Chapter 20, Problem 14QP

a.

Summary Introduction

To determine: The ex-rights stock price, the value of a right, and the subscription price.

Rights Offer:

In rights offer, common stock is issued to the existing shareholders. Here, the shareholder issues an option in which a certain number of shares can be bought at a specific price and at a specific duration.

Ex-rights stock price:

The ex-rights stock price is where the right, which are connected with the stock is separated.

Explanation of Solution

Solution:

Given,

The selling price of company stock is $37 per share.

The number of outstanding shares is 1 million.

The firm plans to raise $2.5 million to finance a new project.

Two shares of outstanding stock are entitled to purchase one additional share of the new issue.

Calculation of the ex-rights stock price:

The formula to calculate the ex-rights stock price is,

$\text{Ex-rights}\text{stock}\text{price}=\frac{\text{Current}\text{market}\text{value}+\text{Proceeds}\text{from}\text{offer}}{\left(\text{Old}\text{shares}+\text{New}\text{shares}\right)}$

Substitute $37,000,000 for the current market value, $2,500,000 for proceeds from the offer, 1,000,000 for the number of old shares and 500,000 for the new shares (refer working note) in the above formula.

$\begin{array}{c}\text{Ex-rights}\text{stock}\text{price}=\frac{\$37,000,000+\$2,500,000}{1,000,000+500,000}\\ =\frac{\$39,500,000}{1,500,000}\\ =\$26.33\end{array}$

Hence, The ex-rights stock price is $26.33.

Calculation of the subscription price:

The formula to calculate the subscription price is:

$\text{Subscription}\text{price}=\frac{\text{Amount}\text{raised}}{\text{Number}\text{of}\text{shares}\text{offered}}$

Substitute $2,500,000 for the amount raised and 500,000 for the number of shares offered in the above formula.

$\begin{array}{c}\text{Subscription}\text{price}=\frac{\$2,500,000}{500,000}\\ =\$5\end{array}$

Hence, The subscription price is $5.

Calculation of the value of a right:

The formula to calculate the value of a right is:

$\text{Value}\text{of}\text{a}\text{right}=\frac{\left(\text{Ex-rights}\text{price}-\text{Subscription}\text{price}\right)}{\text{Rights}\text{needed}\text{to}\text{buy}\text{a}\text{share}\text{of}\text{a}\text{stock}}$

Substitute $26.33 for the ex-rights price, $5 for the subscription price and 2 for the rights needed to buy a share of stock in the above formula.

$\begin{array}{c}\text{Value}\text{of}\text{a}\text{right}=\frac{\left(\$26.33-\$5\right)}{2}\\ =\$10.67\end{array}$

Hence, The value of a right is $10.67.

Working note:

Calculation of the new shares:

$\begin{array}{c}\text{New}\text{shares}=\frac{\text{Existing}\text{shares}}{\text{Rights}\text{per}\text{shares}}\\ =\frac{1,000,000}{2}\\ =500,000\end{array}$

The new shares offered is 500,000.

Calculation of the current market value:

$\begin{array}{c}\text{Current}\text{market}\text{value}=\text{Number}\text{of}\text{shares}\times \text{Price}\text{of}\text{share}\\ \text{=1,000,000}\times \text{\$37}\\ \text{=\$37,000,000}\end{array}$

Hence, the current market value is $37,000,000.

Thus, the ex-rights stock price is $26.33, the subscription price is $5 and the value of a right is $10.67.

b.

Summary Introduction

To determine: The ex-rights stock price, the value of a right and the subscription price.

Explanation of Solution

Solution:

Given,

The selling price of company stock is $37 per share.

The number of outstanding shares is 1 million.

The firm plans to raise $2.5 million to finance a new project.

Four shares of outstanding stock are entitled to purchase one additional share of the new issue.

Calculation of the ex-rights stock price:

The formula to calculate the ex-rights stock price:

$\text{Ex-rights}\text{stock}\text{price}=\frac{\text{Current}\text{market}\text{value}+\text{Proceeds}\text{from}\text{offer}}{\left(\text{Old}\text{shares}+\text{New}\text{shares}\right)}$

Substitute $37,000,000 for the current market value, $2,500,000 for proceeds from the offer, 1,000,000 for the number of old shares and 250,000 for the new shares (refer working note) in the above formula.

$\begin{array}{c}\text{Ex-rights}\text{stock}\text{price}=\frac{\$37,000,000+\$2,500,000}{1,000,000+250,000}\\ =\frac{\$39,500,000}{1,250,000}\\ =\$31.6\end{array}$

Hence, the ex-rights stock price is $31.6.

Calculation of the subscription price:

The formula to calculate the subscription price:

$\text{Subscription}\text{price}=\frac{\text{Amount}\text{raised}}{\text{Number}\text{of}\text{shares}\text{offered}}$

Substitute $2,500,000 for the amount raised and 250,000 for the number of shares offered in the above formula.

