Chapter 29, Problem 15QP

a.

Summary Introduction

To calculate: The value of firm Pa to firm Pl

Merger:

Merger is the combination of two entities into one in which shareholders of both the companies merge their resources into the new company. The merger is basically the result of merging the two or more companies into one.

Purchase Accounting Method for Mergers:

In the purchase accounting method, the assets of the targeted company have to be recording the current market value in the books of acquiring companies and goodwill assets account has to be created. The goodwill is the difference of current market value and the purchase price.

Earnings per Share:

Earnings per share is a profitability ratio. It is used to compute the earnings earned per share by the shareholders. It tells about that how much amount a shareholder earns by holding per share.

Explanation of Solution

Given,

Shares outstanding of firm Pa are 750,000.

Market price per share of firm Pa after new growth is $21.47(Working notes).

Formula to calculate value of firm Pa to firm Pl,

$\text{Value}\text{of}\text{firm}\text{Pa}\text{to}\text{firm}\text{Pl}=\left(\begin{array}{l}\text{Shares}\text{outstanding}\text{of}\text{firm}\text{Pa}\\ \times \text{Price}\text{per}\text{share}\text{of}\text{firm}\text{Pa}\text{after}\text{new}\text{growth}\end{array}\right)$

Substitute 750,000 for shares outstanding of firm Pa and $21.47 for price per share of firm Pa after new growth.

$\begin{array}{c}\text{Value}\text{of}\text{firm}\text{Pa}\text{to}\text{firm}\text{Pl}=750,000\times \$21.47\\ =\$16,102,500\end{array}$

Working notes:

Given,

Earnings of firm Pa are $960,000.

Shares outstanding of firm Pa are 750,000.

Calculation of EPS of firm Pa,

$\begin{array}{c}\text{EPS}=\frac{\text{Earnings}}{\text{Shares}\text{}\text{outstanding}}\\ =\frac{\$960,000}{750,000}\\ =\$1.28\text{per}\text{share}\end{array}$

The EPS of firm Pa is $1.28 per share.

Given,

Price-earnings ratio(P/E ratio) of firm Pa is 10.

The EPS of firm Pa is $1.28 per share (calculated above).

Calculation of market price per share of firm Pa,

$\begin{array}{c}\text{Market}\text{price}\text{per}\text{share}=\text{P/E}\text{ratio}\times \text{EPS}\\ =\text{10}\times \text{\$1}\text{.28}\text{per}\text{share}\\ =\$12.8\text{per}\text{share}\end{array}$

The market price per share of firm Pa is $12.8 per share.

Given,

Dividends of firm Pa is 470,000.

Shares outstanding of firm Pa are 750,000.

Calculation of dividend per share,

$\begin{array}{c}\text{Dividend}\text{per}\text{share}=\frac{\text{Dividends}}{\text{Shares}\text{outstanding}}\\ =\frac{470,000}{750,000}\\ =0.63\text{per}\text{share}\end{array}$

The dividend per share of firm Pa is 0.63 per share.

Given,

Growth rate of firm Pa before merger is 4% (0.04).

Dividend per share of firm Pa is $0.63 per share (calculated above).

Market price per share of firm Pa is $12.8 per share (calculated above).

Calculation of current return of the shareholders of firm Pa,

$\begin{array}{c}\text{Current}\text{return}=\frac{\text{Dividend}\text{per}\text{share}\times \left(1+\text{Growth}\text{rate}\right)}{\text{Market}\text{price}\text{per}\text{share}}+\text{Growth}\text{rate}\\ =\frac{0.63\times \left(1+0.04\right)}{12.8}+0.04\\ =0.052+0.04\\ =0.0911\end{array}$

The current return of the shareholders of firm Pa is 0.0911 per share.

Given,

New growth rate is 6% (0.06).

Dividend per share of firm Pa is 0.63 per share (calculated above).

Current return of the shareholders of firm Pa is 0.911 per share (calculated above).

Calculation of market price per share of firm Pa with the new growth rate is,

$\begin{array}{c}\left[\begin{array}{l}\text{Market}\text{price}\text{per}\\ \text{share}\text{with}\text{new}\text{growth}\end{array}\right]=\left[\frac{\text{Dividend}\text{per}\text{}\text{share}\times \left(1+\text{New}\text{growth}\text{rate}\right)}{\text{Current}\text{return}-\text{New}\text{growth}\text{}\text{rate}}\right]\\ =\frac{0.63\times \left(1+0.06\right)}{0.0911-0.06}\\ =\frac{0.63\times 1.06}{0.0311}\\ =21.47\end{array}$

The market price per share of firm Pa with the new growth rate is $21.47.

