CHAPTER 19 B – 1
CHAPTER 19
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
3. They are riskier and harder to market from an investment bank’s perspective.
4. Yields on comparable bonds can usually be readily observed, so pricing a bond issue accurately is
much less difficult.
5. It is clear that the stock was sold too cheaply, so Shake Shack had reason to be unhappy.
6. No, but in fairness, pricing the stock in such a situation is extremely difficult.
7. It’s an important factor. Only 5 million of the shares were underpriced. The other 6.4 million were, in
effect, priced completely correctly.
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 issues
10. a. The price will probably go up because IPOs are generally underpriced. This is especially true for
b. It is probably safe to assume that they are having trouble moving the issue, and it is likely that
CHAPTER 19 B – 2
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 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 the right is:
e. A rights offering usually costs less; it protects the proportionate interests of existing shareholders
2. a. The maximum subscription price is the current stock price, or $34. The minimum price is
b. The number of new shares will be the amount raised divided by the subscription price, so:
Number of new shares = $45,000,000/$31
Number of new shares = 1,451,613 shares
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:
c. A shareholder can buy 1.86 rights-on shares for:
1.86($34) = $63.24
The shareholder can exercise these rights for $31, at a total cost of:
$63.24 + 31 = $94.24
The investor will then have:
d. Before the offer, a shareholder will have the shares owned at the current market price, or:
Portfolio value = (1,000 shares)($34)
Portfolio value = $34,000
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:
PX = $74.30 = [N($78) + $50]/(N + 1)
N = 6.568
The number of new shares is the amount raised divided by the per-share subscription price, so:
Number of old shares = 1,576,216
4. If you receive 1,000 shares of each, the profit is:
Profit = 1,000($8) – 1,000($5)
CHAPTER 19 B – 4
Since you will only receive one-half of the shares of the oversubscribed issue, your profit will be:
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 $1,300,000 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:
Part of the direct costs are given in the problem, but the company also had to pay the underwriters.
The stock was offered at $23 per share, and the company received $21.39 per share. The difference,
which is the underwriters spread, is also a direct cost. The total direct costs were:
Total indirect costs = $58,575,000
CHAPTER 19 B – 5
This makes the total costs:
The flotation cost 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:
Number of rights needed = 135,000 old shares/33,750 new shares
Number of rights needed = 4 rights per new share.
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:
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 par value per share is $1, the old book value of the shares is the current number of
shares outstanding. From the previous solution, we can see the company will sell 352,941 shares,
and these will have a book value of $51 per share. The sum of these two values will give us the
total book value of the company, if we divide this by the new number of shares outstanding.
Doing so, we find the new book value per share will be:
New book value per share = $21.10
The current EPS for the company is:
CHAPTER 19 B – 6
And the current PE is:
If the net income increases by $690,000, the new EPS will be:
Assuming the PE remains constant, the new share price will be:
The current market-to-book ratio is:
Current market-to-book = $51/$18
Current market-to-book = 2.83
Using the new share price and book value per share, the new market-to-book ratio will be:
NPV = –$1,721,633
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:
10. The current ROE of the company is:
The company’s current earnings per share are:
EPS0 = $14.84
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:
So the current and new market-to-book ratios are:
The NPV of the project is the new market value of the firm minus the current market value of the firm,
or:
CHAPTER 19 B – 8
NPV = –$950,000 + [$67.01(56,380) – $71(43,000)]
NPV = –$224,913
dilution has occurred since the firm is investing in a negative NPV project.
11. Using the PE ratio to find the necessary EPS after the stock issue, we get:
P1 = $71 = 4.785(EPS1)
EPS1 = $14.84
The additional net income level must be the EPS times the new shares outstanding, so:
NI = $14.84(13,380 shares)
NI = $198,526
And the new ROE is:
ROE1 = $198,526/$950,000
takes place because the firm is investing in a zero NPV project.
exercise your rights is:
Value of holdings = 3($86)
Value of holdings = $258
When you exercise, you must remit the three rights you receive for owning three shares, and $7.
You have increased your equity investment by $7. The value of your holdings after surrendering
CHAPTER 19 B – 9
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
before the ex-rights date, you will receive the rights. If you purchase the stock on or after the ex-
13. 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:
P = (Current market value + Proceeds from offer)/(Old shares + New shares)
The subscription price is the amount raised divided by the number of new shares offered, or:
Subscription price = $2,400,000/650,000
And the value of a right is:
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:
offered, or:
CHAPTER 19 B – 10
Subscription price = $2,400,000/325,000
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
four 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($27)
Current portfolio value = $108
After exercise, the value of the portfolio will be the new number of shares times the ex-rights
price, less the subscription price paid. Under a, the investor gets two new shares, so the portfolio
value will be:
New portfolio value = 6($19.23) – 2($3.69)
14. The number of new shares is the amount raised divided by the subscription price, so:
Number of new shares = $58,000,000/PS
And the ex-rights number of shares (N) is equal to:
N = Old shares outstanding/New shares outstanding
N = 10,000,000/($58,000,000/PS)
N = .1724PS
We know the equation for the ex-rights stock price is:
PX = [NPRO + PS]/(N + 1)
CHAPTER 19 B – 11
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:
15. 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:
16. Using the equation for valuing a stock ex-rights, we find:
PX = [NPRO + PS]/(N + 1)
PX = [4($75) + $40]/5
PX = $68
The stock is correctly priced. Calculating the value of a right, we find:
Value of a right = PRO – PX