$\begin{array}{c}\text{Subscription}\text{price}=\frac{\$2,500,000}{250,000}\\ =\$10\end{array}$

Hence, the subscription price is $10.

Calculation of the value of a right:

The formula to calculate the value of a right:

$\text{Value}\text{of}\text{a}\text{right}=\frac{\left(\text{Ex-rights}\text{price}-\text{Subscription}\text{price}\right)}{\text{Rights}\text{needed}\text{to}\text{buy}\text{a}\text{share}\text{of}\text{a}\text{stock}}$

Substitute $31.60 for the ex-rights price, $10 for the subscription price and 4 for the rights needed to buy a share of stock in the above formula.

$\begin{array}{c}\text{Value}\text{of}\text{a}\text{right}=\frac{\left(\$31.6-\$10\right)}{4}\\ =\$5.40\end{array}$

Hence, the value of a right is $5.40.

Working note:

Calculation of the new shares:

$\begin{array}{c}\text{New}\text{shares}=\frac{\text{Existing}\text{shares}}{\text{Rights}\text{per}\text{shares}}\\ =\frac{1,000,000}{4}\\ =250,000\end{array}$

Hence, the new shares offered is 250,000.

Calculation of the current market value:

$\begin{array}{c}\text{Current}\text{market}\text{value}=\text{Number}\text{of}\text{shares}\times \text{Price}\text{of}\text{share}\\ \text{=1,000,000}\times \text{\$37}\\ =\text{\$37,000,000}\end{array}$

Hence, the current market value is $37,000,000.

Thus, the ex-rights stock price is $31.60, the subscription price is $10 and the value of a right is $5.40.

c.

Summary Introduction

To determine: The change in the wealth of the stockholder from part a. to part b.

Explanation of Solution

Solution:

Given,

The selling price of company stock is $37 per share.

The number of outstanding shares is 1 million.

The firm plans to raise $2.5 million to finance a new project.

The assumption is that the shareholder holds 4 shares and it will implement  in both the cases.

Calculation of the current portfolio value:

The formula to calculate the current portfolio value is:

$\text{Current}\text{portfolio}\text{value}=\text{Number}\text{of}\text{shares}\times \text{Stock}\text{price}$

Substitute 4 (assumed) for the number of shares and $37 for the stock price in the above formula.

$\begin{array}{c}\text{Current}\text{portfolio}\text{value}=4\times \$37\\ =\$148\end{array}$

Hence, the current portfolio value is $148.

Calculation of the new portfolio value in case of part a.

The formula to calculate the new portfolio value is,

$\text{New}\text{portfolio}\text{value}=\left[\begin{array}{c}\left(\text{New}\text{number}\text{of}\text{shares}\times \text{Ex-rights}\text{price}\right)\\ -\left(\text{Subscription}\text{price}\times \text{Number of rights}\right)\end{array}\right]$

Substitute 6 for the number of shares (refer working note) and $26.33 for the ex-rights price, 2 for numebr of rights and $5 for the subscription price in the above formula.

$\begin{array}{c}\text{New}\text{portfolio}\text{value}=\left(6\times \$26.33\right)-\left(2\times \$5\right)\\ =\$157.98-\$10\\ =\$147.98\end{array}$

Hence, the new portfolio value is $147.98.

Calculation of the new portfolio value in case of b:

The formula to calculate the new portfolio value:

$\text{New}\text{portfolio}\text{value}=\left[\begin{array}{c}\left(\text{New}\text{number}\text{of}\text{shares}\times \text{Ex-rights}\text{price}\right)\\ -\left(\text{Subscription}\text{price}\times \text{Number of rights}\right)\end{array}\right]$

Substitute 5 for the number of shares (refer working note) and $31.60 for the ex-rights price and $10 for the subscription price and 1 for the number of right in the above formula.

$\begin{array}{c}\text{New}\text{portfolio}\text{value}=\left(5\times \$31.6\right)-\left(1\times \$10\right)\\ =\$158-\$10\\ =\$148\end{array}$

Hence, the new portfolio value is $148.

Working note:

Calculation of the new number of shares in case of part a.:

In this case, the investor will get 2 new shares and so the new number of shares will be 6 $\left(4+2\right)$

Calculation of the new number of shares in case of part b:

In this case, the investor will get 1 new share and so the new number of shares will be 5 $\left(4+1\right)$

Calculation of the difference of the portfolio value:

$\begin{array}{c}\text{Difference}=\left(\text{New}\text{portfolio}\text{value}-\text{Old}\text{portfolio}\text{value}\right)\\ =\left(\$148-\$147.98\right)\\ =\$0.02\end{array}$

Hence, the difference in the portfolio value is $0.02.

Thus, the position of the shareholder will increase by $0.02 $\left(\$148-\$147.98\right)$ $in the case he goes with rights issue or by the rights issue that the firm has chosen.