Chapter 12, Problem 4PA

Summary Introduction

(a)

To determine:

Price-to-book ratio, price/earnings ratio and book value per share.

Introduction:

Price-to-book-ratio is used in comparison of present market value of a company’s equity share with it’s per share value based on equity shares available to common stockholders.

Price earnings ratio is the connection between the present market price of company’s stock and its profit per share.

Book value per share is the accounting value of each share of stock of a company. It is calculated by dividing the total book value of shares by total number of shares which are currently held by general public, shareholders of the company and its officials.

Explanation of Solution

Given,

Earnings/revenue is $1,500,000.

Value of assets is $7,000,000.

Value of liabilities is $1,500,000.

Number of shares outstanding is 500,000.

Market price per share is $33.

Formula to calculate price-to-book ratio is,

$\text{Price}\text{to}\text{book}\text{ratio}=\frac{\text{Market}\text{price}\text{per}\text{share}}{\text{Book}\text{value}\text{per}\text{share}}$

Substitute $33 for market price per share and $11 for book value of share in the above equation.

$\begin{array}{c}\text{Price}\text{to}\text{book}\text{ratio}=\frac{\$33}{\$11}\\ =\$3\end{array}$

Price to book ratio is $3.

Given,

Earnings/revenue is $1,500,000.

Value of assets is $7,000,000.

Value of liabilities is $1,500,000.

Number of shares outstanding is 500,000.

Market price per share is $33.

Formula to calculate price/earnings ratio is,

$\text{Price}\text{earning}\text{ratio}=\frac{\text{Market}\text{price}\text{per}\text{share}}{\text{Earnings}\text{per}\text{share}}$

Substitute $33 for market price per share and $3 for earnings per share in the above equation.

$\begin{array}{c}\text{Price}\text{earning}\text{ratio}=\frac{\$33}{\$3}\\ =11\end{array}$

Price earnings ratio is 11 times.

Given,

Earnings/revenue is $1,500,000.

Value of assets is $7,000,000.

Value of liabilities is $1,500,000.

Number of shares outstanding is 500,000.

Market price per share is $33.

Formula to calculate book value per share is,

$\text{Book}\text{value}\text{per}\text{share}=\frac{\text{Assets}-\text{Liabilities}}{\text{Total}\text{number}\text{of}\text{shares}\text{outstanding}}$

Substitute $7,000,000 for assets, $1,500,000 for liabilities and 500,000 for total number of shares outstanding in the above equation.

$\begin{array}{c}\text{Book}\text{value}\text{per}\text{share}=\frac{\$7,000,000-\$1,500,000}{500,000}\\ =\frac{\$5,500,000}{500,000}\\ =\$11\end{array}$

Book value per share is $11.

Working note:

Calculation of book value per share,

$\begin{array}{c}\text{Book}\text{value}\text{per}\text{share}=\frac{\text{Assets}-\text{Liabilities}}{\text{Total}\text{number}\text{of}\text{shares}\text{outstanding}}\\ =\frac{\$7,000,000-\$1,500,000}{500,000}\\ =\frac{\$5,500,000}{500,000}\\ =\$11\end{array}$

Book value per share is $11.

Calculation of earnings per share,

$\begin{array}{c}\text{Earnings}\text{per}\text{share}=\frac{\text{Earnings/Revenue}}{\text{Number}\text{of}\text{shares}\text{outstanding}}\\ =\frac{\$1,500,000}{500,000}\\ =\$3\end{array}$

Earnings per share are $3.

Conclusion

Hence, the price-to-book ratio of W Corporation is $3, the price earnings ratio of W Corporation is 11 times and book value of share of W Corporation is $11.

Summary Introduction

(b)

To determine:

Price-to-book ratio, price/earnings ratio and book value per share when earnings falls to $1,000,000.

Explanation of Solution

Given,

Earnings/revenue is $1,000,000

Value of assets is $7,000,000.

Value of liabilities is $1,500,000.

Number of shares outstanding is 500,000.

