CHAPTER 20
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
easier and less risky to sell from an investment bank’s perspective. The two main reasons are that very
4. Yields on comparable bonds can usually be readily observed, so pricing a bond issue accurately is
much less difficult.
6. No, but in fairness, pricing the stock in such a situation is extremely difficult.
8. The evidence suggests that a non-underwritten rights offering might be substantially cheaper than a
9. He could have done worse since his access to the oversubscribed and, presumably, underpriced issues
10. a. The price will probably go up because IPOs are generally underpriced. This is especially true for
11. Competitive offer and negotiated offer are two methods to select investment bankers for underwriting.
Under competitive offers, the issuing firm can award its securities to the underwriter with the highest
12. There are two possible reasons for stock price drops on the announcement of a new equity issue: 1)
Management may attempt to issue new shares of stock when the stock is overvalued, that is, the
13. If the interest of management is to increase the wealth of the current shareholders, a rights offering
may be preferable because issuing costs as a percentage of capital raised are lower for rights offerings.
14. Reasons for shelf registration include: 1) Flexibility in raising money only when necessary without
incurring additional issuance costs. 2) Issuance of securities is greatly simplified.
3) The underwriter price stabilization of the aftermarket and, 4) Issuing costs are higher in negotiated
deals than in competitive ones.
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.
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:
New market value = $58,305,000
b. The number of rights associated with the old shares is the number of shares outstanding divided
by the rights 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 a right is the difference between the current price and the ex-rights price, so:
Value of a right = $87 – 85.74
2. a. The maximum subscription price is the current stock price, or $34. The minimum price is
anything greater than $0.
b. The number of new shares will be the amount raised divided by the subscription price, so:
Number of new shares = $26,000,000/$27
Number of new shares = 962,963 shares
c. A shareholder can buy 2.80 rights-on shares for:
2.80($34) = $95.33
The shareholder can exercise these rights for $27, at a total cost of:
$95.33 + 27 = $122.33
The investor will then have:
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:
4. If you receive 1,000 shares of each, the profit is:
Profit = 1,000($13) – 1,000($4)
5. Using X to stand for the required sale proceeds, the equation to calculate the total sale proceeds,
including flotation costs, is:
6. This is basically the same as the previous problem, except we need to include the $1,900,000 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:
Net amount raised = (7,500,000 shares)($36.27) – 2,250,000 – 475,000
Net amount raised = $269,300,000
8. The number of rights needed per new share is:
Number of rights needed = 155,000 old shares/30,000 new shares = 5.17 rights per new share
9. In general, the new price per share after the offering will be:
P = (Current market value + Proceeds from offer)/(Old shares + New shares)
The current market value of the company is the number of shares outstanding times the share price,
or:
Market value of company = 60,000($45)
10. 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:
Number of shares after offering = 6,800,0000 + $30,000,000/$65
Number of shares after offering = 7,261,538
Since the par value per share is $1, the old book value of the shares is the current number of
And the current PE is:
(PE)0 = $65/$1.69
(PE)0 = 38.43
If the net income increases by $675,000, the new EPS will be:
EPS1 = NI1/shares1
New market-to-book = $64.44/$22.86
New market-to-book = 2.8189
Accounting dilution has occurred because new shares were issued when the market–to–book ratio
was less than one; market value dilution has occurred because the firm financed a negative NPV
project. The cost of the project is given at $30 million. The NPV of the project is the new market
b. For the price to remain unchanged when the PE 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:
11. The current ROE of the company is:
ROE0 = NI0/TE0
ROE0 = $980,000/($9,400,000 – 4,100,000)
ROE0 = .1849, or 18.49%
The new net income will be the ROE times the new total equity, or:
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:
EPS1 = $1,257,358/(65,000 shares + 20,000 shares)
EPS1 = $14.79
The current PE ratio is:
(PE)0 = $75/$15.08
(PE)0 = 4.974
Assuming the PE remains constant, the new stock price will be:
So the current and new market-to-book ratios are:
Market-to-book0 = $75/$81.54
Market-to-book0 = .9198
12. Using the PE ratio to find the necessary EPS after the stock issue, we get:
P1 = $75 = 4.974(EPS1)
EPS1 = $15.08
The additional net income level must be the EPS times the new shares outstanding, so:
13. a. Assume you hold three shares of the company’s stock. The value of your holdings before you
exercise your rights is:
Value of holdings = 3($87)
Value of holdings = $261
When you exercise, you must remit the three rights you receive for owning three shares, and $20.
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:
New shares = 1,300,000/2
New shares = 650,000
And the new price per share after the offering will be:
b. Following the same procedure, the number of new shares offered through the rights offering is:
New shares = 1,300,000/4
New shares = 325,000
And the new price per share after the offering will be:
P = (Current market value + Proceeds from offer)/(Old shares + New shares)
P = [1,300,000($43) + 2,900,000]/(1,300,000 + 325,000)
P = $36.18
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:
Current portfolio value = Number of shares × Stock price
Current portfolio value = 4($43)
15. The number of new shares is the amount raised divided by the subscription price, so:
Number of new shares = $45,000,000/$PS
And the ex-rights number of shares (N) is equal to:
N = Old shares outstanding/New shares outstanding
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:
PX = [NPRO + PS]/(N + 1)
17. The net proceeds to the company on a per share basis are the subscription price times one minus the
underwriter spread, so:
Net proceeds to the company = $30(1 – .06)
Net proceeds to the company = $28.20 per share
So, to raise the required funds, the company must sell:
18. Using the equation for valuing a stock ex-rights, we find:
PX = [NPRO + PS]/(N + 1)
PX = [4($60) + $30]/5 = $54