$

Hence, the market value of Company B is $62,349,980.

Formula to calculate the price of the stock in the merged firm:

${\text{P}}_{\text{Merged firm }}=\frac{\left({\text{V}}_{\text{B}}+{\text{V}}_{\text{T}}\right)}{\left(\begin{array}{l}\text{Outstanding shares of Company B +}\\ \text{Number of shares offered for exchange}\end{array}\right)}$

Calculate the price of the stock in the merged firm:

$\begin{array}{c}{\text{P}}_{\text{Merged firm }}=\frac{\left({\text{V}}_{\text{B}}+{\text{V}}_{\text{T}}\right)}{\left(\begin{array}{l}\text{Outstanding shares of Company B +}\\ \text{Number of shares offered for exchange}\end{array}\right)}\\ =\frac{\$62,349,980+\$9,857,250}{1,400,000+205,000}\\ =\$44.99\end{array}$

Hence, the price of the merged firm stock is $44.99.

Formula to calculate the NPV:

${\text{NPV=V}}_{\text{I}}-\text{Number of shares offered for exchange}\left({\text{P}}_{\text{Merged firm}}\right)$

Calculate the NPV:

$\begin{array}{c}{\text{NPV=V}}_{\text{I}}-\text{Number of shares offered for exchange}\left({\text{P}}_{\text{Merged firm}}\right)\\ =\$9,857,250-205,000\left(\$44.99\right)\\ =\$634,300\end{array}$

Hence, NPV is $634,300, if Company B offers 205,000 shares in exchange for outstanding stock of Publications I.

f)

Summary Introduction

To discuss: Whether the acquisition must be attempted and the acquisition that must be tried.

Introduction:

Merger is the complete absorption of one company by another company. The acquiring company acquires all the assets and liabilities of the acquired firm and acquiring firm retains its name and identity. The acquired firm ceases to exist as a separate business entity after a merger.

Explanation of Solution

Given information:

“Company B” is analysing the purchase of “Publications I”. Company B expects that earnings and dividends of Publications I to grow at a constant rate of 5% every year. Because of synergy, Company B’s growth rate will increase to 7% each year.

The price earnings ratio of Company B and Publications I are 14.5% and 9.2% respectively. The outstanding shares of Company B and Publications I are $1,400,000 and $195,000 respectively. The earnings of Company B and Publications I are $4,300,000 and $705,000 respectively and the dividends of Company B and Publications I are $1,075,000 and $375,000 respectively.

Yes, the acquisition should go further, and Company B should offer cash of $38 for each share of Publications I.

g)

Summary Introduction

To compute: The NPV, if the outside financial consultants of Company B feel that the growth rate is very optimistic at 7% and it is realistic at 6%.

Introduction:

Merger is the complete absorption of one company by another company. The acquiring company acquires all the assets and liabilities of the acquired firm and acquiring firm retains its name and identity. The acquired firm ceases to exist as a separate business entity after a merger.

Answer to Problem 14QP

The reduction in growth rate, results in positive NPV for cash offer and negative NPV for stock offer.

Explanation of Solution

Given information:

“Company B” is analysing the purchase of “Publications I”. Company B expects that earnings and dividends of Publications I to grow at a constant rate of 5% every year. Because of synergy, Company B’s growth rate will increase to 7% each year.

The price earnings ratio of Company B and Publications I are 14.5% and 9.2% respectively. The outstanding shares of Company B and Publications I are $1,400,000 and $195,000 respectively. The earnings of Company B and Publications I are $4,300,000 and $705,000 respectively and the dividends of Company B and Publications I are $1,075,000 and $375,000 respectively.

Formula to calculate the share price of the target company with changed growth rate:

${\text{P}}_{\text{I}}=\frac{{\text{DPS}}_{\text{T}}\times \left(1+\text{New growth rate}\right)}{\left(\begin{array}{l}\text{Required rate of return of target }\\ \text{company}-\text{New growth rate}\end{array}\right)}$

Calculate the share price of the target company with changed growth rate.