Conclusion

The value of firm Pa to firm Pl is $16,102,500.

b.

Summary Introduction

To calculate:Firm Pl’s gain from the acquisition.

Purchase Accounting Method for Mergers:

In the purchase accounting method, the assets of the targeted company has to be recorded into the current market value in the books of acquiring company and goodwill assets account has to be created. Goodwill is the difference of current market value and purchase price.

Explanation of Solution

Given,

The value of firm Pa to firm Pl is $16,102,500 (refer part a).

Market value of firm Pa is $9,600,000 (working notes).

Formula to calculate the gain to firm Pl,

$\text{Gain}\text{to}\text{firm}\text{Pl}=\text{Value}\text{of}\text{firm}\text{Pa}\text{to}\text{firm}\text{Pl}-\text{Market}\text{value}\text{of}\text{firm}\text{Pa}$

Substitute $16,102,500for the value of firm Pa to firm Pl and $9,600,000 for the market value of firm Pa.

$\begin{array}{c}\text{Gain}\text{to}\text{firm}\text{}\text{Pl}=\$16,102,500-\$9,600,000\\ =\$6,502,500\end{array}$

Working notes:

Given,

Shares outstanding of firm Pa is 750,000.

Market price per share of firm Pa before new growth rate is $12.8 per share (refer part a).

Calculation of market value of firm Pa,

$\begin{array}{c}\text{Market}\text{}\text{value}\text{of}\text{}\text{firm}\text{Pa}=\text{Shares}\text{outstanding}\times \text{Price}\text{per}\text{share}\\ =750,000\times \$12.80\\ =\$9,600,000\end{array}$

Conclusion

The gain of firm Pl from the acquisition is $6,502,500.

c.

Summary Introduction

To calculate:The NPV of the acquisition if the firm Pl offers $20 in cash for each share of firm Pa.

Net Present Value (NPV):

Net present value is a capital budgeting technique which helps to find out the difference of present value of cash inflow and cash outflow of a future project.

Explanation of Solution

Given,

The value of firm Pa to firm Pl is $16,102,500(refer part a).

Cost of acquisition is $15,000,000 (working notes).

Formula to calculate the NPV of the acquisition,

$\text{NPV}=\text{Value}\text{of}\text{}\text{firm}\text{}\text{Pa}\text{to }\text{}\text{firm}\text{Pl}-\text{Cost}\text{of}\text{acquisition}$

Substitute $16,102,500 for the value of firm Pa to firm Pl and $15,000,000 (Refer working notes) for the cost of acquisition.

$\begin{array}{c}\text{NPV}=\$16,102,500-\$15,000,000\\ =\$1,102,500\end{array}$

Working notes:

Given,

Shares outstanding of firm Pa is 750,000.

Cash offer for each shareholder of firm Pa is $20.

Calculation of cost of acquisition,

$\begin{array}{c}\text{Cost}\text{of}\text{acquisition}=\left[\begin{array}{l}\text{Shares}\text{ouststanding}\\ \times \text{Cash}\text{offer }\text{}\text{for}\text{each}\text{shareholder}\text{of}\text{firm}\text{Pa}\end{array}\right]\\ =750,000\times \$20\\ =\$15,000,000\end{array}$

Cost of acquisition is $15,000,000.

Conclusion

The NPV of the acquisition if $20 in cash is offer for each share of firm Pa is $1,102,500.

d.

Summary Introduction

To calculate: Maximum bid price firm Pl will be willing to pay in cash per share for the stock of firm Pa.

Net Present Value (NPV):

Net present value is a capital budgeting technique which helps to find out the difference of present value of cash inflow and cash outflow of a future project.

Explanation of Solution

Given,

Cash offer for each shareholder of firm Pa is $20.

NPV per share when cash offers to firm Pa is $1.47 per share (working notes).

Formula to calculate maximum bid price,

$\text{Maximum}\text{bid}\text{price}=\text{Cash}\text{}\text{offer}\text{per}\text{share}+\text{NPV}\text{per}\text{share}$

Substitute $20 for cash offer per share and $1.47 for NPV per share.