Market price per share is $33.

Formula to calculate price-to-book ratio is,

$\text{Price}\text{to}\text{book}\text{ratio}=\frac{\text{Market}\text{price}\text{per}\text{share}}{\text{Book}\text{value}\text{per}\text{share}}$

Substitute $33 for market price per share and $11 for book value of share in the above equation.

$\begin{array}{c}\text{Price}\text{to}\text{book}\text{ratio}=\frac{\$33}{\$11}\\ =\$3\end{array}$

Price to book ratio is $3.

Given,

Earnings/revenue is $1,000,000.

Value of assets is $7,000,000.

Value of liabilities is $1,500,000.

Number of shares outstanding is 500,000.

Market price per share is $33.

Formula to calculate price/earnings ratio is,

$\text{Price}\text{earning}\text{ratio}=\frac{\text{Market}\text{price}\text{per}\text{share}}{\text{Earnings}\text{per}\text{share}}$

Substitute $33 for market price per share and $3 for earnings per share in the above equation.

$\begin{array}{c}\text{Price}\text{earning}\text{ratio}=\frac{\$33}{\$2}\\ =16.5\end{array}$

Price earnings ratio is 16.5 times.

Given,

Earnings/revenue is $1,500,000.

Value of assets is $7,000,000.

Value of liabilities is $1,500,000.

Number of shares outstanding is 500,000.

Market price per share is $33.

Formula to calculate book value per share is,

$\text{Book}\text{value}\text{per}\text{share}=\frac{\text{Assets}-\text{Liabilities}}{\text{Total}\text{number}\text{of}\text{shares}\text{outstanding}}$

Substitute $7,000,000 for assets, $1,500,000 for liabilities and 500,000 for total number of shares outstanding in the above equation.

$\begin{array}{c}\text{Book}\text{value}\text{per}\text{share}=\frac{\text{Assets}-\text{Liabilities}}{\text{Total}\text{number}\text{of}\text{shares}\text{outstanding}}\\ =\frac{\$7,000,000-\$1,500,000}{500,000}\\ =\frac{\$5,500,000}{500,000}\\ =\$11\end{array}$

Book value per share is $11.

Conclusion

Hence, the price-to-book ratio of W Corporation is $3, the price earnings ratio of W Corporation is 16.5 times and book value of share of W Corporation is $11.

Working note:

Calculation of book value per share,

$\begin{array}{c}\text{Book}\text{value}\text{per}\text{share}=\frac{\text{Assets}-\text{Liabilities}}{\text{Total}\text{number}\text{of}\text{shares}\text{outstanding}}\\ =\frac{\$7,000,000-\$1,500,000}{500,000}\\ =\frac{\$5,500,000}{500,000}\\ =\$11\end{array}$

Book value per share is $11.

Calculation of earnings per share,

$\begin{array}{c}\text{Earnings}\text{per}\text{share}=\frac{\text{Earnings/Revenue}}{\text{Number}\text{of}\text{shares}\text{outstanding}}\\ =\frac{\$1,000,000}{500,000}\\ =\$2\end{array}$

Earnings per share are $2.

Summary Introduction

(c)

To determine:

Price-to-book ratio, price/earnings ratio and book value per share when liabilities increase to $2,500,000

Explanation of Solution

Given,

Earnings/revenue is $1,500,000

Value of assets is $7,000,000.

Value of liabilities is $2,500,000.

Number of shares outstanding is 500,000.

Market price per share is $33.

Formula to calculate price-to-book ratio is,

$\text{Price}\text{to}\text{book}\text{ratio}=\frac{\text{Market}\text{price}\text{per}\text{share}}{\text{Book}\text{value}\text{per}\text{share}}$

Substitute $33 for market price per share and $11 for book value of share in the above equation.

$\begin{array}{c}\text{Price}\text{to}\text{book}\text{ratio}=\frac{\$33}{\$9}\\ =\$3.67\end{array}$

Price to book ratio is $3.67.

