Note: This document contains suggested answers to all of the questions in Chapter 15. Please refer to your course note for assigned questions.
Chapter 20: Issuing Equity Securities to the Public
20.1a. 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 = 350,000($85) + 70,000($70) = $34,650,000
b. The number of rights associated with the old shares is the number of shares outstanding divided by the rights offered, so:
Number of rights needed = 350,000 old shares/70,000 new shares = 5 rights per new share
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:
Me =$34,650,000/(350,000 +70,000) =$82.50
d. The value of the right,
Value of a right= $85.00 – 82.50 = $2.50
or
Value of right = ($85.00-$70.00)/(5+1) = $2.50
e. A rights offering usually costs less, it protects the proportionate interests of existing shareholdersand also protects against underpricing.
20.2a. The maximum subscription price is the current stock price, or $20. The minimum price isanything greater than $0.
b. The number of new shares will be the amount raised divided by the subscription price, so:
Number of new shares = $30,000,000/$15 = 2,000,000 shares
And the number of rights needed to buy one share will be the current shares outstandingdivided by the number of new share offered, so:
Number of rights needed = 5,200,000 shares outstanding/2,000,000 shares =2.6
c. A shareholder can buy 2.6 rights on shares for:
2.6($20) = $52
The shareholder can exercise these rights for $15, at a total cost of:
$52 + $15 = $67
The investor will then have:
Ex–rights shares = 1 + 2.6
Ex–rights shares = 3.6
The ex–rights price per share is:
Re= [2.6($20) + $15]/3.6 = $18.61
So, the value of a right is:
Value of a right = $20 – 18.61 = $1.39
d. Before the offer, a shareholder will have the shares owned at the current market price, or:
Portfolio value = (1,000 shares)($20) = $20,000
After the rights offer, the share price will fall, but the shareholder will also hold the rights, so:
Portfolio value = (1,000 shares)($18.61) + (1,000 rights)($1.39) = $20,000
20.3Using 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:
Me= $74.50 = [N($80) + $40]/(N + 1)
N = 6.273
The number of new shares is the amount raised divided by the per–share subscription price, so:
Number of new shares = $15,000,000/$40 = 375,000
And the number of old shares is the number of new shares times the number of shares ex–rights, so:
Number of old shares = 6.273(375,000) = 2,352,375
20.4a. Assume you hold three shares of the company’s stock. The value of your holdings before youexercise your rights is:
Value of holdings = 3($65)
Value of holdings = $195
When you exercise, you must remit the three rights you receive for owning three shares, andten dollars. You have increased your equity investment by $20. The value of your holdingsafter surrendering your rights is:
New value of holdings = $195+$20
New value of holdings = $215
After exercise, you own four shares of stock. Thus, the price per share of your stock is:
Stock price = $215/4
Stock price = $53.75
b. The value of a right is the difference between the rights–on price of the stock and the ex– rightsprice of the stock:
Value of rights = Rights–on price – Ex–rights price
Value of rights = $65– $53.75
Value of rights = $11.25
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 stockbefore the ex–rights date, you will receive the rights. If you purchase the stock on or after theex–rights date, you will not receive the rights. Since rights have value, the stockholder receivingthe rights must pay for them. The stock price drop on the ex–rights day is similar to the stockprice drop on an ex–dividend day.