$\begin{array}{c}\text{Maximum}\text{bid}\text{price}=\$20+\$1.47\\ =\$21.47\end{array}$

Working notes:

Given,

Shares outstanding f firm Pa is 750,000.

Total NPV when $20 in cash is offer for each share of firm Pa is 1,102,500(refer part c).

Calculation of NPV per share,

$\begin{array}{c}\text{NPV}\text{per}\text{share}=\frac{\text{Total}\text{NPV}}{\text{Shares}\text{outstanding}}\\ =\frac{\$1,102,500}{750,000}\\ =\$1.47\text{per}\text{share}\end{array}$

Conclusion

The maximum bid price that firm Pl should be willing to pay in cash per share for the stock of firm Pa is $21.47.

e.

Summary Introduction

To calculate:The NPV, if firm Pl offers 225,000 of its share in exchange for the outstanding stock of firm Pa.

Net Present Value (NPV):

Net present value is a capital budgeting technique which helps to find out the difference of present value of cash inflow and cash outflow of a future project.

Earnings per Share:

Earnings per share is a profitability ratio. It is used to calculate the earnings earned per share by the shareholders. It tells about that how much amount a shareholders earns by holding per share

Explanation of Solution

Given,

Value of firm Pa to firm Pl is $16,102,500 (refer part a).

Cost of acquisition is $10,044,000(working notes).

Formula to calculate the NPV,

$\text{NPV}=\text{Value}\text{of}\text{}\text{firm}\text{}\text{Pa}\text{to}\text{}\text{firm}\text{Pl}-\text{Cost}\text{of}\text{acquisition}$

Substitute $16,102,500 for value of firm Pa to firm Pl and $10,044,000 for cost of acquisition.

$\begin{array}{c}\text{NPV}=\$16,102,500-\$10,044,000\\ =\$6,058,500\end{array}$

Working notes:

Given,

Earnings of firm Pl is $4,200,000.

Shares outstanding of firm Pl is 1,500,000.

Calculation of EPS of firm Pl,

$\begin{array}{c}\text{EPS}=\frac{\text{Earnings}}{\text{Shares}\text{}\text{outstanding}}\\ =\frac{\$4,200,000}{1,500,000}\\ =\$2.8\text{per}\text{share}\end{array}$

Given,

Price earnings ratio is 14.5.

EPS of firm Pl is $2.8 per share (as calculated above).

Calculation of market price per share,

$\begin{array}{c}\text{Market}\text{price}\text{per}\text{share}=\text{P/E}\text{ratio}\times \text{EPS}\\ =14.5\times \text{\$2}\text{.8per}\text{share}\\ =\$40.6\text{per}\text{share}\end{array}$

Given,

Shares outstanding of firm Pl are 1,500,000.

Market price per share of firm Pl is $40.6 per share (calculated as above).

Calculation of market value of firm Pl,

$\begin{array}{c}\text{Market}\text{value}\text{of}\text{}\text{firm}\text{Pl}=\left(\begin{array}{l}\text{Shares}\text{outstanding}\\ \times \text{Market}\text{price}\text{per}\text{share}\end{array}\right)\\ =1,500,000\times \$40.6\\ =\$60,900,000\end{array}$

Given,

Market value of firm Pl is $60,900,000 (calculated as above).

Value of firm Pa to firm Pl is 16,102,500(refer part a).

Calculation of market value of merged firm,

$\begin{array}{c}\text{Market}\text{value}\text{of}\text{merged}\text{firm}=\left[\begin{array}{l}\text{Market}\text{value}\text{of}\text{}\text{acquiring}\text{firm}\\ +\text{Market}\text{value}\text{of}\text{target}\text{firm}\text{to}\text{acquiring}\text{firm}\end{array}\right]\\ =\$60,900,000+\$16,102,500\\ =\$77,002,500\end{array}$

Given,

Shares outstanding of firm Pl is 1,500,000.

Shares offered to firm Pa are 225,000.

Calculation of number of shares outstanding of merged firm,

$\begin{array}{c}\text{Shares}\text{outstanding}\text{of}\text{merged}\text{firm}=\left[\begin{array}{l}\text{Shares}\text{outstanding}\text{of}\text{}\text{firm}\text{Pl}\\ +\text{Shares}\text{offered}\text{to}\text{}\text{firm}\text{Pa}\end{array}\right]\\ =1,500,000+225,000\\ =1,725,000\end{array}$

Given,

Market value of merged firm is $77,002,500 (as calculated above).

Shares outstanding of merged firm are 1,725,000 (calculated as above).