$\begin{array}{c}{\text{P}}_{\text{I}}=\frac{{\text{DPS}}_{\text{T}}\times \left(1+\text{New growth rate}\right)}{\left(\begin{array}{l}\text{Required rate of return of target }\\ \text{company}-\text{New growth rate}\end{array}\right)}\\ =\frac{\text{\$1}\text{.923}\times \left(1+\text{0}\text{.06}\right)}{\left(\text{0}\text{.1107}-\text{0}\text{.06}\right)}\\ =\frac{\text{\$}2.03838}{0.0507}\\ =\$40.20\end{array}$

Hence, the share price of the target company with changed rate of growth is $40.20.

Formula to calculate the value of Publications I to Company B:

${\text{V}}_{\text{I}}\text{*=Outstanding shares of Publications I }\left({\text{P}}_{\text{T}}\right)$

Calculate the value of Publications I to Company B:

$\begin{array}{c}{\text{V}}_{\text{I}}\text{*=Outstanding shares of Publications I }\left({\text{P}}_{\text{T}}\right)\\ =195,000\times \$40.20\\ =\$7,839,000\end{array}$

Hence, the value of Publications I to Company B is $7,839,000.

Formula to calculate Company B’s gain from acquisition:

$\text{Gain = }\left(\begin{array}{l}\text{Value of publications I to Company B}-\\ \text{Outstanding share of Publications I}\times \text{Share price}\end{array}\right)$

Calculate Company B’s gain from acquisition:

$\begin{array}{c}\text{Gain = }\left(\begin{array}{l}\text{Value of publications I to Company B}-\\ \text{Outstanding share of Publications I}\times \text{Share price}\end{array}\right)\\ =\$7,839,000-195,000\times \$33.261496\\ =\$6,485,991.72\end{array}$

Hence, the gain is $6,485,991.72.

Formula to calculate the NPV of the acquisition, if Company B offers $38 in cash for each share of Publications I.

${\text{NPV for cash= V}}_{\text{I}}-\text{Outstanding share of Publications I}\left(\text{Offer price per share}\right)$

Calculate the NPV of the acquisition, if Company B offers $38 in cash for each share of Publications I.

$\begin{array}{c}{\text{NPV for cash= V}}_{\text{I}}-\text{Outstanding share of Publications I}\left(\text{Offer price per share}\right)\\ =\$7,839,000-195,000\left(38\right)\\ =\$429,000\end{array}$

Hence, the NPV for cash is 429,000.

Formula to calculate the price of the stock in the merged firm:

${\text{P}}_{\text{Merged firm }}=\frac{\left({\text{V}}_{\text{B}}+{\text{V}}_{\text{I}}\right)}{\left(\begin{array}{l}\text{Outstanding shares of Company B +}\\ \text{Number of shares offered for exchange}\end{array}\right)}$

Calculate the price of the stock in the merged firm:

$\begin{array}{c}{\text{P}}_{\text{Merged firm }}=\frac{\left({\text{V}}_{\text{B}}+{\text{V}}_{\text{I}}\right)}{\left(\begin{array}{l}\text{Outstanding shares of Company B +}\\ \text{Number of shares offered for exchange}\end{array}\right)}\\ =\frac{\$62,349,980+\$7,839,000}{1,400,000+205,000}\\ =\$43.73\end{array}$

Hence, the price of the merged stock firm is $43.73.

Formula to calculate the NPV for stock offer:

${\text{NPV for stock=V}}_{\text{I}}-\text{Number of shares offered for exchange}\left({\text{P}}_{\text{Merged firm}}\right)$

Calculate the NPV for stock offer:

$\begin{array}{c}{\text{NPV for stock=V}}_{\text{I}}-\text{Number of shares offered for exchange}\left({\text{P}}_{\text{Merged firm}}\right)\\ =\$7,839,000-205,000\left(\$43.73\right)\\ =-\$1,125,650\end{array}$

Note:

• EPS represents Earnings Per Share
• NPV represents Net Present Value
• P represents Share price
• DPS represents Dividend Per Share
• V represents Market Value

Hence, the NPV for stock is -$1,125,650.