Given,

Earnings/revenue is $1,500,000.

Value of assets is $7,000,000.

Value of liabilities is $2,500,000.

Number of shares outstanding is 500,000.

Market price per share is $33.

Formula to calculate price/earnings ratio is,

$\text{Price}\text{earning}\text{ratio}=\frac{\text{Market}\text{price}\text{per}\text{share}}{\text{Earnings}\text{per}\text{share}}$

Substitute $33 for market price per share and $3 for earnings per share in the above equation.

$\begin{array}{c}\text{Price}\text{earning}\text{ratio}=\frac{\$33}{\$3}\\ =11\end{array}$

Price earnings ratio is 11 times.

Given,

Earnings/revenue is $1,500,000

Value of assets is $7,000,000.

Value of liabilities is $2,500,000.

Number of shares outstanding is 500,000.

Market price per share is $33.

Formula to calculate book value per share is,

$\text{Book}\text{value}\text{per}\text{share}=\frac{\text{Assets}-\text{Liabilities}}{\text{Total}\text{number}\text{of}\text{shares}\text{outstanding}}$

Substitute $7,000,000 for assets, $2,500,000 for liabilities and 500,000 for total number of shares outstanding in the above equation.

$\begin{array}{c}\text{Book}\text{value}\text{per}\text{share}=\frac{\text{Assets}-\text{Liabilities}}{\text{Total}\text{number}\text{of}\text{shares}\text{outstanding}}\\ =\frac{\$7,000,000-\$2,500,000}{500,000}\\ =\frac{\$4,500,000}{500,000}\\ =\$9\end{array}$

Book value per share is $9.

Working note:

Calculation of book value per share,

$\begin{array}{c}\text{Book}\text{value}\text{per}\text{share}=\frac{\text{Assets}-\text{Liabilities}}{\text{Total}\text{number}\text{of}\text{shares}\text{outstanding}}\\ =\frac{\$7,000,000-\$2,500,000}{500,000}\\ =\frac{\$4,500,000}{500,000}\\ =\$9\end{array}$

Book value per share is $11.

Calculation of earnings per share,

$\begin{array}{c}\text{Earnings}\text{per}\text{share}=\frac{\text{Earnings/Revenue}}{\text{Number}\text{of}\text{shares}\text{outstanding}}\\ =\frac{\$1,500,000}{500,000}\\ =\$3\end{array}$

Earnings per share are $3.

Conclusion

Hence, the price-to-book ratio of W Corporation is $3.67, the price earnings ratio of W Corporation is 11 times and book value of share of W Corporation is $9.

Summary Introduction

(d)

To determine:

Price-to-book ratio, price/earnings ratio and book value per share after a three-for-one share split.

Introduction:

Stock Split is the breakdown of shares of a company which increases the number of shares available to trade in market without affecting the market value or market capitalization of company.

Explanation of Solution

Given,

Earnings/revenue is $1,500,000.

Value of assets is $7,000,000.

Value of liabilities is $1,500,000.

Number of shares outstanding is 500,000.

Market price per share is $33.

Split ratio is three-for-one.

Formula to calculate price-to-book ratio is,

$\text{Price}\text{to}\text{book}\text{ratio}=\frac{\text{Market}\text{price}\text{per}\text{share}}{\text{Book}\text{value}\text{per}\text{share}}$

Substitute $11 for market price per share and $3.67 for book value of share in the above equation.

$\begin{array}{c}\text{Price}\text{to}\text{book}\text{ratio}=\frac{\$11}{\$3.67}\\ =\$2.99\end{array}$

Price to book ratio is $2.99.

Given,

Earnings/revenue is $1,500,000.

Value of assets is $7,000,000.

Value of liabilities is $1,500,000.

Number of shares outstanding is 500,000.

Market price per share is $33.

Split ratio is three-for-one.

Formula to calculate price/earnings ratio is,

$\text{Price}\text{earning}\text{ratio}=\frac{\text{Market}\text{price}\text{per}\text{share}}{\text{Earnings}\text{per}\text{share}}$

Substitute $11 for market price per share and $1 for earnings per share in the above equation.