Calculation of Stock price of merged firm,

$\begin{array}{c}\text{Stock}\text{price}\text{of}\text{}\text{merged}\text{firm}=\frac{\text{Value}\text{of}\text{merged}\text{firm}}{\text{Shares}\text{outstanding}\text{of}\text{merged}\text{firm}}\\ =\frac{\$77,002,500}{1,725,000}\\ =\$44.64\end{array}$

Given,

Shares offer to firm Pa are 225,000.

Stock price of merged firm is $44.64 per share (calculated as above).

Calculation of cost of acquisition,

$\begin{array}{c}\text{Cost}\text{of}\text{}\text{acquisition}=\left[\begin{array}{l}\text{Shares}\text{}\text{offered}\text{to}\text{target}\text{firm}\\ \times \text{Stock}\text{price}\text{per}\text{share}\end{array}\right]\text{}\\ =225,000\times \$44.64\\ =\$10,044,000\end{array}$

Conclusion

The NPV is $6,058,500 when stock is offer to the target firm.

f.

Summary Introduction

To detemine:Whether acquisition should be attempted and the offer should be made for pay off the target firm.

Answer to Problem 15QP

• Yes, the acquisition should be attempted.
• Firm should make the stock offer since its NPV is higher.

Explanation of Solution

• The alternative with higher NPV is preferred as it gives higher benefits.
• The net present value is computed on the discounting factor of future benefits of cost.

Conclusion

The acquisition should be attempted. The payment should be makes to the target firm with stock offer.

g.

Summary Introduction

To identify:The change of growth rate from 6% to 5% and their effect on above answers.

Merger:

Merger is the combination of two entities into one in which shareholders of both the companies merge their resources into the new company. A merger is basically the result of mergingthe two or more companies into one.

Purchase Accounting Method for Mergers:

In the purchase accounting method the assets of the targeted company haveto be recorded in the current market value in the books of acquiring companiesand goodwill assets account has to be created. The goodwill is the difference of current market value and the purchase price.

Earnings per Share:

Earnings per share is a profitability ratio. It is used to compute the earnings earned per share by the shareholders. It tells about that how much amount a shareholder earns by holding per share

Net Present Value (NPV):

Net present value is a capital budgeting technique which helps to find out the difference of present value of cash inflow and cash outflow of a future project.

Explanation of Solution

Calculation of market price per share of firm Pa with the new growth rate is,

Given,

New growth rate is 5% (0.05).

Dividend per share of firm Pa is $0.63 per share (refer part a).

Current return of the shareholders of firm Pa is $0.911 per share (refer part a).

Formula to calculate the market price per share of firm Pa with the new growth rate,

$\left[\begin{array}{l}\text{Market}\text{price}\text{per}\\ \text{share}\text{with}\text{new}\text{growth}\end{array}\right]=\left[\frac{\text{Dividend}\text{per}\text{}\text{share}\times \left(1+\text{New}\text{growth}\text{rate}\right)}{\text{Current}\text{return}-\text{New}\text{growth}\text{}\text{rate}}\right]$

Substitute $0.63 for dividend per share, 0.05 for new growth rate and $0.0911 for current return.

$\begin{array}{c}\text{Market}\text{price}\text{per}\text{share}\text{with}\text{new}\text{growth}=\frac{0.63\times \left(1+0.05\right)}{0.0911-0.05}\\ =\frac{0.63\times 1.05}{0.0411}\\ =16.09\end{array}$

The market price per share of firm Pa with the new growth rate is $16.09.

Calculation of value of firm Pa to firm Pl

Given,

Shares outstanding of firm Pa are 750,000.

Market price per share of firm Pa after new growth is $16.09.

Formula to calculate value of firm Pa to firm Pl,

$\text{Value}\text{of}\text{firm}\text{Pa}\text{to}\text{firm}\text{Pl}=\left(\begin{array}{l}\text{Shares}\text{outstanding}\text{of}\text{firm}\text{Pa}\\ \times \text{Price}\text{per}\text{share}\text{of}\text{firm}\text{Pa}\text{after}\text{new}\text{growth}\end{array}\right)$

Substitute 750,000 for shares outstanding of firm Pa and $16.09 for price per share of firm Pa after new growth.

$\begin{array}{c}\text{Value}\text{of}\text{firm}\text{Pa}\text{to}\text{firm}\text{Pl}=750,000\times \$16.09\\ =\$12,067,500\end{array}$

Calculation of firm Pl’s gain from the acquisition

Given,

The value of firm Pa to firm Pl is $12,067,500.