20.5a. The number of new shares offered through the rights offering is the existing shares divided bythe rights per share, or:
New shares = 1,000,000 / 2
New shares = 500,000
And the new price per share (Me) after the offering will be:
= $10.00
The subscription price is the amount raised divided by the number of number of new shares
offered, or:
Subscription price = $2,000,000 / 500,000
Subscription price = $4
And the value of a right is:
Value of a right = (Ex–rights price – Subscription price) / Rights needed to buy a share
Value of a right = ($10 – 4) / 2
Value of a right = $3
b. Following the same procedure, the number of new shares offered through the rights offering is:
New shares = 1,000,000 / 4
New shares = 250,000
And the new price per share after the offering will be:
= $12.00
The subscription price is the amount raised divided by the number of number of new shares
offered, or:
Subscription price = $2,000,000 / 250,000
Subscription price = $8
And the value of a right is:
Value of a right = (Ex–rights price – Subscription price) / Rights needed to buy a share of stock
Value of a right = ($12 – 8) / 4
Value of a right = $1
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 more clear. 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($13)
Current portfolio value = $52
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 portfolio
value will be:
New portfolio value = 6($10) – 2($4)
New portfolio value = $52
Under b, the investor gets 1 new share, so portfolio value will be:
New portfolio value = 5($12) – 1($8)
New portfolio value = $52
So, the shareholder's wealth position is unchanged either by the rights issue itself, or the choice
of which right's issue the firm chooses.
20.6The number of new shares is the amount raised divided by the subscription price(S), so:
Number of new shares = $60M/S
And the ex-rights number of shares (N) is equal to:
N = Old shares outstanding/New shares outstanding
N = 5M/($60M/S)
N = 0.0833S
We know the equation for the ex-rights stock price (Me) is:
Me = [N($55)+ S]/(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:
$52 = [(0.0833S)55+ S]/(0.0833S + 1)
$52 = 5.5815S/(1 + 0.0833S)
S = $41.60
20.7 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 = $22(1 – 0.06) = $20.68 per share
So, to raise the required funds, the company must sell:
New shares offered = $3.65M/$20.68 = 176,499
The number of rights needed per share is the current number of shares outstanding divided by the
new shares offered, or:
Number of rights needed = 490,000 old shares/176,499 new shares
Number of rights needed = 2.78 rights per share
The ex–rights stock price will be:
Me = [NMO + S]/(N + 1)
Pe = [2.78($30) + $22]/3.78 = $27.88
So, the value of a right is:
Value of a right = $30 – $27.88 = $2.12
And your proceeds from selling your rights will be:
Proceeds from selling rights = 6,000($2.12) = $12,720.
20.8Using the equation for valuing a stock ex–rights, we find:
Me = [NMO + S]/(N + 1)
Me = [4($80) + $40]/5 = $72
The stock is correctly priced. Calculating the value of a right, we find:
Value of a right = MO – Me
Value of a right = $80 – $72 = $8
So, the rights are underpriced. You can create an immediate profit on the ex–rights day if the stock is
selling for $72 and the rights are selling for $6 by executing the following transactions:
Buy 4 rights in the market for 4($6) = $24. Use these rights to purchase a new share at the
subscription price of $40. Immediately sell this share in the market for $72, creating an instant $8
profit.
20.9Using MOas the rights–on price, and S as the subscription price, we can express the price per share
of the stock ex–rights as:
Me = [NMO + S]/(N + 1)
And the equation for the value of a right is:
Value of a right = MO – Me
Substituting the ex–rights price equation into the equation for the value of a right and rearranging, we
get:
Value of a right = MO – {[NMO + PS]/(N + 1)}
Value of a right = [(N + 1)MO – NMO – S]/(N+1)
Value of a right = [MO – S]/(N + 1)
20.10The number of rights needed per new share is:
Number of rights needed = 24,000 old shares/6,000 new shares = 4 rights per new share.
Using MO as the rights–on price, and S as the subscription price, we can express the price per share
of the stock ex–rights as:
Me = [NMO + S]/(N + 1)
a. Me = [4($42)+$24]/5 = $38.40; Price drops by $3.60 per share.
b. Me = [4($42)+$38]/5 = $41.20; Price drops by $0.80 per share
c.Me = [4($42)+$45]/5 = $42.60; Price rises by $0.60 per share
20.11The poor performance result should not surprise the professor. Since he subscribed to every initial public offering, he was bound to get fewer superior performers and more poor performers. Financial analysts studied the companies and separated the bad prospects from the good ones. The analysts invested in only the good prospects. These issues became oversubscribed. Since these good prospects were oversubscribed, the professor received a limited amount of stock from them. The poor prospects were probably under–subscribed, so he received as much of their stock as he desired. The result was that his performance was below average because the weight on the poor performers in his portfolio was greater than the weight on the superior performers. This result is called the winner’s curse. The professor “won” the shares, but his bane was that the shares he “won” were poor performers.