$\begin{array}{c}\text{Price}\text{earning}\text{ratio}=\frac{\$11}{\$1}\\ =11\end{array}$

Price earnings ratio is $11 times.

Given,

Earnings/revenue is $1,500,000.

Value of assets is $7,000,000.

Value of liabilities is $1,500,000.

Number of shares outstanding is 500,000.

Market price per share is $33.

Split ratio is three-for-one.

Formula to calculate book value per share is,

$\text{Book}\text{value}\text{per}\text{share}=\frac{\text{Assets}-\text{Liabilities}}{\text{Total}\text{number}\text{of}\text{shares}\text{outstanding}}$

Substitute $7,000,000 for assets, $1,500,000 for liabilities and 1,500,000 for total number of shares outstanding in the above equation.

$\begin{array}{c}\text{Book}\text{value}\text{per}\text{share}=\frac{\$7,000,000-\$1,500,000}{1,500,000}\\ =\frac{\$5,500,000}{1,500,000}\\ =\$3.67\end{array}$

Book value per share is $3.67.

Working note:

Calculation of book value per share,

$\begin{array}{c}\text{Book}\text{value}\text{per}\text{share}=\frac{\text{Assets}-\text{Liabilities}}{\text{Total}\text{number}\text{of}\text{shares}\text{outstanding}}\\ =\frac{\$7,000,000-\$1,500,000}{1,500,000}\\ =\frac{\$5,500,000}{1,500,000}\\ =\$3.67\end{array}$

Book value per share is $3.67.

Calculation of number of shares after three-for-one split,

$\begin{array}{c}\text{New}\text{number}\text{of}\text{shares}=\text{Number}\text{of}\text{shares}\times \text{Split}\text{ratio}\\ =5\text{00,000}\times 3\\ =1,500,000\end{array}$

Number of shares after split is 1,500,000.

Calculation of market price of share after three-for-one split,

$\begin{array}{c}\text{Market}\text{price}\text{after}\text{split}=\frac{\text{Market}\text{price}\text{of}\text{share}\text{before}\text{split}}{\text{Split}\text{ratio}}\\ =\frac{\$33}{3}\\ =\$11\end{array}$

Market price per share after split is $11.

Calculation of earnings per share,

$\begin{array}{c}\text{Earnings}\text{per}\text{share}=\frac{\text{Earnings/Revenue}}{\text{Number}\text{of}\text{shares}\text{outstanding}}\\ =\frac{\$1,500,000}{1,500,000}\\ =\$1\end{array}$

Earnings per share is $1.

Calculation of number of shares after three-for-one split,

$\begin{array}{c}\text{New}\text{number}\text{of}\text{shares}=\text{Number}\text{of}\text{shares}\times \text{Split}\text{ratio}\\ =\text{500,000}\times 3\\ =1,500,000\end{array}$

New number of shares after split is 1,500,000 shares.

Conclusion

Hence, the price-to-book ratio of W Corporation is $2.99, the price earnings ratio of W Corporation is $11 times and book value of share of W Corporation is $3.67 respectively after three-for-one split.

Summary Introduction

(e)

To determine:

Price-to-book ratio, price/earnings ratio and book value per share after the repurchase of 20 percent shares incurring additional liability.

Introduction:

Stock repurchase is purchase of a company’s own shares from the open market to decrease the quantity of shares presently owned by all the stockholders of the company.

Explanation of Solution

Given,

Earnings/revenue is $1,500,000.

Value of assets is $7,000,000.

Value of liabilities is $1,500,000.

Number of shares outstanding is 500,000.

Market price per share is $33.

Calculated values,

Number of stocks repurchased is 100,000.

Additional liability to finance the purchase is $3,300,000.

Formula to calculate price-to-book ratio is,

$\text{Price}\text{to}\text{book}\text{ratio}=\frac{\text{Market}\text{price}\text{per}\text{share}}{\text{Book}\text{value}\text{per}\text{share}}$

Substitute $33 for market price per share and $5.5 for book value of share in the above equation.

