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CHAPTER 15
RAISING CAPITAL
Answers to Concepts Review and Critical Thinking Questions
1. A company’s internally generated cash flow provides a source of equity financing. For a profitable
company, outside equity may never be needed. Debt issues are larger because large companies have
2. From the previous question, economies of scale are part of the answer. Beyond this, debt issues are
7. It’s an important factor. Only 9.68 million of the shares were underpriced. The other 30 million were,
8. The evidence suggests that a nonunderwritten rights offering might be substantially cheaper than a
9. He could have done worse since his access to the oversubscribed and, presumably, underpriced
10. a. The price will probably go up because IPOs are generally underpriced. This is especially true
b. It is probably safe to assume that they are having trouble moving the issue, and it is likely that
CHAPTER 15 - 2
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
Basic
1. a. The new market value will be the current shares outstanding times the stock price plus the
rights offered times the rights price, so:
b. The number of rights associated with the old shares is the number of shares outstanding divided
by the shares offered, so:
c. The new price of the stock will be the new market value of the company divided by the total
number of shares outstanding after the rights offer, which will be:
d. The value of the right is:
e. A rights offering usually costs less; it protects the proportionate interests of existing share-
2. a. The maximum subscription price is the current stock price, or $52. The minimum price is
b. The number of new shares will be the amount raised divided by the subscription price, so:
And the number of rights needed to buy one share will be the current shares outstanding
divided by the number of new shares offered, so:
CHAPTER 15 - 3
c. A shareholder can buy 5.98 rights-on shares for:
The shareholder can exercise these rights for $46, at a total cost of:
The investor will then have:
The ex-rights price per share is:
So, the value of a right is:
d. Before the offer, a shareholder will have the shares owned at the current market price, or:
After the rights offer, the share price will fall, but the shareholder will also hold the rights, so:
3. Using the equation we derived in Problem 2, part c to calculate the price of the stock ex-rights, we
can find the number of shares a shareholder will have ex-rights, which is:
The number of new shares is the amount raised divided by the per-share subscription price, so:
And the number of old shares is the number of new shares times the number of rights per share, so:
CHAPTER 15 - 4
4. If you receive 1,000 shares of each, the profit is:
Since you will only receive one-half of the shares of the oversubscribed issue, your profit will be:
This is an example of the winner’s curse.
5. Using X to stand for the required sale proceeds, the equation to calculate the total sale proceeds,
including flotation costs is:
So the number of shares offered is the total amount raised divided by the offer price, which is:
6. This is the same as the previous problem, except we need to include the $900,000 of expenses in the
amount the company needs to raise, so:
7. We need to calculate the net amount raised and the costs associated with the offer. The net amount
raised is the number of shares offered times the price received by the company, minus the costs
associated with the offer, so:
The company received $463,730,000 from the stock offering. Now we can calculate the direct costs.
CHAPTER 15 - 5
We are given part of the indirect costs in the problem. Another indirect cost is the immediate price
appreciation. The total indirect costs were:
This makes the total costs:
The flotation costs as a percentage of the amount raised is the total cost divided by the amount
raised, so:
8. The number of rights needed per new share is:
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:
PX = [NPRO + PS] / (N + 1)
a. PX = [6.50($73) + $73] / (6.50 + 1) = $73.00; No change.
Intermediate
9. a. The number of shares outstanding after the stock offer will be the current shares outstanding,
plus the amount raised divided by the current stock price, assuming the stock price doesn’t
change. So:
Since the book value per share is $7, the old book value of the shares is the current number of
shares outstanding times 7. We can see the company will sell 1,551,724 shares, and these will
CHAPTER 15 - 6
The current EPS for the company is:
EPS0 = NI0 / Shares0
And the current P/E is:
If the net income increases by $900,000, the new EPS will be:
EPS1 = NI1 / shares1
Assuming the P/E remains constant, the new share price will be:
P1 = (P/E)0(EPS1)
The current market-to-book ratio is:
Using the new share price and book value per share, the new market-to-book ratio will be:
Market value dilution has occurred because the firm financed a negative NPV project. The cost
b. For the price to remain unchanged when the P/E ratio is constant, EPS must remain constant.
The new net income must be the new number of shares outstanding times the current EPS,
which gives:
10. The total equity of the company is total assets minus total liabilities, or:
The new net income will be the ROE times the new total equity, or:
NI1 = (ROE0)(TE1)
The company’s current earnings per share are:
EPS0 = NI0 / Shares outstanding0
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 P/E ratio is:
Assuming the P/E 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
CHAPTER 15 - 8
So the current and new market-to-book ratios are:
The NPV of the project is the cost of the project plus 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.
11. Using the P/E 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 cost of the project plus
the new market value of the firm minus the current market value of the firm, or:
12. 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:
N = Old shares outstanding/New shares outstanding
CHAPTER 15 - 9
We know the equation for the ex-rights stock price is:
PX = [NPRO + PS] / (N + 1)
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:
PX = $74 = [N($79) + $PS] / (N + 1)
13. 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:
PX = [NPRO + PS]/(N + 1)
And the equation for the value of a right is:
14. The net proceeds to the company on a per share basis is the subscription price times one minus the
underwriter spread, so:
Net proceeds to the company = $20(1 – .06)
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:
PX = [NPRO + PS] / (N + 1)
CHAPTER 15 - 10
So, the value of a right is:
And your proceeds from selling your rights will be:
15. Using the equation for valuing a stock ex-rights, we find:
PX = [NPRO + PS] / (N + 1)
The stock is incorrectly priced. Calculating the value of a right using the actual stock price, we find:
Value of a right = PRO – PX
So, the rights are underpriced. You can create an immediate profit on the ex-rights day if the stock is
Buy four rights in the market for 4($3) = $12. Use these rights to purchase a new share at the