20.12a.It is clear that the stock was sold too cheaply, so Life Sentence had reason to be unhappy.
b.No, but, in fairness, pricing the stock in such a situation is extremely difficult.
c.It’s an important factor. Only 2 million of the shares were underpriced. The other 12 million were, in effect, priced completely correctly.
20.13 If you receive 1,000 shares of each, the profit is:
Profit = 1,000($1.20) – 1,000($0.60) = $600
Since you will only receive one–half of the shares of the oversubscribed issue, your profit will be:
Expected profit = 500($1.20) – 1,000($0.60) = $0
This is an example of the winner’s curse.
20.14a. The price will probably go up because IPO’s are generally underpriced. This is especially true for smaller issues such as this one.
b. It is probably safe to assume that they are having trouble moving the issue, and it is
likely that the issue is not substantially underpriced.
MINI CASEDeck Out My Yacht Goes Public
1.The main difference in the costs is the reduced possibility of underpricing in a Dutch auction. As to
which is better, we don’t actually know. In theory, the Dutch auction should be better since it should
eliminate underpricing. However, as Google shows, underpricing can still exist in a Dutch auction.
Whether the underpricing is a severe in a Dutch auction as it would be in a traditional underwritten
offer is unknown.
2. There is no way to calculate the optimum size of the IPO, so whether management is correct, it will only be told in time. The disadvantages of raising the extra cash in the IPO include the
agency costs of excess cash. The extra cash may encourage management to act carelessly. The extra
cash will also earn a small return unless invested in income producing assets. At best, cash and short terminvestments are a zero NPV investment. The advantages of the increased IPO size include the
increased liquidity for the company, and the lower probability that the company will have to go back
to the primary market in the near term future. The increased size will also reduce the costs of the IPO
on a percentage of funds raised, although this may not be a large advantage.
3. The underwriter fee is 7 percent of the amount raised, or:
Underwriter fee = $60,000,000(0.07)
Underwriter fee = $4,200,000
Since the company must currently provide audited financial statements due to the bond covenants,
the audit costs are not incremental costs and should not be included in the calculation of the fees. So,
the sum of the other fees is:
Total other fees = $1,450,000 + 16,000 + 12,000 + 160,000 + 8,500 + 490,000 + 65,000
Total other fees = $2,201,500
This means the total fees are:
Total fees = $4,200,000 + $2,201,500
Total fees = $6,401,500
The net amount raised is the IPO offer size minus the underwriter fee, or:
Net amount raised = $60,000,000 – $4,200,000
Net amount raised = $55,800,000
So, the fees as a percentage of the net amount to the company are:
Fee percentage = $6,401,500/ $55,800,000
Fee percentage = 0.1147 or 11.47%
4. Because of legal repercussions, you should not provide specific advice on which option the
employees should choose. There are advantages and disadvantages to each. If the employee tenders
the stock to be sold in the IPO, the employee will lose out on any underpricing. This could be a
significant cost. However, if the employee retains the stock, he/she must hold the stock for the
lockup period, typically 180 days. Additionally, during the lockup period, the employee is legally
prohibited from hedging the price risk of the stock with any derivatives. And heavy selling by
insiders is considered a negative signal by the market. Another risk in not selling in the IPO is that
after the lockup period expires, the employees may be considered insiders, subject to Provincial Securities Commission restrictions on selling stock.
Answers to End–of–Chapter ProblemsB–1