$\begin{array}{c}\text{Price}\text{to}\text{book}\text{ratio}=\frac{\$33}{\$5.5}\\ =\$6\end{array}$

Price to book ratio is $6

Given,

Earnings/revenue is $1,500,000.

Value of assets is $7,000,000.

Value of liabilities is $1,500,000.

Number of shares outstanding is 500,000.

Market price per share is $33.

Calculated values,

Number of stocks repurchased is 100,000.

Formula to calculate price/earnings ratio is,

$\text{Price}\text{earning}\text{ratio}=\frac{\text{Market}\text{price}\text{per}\text{share}}{\text{Earnings}\text{per}\text{share}}$

Substitute $33 for market price per share and $3.75 for earnings per share in the above equation.

$\begin{array}{c}\text{Price}\text{earning}\text{ratio}=\frac{\$33}{\$3.75}\\ =8.8\end{array}$

Price earnings ratio is $8.8 times.

Given,

Earnings/revenue is $1,500,000

Value of assets is $7,000,000.

Value of liabilities is $1,500,000.

Number of shares outstanding is 500,000.

Market price per share is $33.

Calculated values,

Number of stocks repurchased is 100,000.

Additional liability to finance the purchase is 3,300,000.

Formula to calculate book value per share is,

$\text{Book}\text{value}\text{per}\text{share}=\frac{\text{Assets}-\text{Liabilities}}{\text{Total}\text{number}\text{of}\text{shares}\text{outstanding}}$

Substitute $7,000,000 for assets, $4,800,000 for liabilities and 400,000 for total number of shares outstanding in the above equation.

$\begin{array}{c}\text{Book}\text{value}\text{per}\text{share}=\frac{\$7,000,000-\left(\$1,500,000+3,300,000\right)}{500,000-100,000}\\ =\frac{\$7,000,000-4,800,000}{400,000}\\ =\frac{2,200,000}{400,000}\\ =\$5.5\end{array}$

Book value per share is $5.5.

Working note:

Calculation of book value per share,

$\begin{array}{c}\text{Book}\text{value}\text{per}\text{share}=\frac{\text{Assets}-\text{Liabilities}}{\text{Total}\text{number}\text{of}\text{shares}\text{outstanding}}\\ =\frac{\$7,000,000-\left(\$1,500,000+\$3,300,000\right)}{500,000-100,000}\\ =\frac{\$2,200,000}{400,000}\\ =\$5.5\end{array}$

Book value per share is $5.5.

Calculation of earnings per share,

$\begin{array}{c}\text{Earnings}\text{per}\text{share}=\frac{\text{Earnings/Revenue}}{\text{Number}\text{of}\text{shares}\text{outstanding}}\\ =\frac{\$1,500,000}{500,000-100,000}\\ =\frac{\$1,500,000}{400,000}\\ =\$3.75\end{array}$

Earnings per share is $3.75.

Calculation of number of shares repurchased,

$\begin{array}{c}\text{Stocks}\text{repurchased}=\text{Total}\text{number}\text{of}\text{stocks}\text{outstanding}\times \text{Repurchase}\text{percentage}\\ =500,000\times \frac{20}{100}\\ =\frac{10,000,000}{100}\\ =100,000\end{array}$

Number of stocks repurchases is 100,000.

Calculation of additional liability created to finance the purchase,

$\begin{array}{c}\text{Additional}\text{liability}=\text{Number}\text{of}\text{stocks}\text{repurchased}\times \text{Market}\text{price}\text{per}\text{share}\\ =\text{100,000}\times \text{\$33}\\ =\text{\$3,300,000}\end{array}$

Additional liability created to finance the purchase is $3,300,000.

Conclusion

Hence, the price-to-book ratio of W Corporation is $6, the price earnings ratio of W Corporation is $8.8 times and book value of share of W Corporation is $5.5.