a.
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.
a.
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,
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.
Hence, The ex-rights stock price is $26.33.
Calculation of the subscription price:
The formula to calculate the subscription price is:
Substitute $2,500,000 for the amount raised and 500,000 for the number of shares offered in the above formula.
Hence, The subscription price is $5.
Calculation of the value of a right:
The formula to calculate the value of a right is:
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.
Hence, The value of a right is $10.67.
Working note:
Calculation of the new shares:
The new shares offered is 500,000.
Calculation of the current market value:
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.
To determine: The ex-rights stock price, the value of a right and the subscription price.
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.
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:
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.
Hence, the ex-rights stock price is $31.6.
Calculation of the subscription price:
The formula to calculate the subscription price:
Substitute $2,500,000 for the amount raised and 250,000 for the number of shares offered in the above formula.
Hence, the subscription price is $10.
Calculation of the value of a right:
The formula to calculate the value of a right:
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.
Hence, the value of a right is $5.40.
Working note:
Calculation of the new shares:
Hence, the new shares offered is 250,000.
Calculation of the current market value:
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.
To determine: The change in the wealth of the stockholder from part a. to part b.
c.
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:
Substitute 4 (assumed) for the number of shares and $37 for the stock price in the above formula.
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,
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.
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:
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.
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
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
Calculation of the difference of the portfolio value:
Hence, the difference in the portfolio value is $0.02.
Thus, the position of the shareholder will increase by $0.02
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Chapter 20 Solutions
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