Market value of firm Pa is $9,600,000 (refer part b).

Formula to calculate the gain to firm Pl,

$\text{Gain}\text{to}\text{firm}\text{Pl}=\text{Value}\text{of}\text{firm}\text{Pa}\text{to}\text{firm}\text{Pl}-\text{Market}\text{value}\text{of}\text{firm}\text{Pa}$

Substitute $12,067,500 for the value of firm Pa to firm Pl and $9,600,000 for the market value of firm Pa.

$\begin{array}{c}\text{Gain}\text{to}\text{firm}\text{}\text{Pl}=\$12,067,500-\$9,600,000\\ =\$2,467,500\end{array}$

Calculation of NPV when cash is offer to the target firm

Given,

Value of firm Pa to firm Pl is $12,067,500.

Cost of acquisition is $10,044,000(refer part c).

Formula to calculate the NPV,

$\text{NPV}=\text{Value}\text{of}\text{}\text{firm}\text{}\text{Pa}\text{to}\text{}\text{firm}\text{Pl}-\text{Cost}\text{of}\text{acquisition}$

Substitute $12,067,500 for value of firm Pa to firm Pl and $10,044,000 for cost of acquisition.

$\begin{array}{c}\text{NPV}=\$12,067,500-\$10,044,000\\ =\$2,023,500\end{array}$

Calculation of market value of merged firm,

Calculated,

Market value of firm Pl is $60,900,000.

Value of firm Pa to firm Pl is 12,067,500.

Formula to calculate the market value of merged firm,

$\text{Market}\text{value}\text{of}\text{merged}\text{firm}=\left[\begin{array}{l}\text{Market}\text{value}\text{of}\text{}\text{acquiring}\text{firm}\\ +\text{Market}\text{value}\text{of}\text{target}\text{firm}\text{to}\text{acquiring}\text{firm}\end{array}\right]$

Substitute $60,900,000 for market value of acquiring firm and $12,067,500 for market value of target firm to acquiring firm.

$\begin{array}{c}\text{Market}\text{value}\text{of}\text{merged}\text{firm}=\$60,900,000+\$12,067,500\\ =\$72,967,500\end{array}$

Calculation of Stock price of merged firm

Given,

Market value of merged firm is $72,967,500.

Shares outstanding of merged firm are 1,725,000.

Formula to calculate the stock price of merged firm,

$\text{Stock}\text{price}\text{of}\text{}\text{merged}\text{firm}=\frac{\text{Value}\text{of}\text{merged}\text{firm}}{\text{Shares}\text{outstanding}\text{of}\text{merged}\text{firm}}$

Substitute $72,967,500 for value of merged firm and 1,725,000 for shares outstanding of merged firm.

$\begin{array}{c}\text{Stock}\text{price}\text{of}\text{}\text{merged}\text{firm}=\frac{\$72,967,500}{1,725,000}\\ =\$42.3\end{array}$

Calculation of cost of acquisition when stock is offer to the target firm

Given,

Shares offer to firm Pa are 225,000.

Stock price of merged firm is $42.3 per share.

Formula to calculate the cost of acquisition,

$\text{Cost}\text{of}\text{}\text{acquisition}=\text{Shares}\text{}\text{offered}\text{to}\text{target}\text{firm}\times \text{Stock}\text{price}\text{per}\text{share}$

Substitute 225,000 for shares offered to target firm and $42.3 for stock price per share.

$\begin{array}{c}\text{Cost}\text{of}\text{}\text{acquisition}=225,000\times \$42.3\\ =\$9,517,500\end{array}$

Calculation of NPV when stock is offer to the target firm

Given,

Value of firm Pa to firm Pl is $12,067,500.

Cost of acquisition is $10,044,000.

Formula to calculate the NPV,

$\text{NPV}=\text{Value}\text{of}\text{}\text{firm}\text{}\text{Pa}\text{to}\text{}\text{firm}\text{Pl}-\text{Cost}\text{of}\text{acquisition}$

Substitute $12,067,500 for value of firm Pa to firm Pl and $10,044,000 for cost of acquisition.

$\begin{array}{c}\text{NPV}=\$12,067,500-\$10,044,000\\ =\$2,023,500\end{array}$

Conclusion: The stock offer has positive NPV even with lower projected growth rate.