Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
CHAPTER 20 -
11. The current ROE of the company is:
The new net income will be the ROE times the new total equity, or:
The company’s current earnings per share are:
The number of shares the company will offer is the cost of the investment divided by the current
share price, so:
The earnings per share after the stock offer will be:
The current PE ratio is:
Assuming the PE remains constant, the new stock price will be:
The current book value per share and the new book value per share are:
BVPS0 = TE0 / shares0
BVPS1 = TE1 / shares1
So the current and new market-to-book ratios are:
1
CHAPTER 20 -
The NPV of the project is the new market value of the firm minus the current market value of the
firm, or:
Accounting dilution takes place here because the market-to-book ratio is less than one. Market value
dilution has occurred since the firm is investing in a negative NPV project.
12. Using the PE ratio to find the necessary EPS after the stock issue, we get:
The additional net income level must be the EPS times the new shares outstanding, so:
And the new ROE is:
Next, we need to find the NPV of the project. The NPV of the project is the new market value of the
firm minus the current market value of the firm, or:
13. a. Assume you hold three shares of the company’s stock. The value of your holdings before you
exercise your rights is:
When you exercise, you must remit the three rights you receive for owning three shares, and
$14. You have increased your equity investment by $14. The value of your holdings after
surrendering your rights is:
2
CHAPTER 20 -
After exercise, you own four shares of stock. Thus, the price per share of your stock is:
b. The value of a right is the difference between the rights-on price of the stock and the ex-rights
price of the stock:
c. The price drop will occur on the ex-rights date, even though the ex-rights date is neither the
expiration date nor the date on which the rights are first exercisable. If you purchase the stock
14. a. The number of new shares offered through the rights offering is the existing shares divided by
the rights per share, or:
And the new price per share after the offering will be:
P =
Current market value + Proceeds from offer
Old shares + New shares
P =
1,000,000($37 )+ $2,500,000
1,000,000 + 500,000
P = $26.33
The subscription price is the amount raised divided by the number of new shares offered, or:
And the value of a right is:
b. Following the same procedure, the number of new shares offered through the rights offering is:
3
CHAPTER 20 -
And the new price per share after the offering will be:
P =
Current market value + Proceeds from offer
Old shares + New shares
P =
1,000,000($37 )+ $2,500,000
1,000,000 + 250,000
P = $31.60
The subscription price is the amount raised divided by the number of number of new shares
offered, or:
c. Since rights issues are constructed so that existing shareholders' proportionate share will remain
unchanged, we know that the stockholders’ wealth should be the same between the two
arrangements. However, a numerical example makes this clearer. Assume that an investor holds
4 shares, and will exercise under either a or b. Prior to exercise, the investor's portfolio value is:
After exercise, the value of the portfolio will be the new number of shares time the ex-rights
price, less the subscription price paid. Under a, the investor gets 2 new shares, so the portfolio
value will be:
15. The number of new shares is the amount raised divided by the subscription price, so:
And the ex-rights number of shares (N) is equal to:
4
CHAPTER 20 -
We know the equation for the ex-rights stock price is:
We can substitute in the numbers we are given, and then substitute the two previous results. Doing
so, and solving for the subscription price, we get:
16. Using PRO as the rights-on price, and PS as the subscription price, we can express the price per share
of the stock ex-rights as:
And the equation for the value of a right is:
Substituting the ex-rights price equation into the equation for the value of a right and rearranging, we
get:
17. The net proceeds to the company on a per share basis are the subscription price times one minus the
underwriter spread, so:
So, to raise the required funds, the company must sell:
The number of rights needed per share is the current number of shares outstanding divided by the
new shares offered, or:
The ex-rights stock price will be:
5
CHAPTER 20 -
So, the value of a right is:
And your proceeds from selling your rights will be:
18. Using the equation for valuing a stock ex-rights, we find:
The stock is correctly priced. Calculating the value of a right, we find:
So, the rights are underpriced. You can create an immediate profit on the ex-rights day if the stock is
Buy 4 rights in the market for 4($5) = $20. Use these rights to purchase a new share at the
6
