**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 the greatest access to public debt markets (small companies tend to borrow more from private lenders). Equity issuers are frequently small companies going public; such issues are often quite small.

**2.** From the previous question, economies of scale are part of the answer. Beyond this, debt issues are simply easier and less risky to sell from an investment bank’s perspective. The two main reasons are that very large amounts of debt securities can be sold to a relatively small number of buyers, particularly large institutional buyers such as pension funds and insurance companies, and debt securities are much easier to price.

**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 Eyetech 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 38 million were, in effect, priced completely correctly.

**8.** The evidence suggests that a non-underwritten rights offering might be substantially cheaper than a cash offer. However, such offerings are rare, and there may be hidden costs or other factors not yet identified or well understood by researchers.

**9.** He could have done worse since his access to the oversubscribed and, presumably, underpriced issues was restricted while the bulk of his funds were allocated to stocks from the undersubscribed and, quite possibly, overpriced issues.

**10.** *a.* The price will probably go up because IPOs 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.

**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:

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:

P_{X} = $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

*e*. A rights offering usually costs less, it protects the proportionate interests of existing share-holders and also protects against underpricing.

**2.** *a.* The maximum subscription price is the current stock price, or $40. 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 = $50,000,000/$35 = 1,428,571 shares

And the number of rights needed to buy one share will be the current shares outstanding divided by the number of new share offered, so:

Number of rights needed = 5,200,000 shares outstanding/1,428,571 new shares = 3.64

*c*. A shareholder can buy 3.64 rights on shares for:

3.64($40) = $145.60

The shareholder can exercise these rights for $35, at a total cost of:

$145.60 + 35.00 = $180.60

The investor will then have:

Ex-rights shares = 1 + 3.64

Ex-rights shares = 4.64

The ex-rights price per share is:

P_{X} = [3.64($40) + $35]/4.64 = $38.92

So, the value of a right is:

Value of a right = $40 – 38.92 = $1.08

*d*. Before the offer, a shareholder will have the shares owned at the current market price, or:

Portfolio value = (1,000 shares)($40) = $40,000

After the rights offer, the share price will fall, but the shareholder will also hold the rights, so:

Portfolio value = (1,000 shares)($38.92) + (1,000 rights)($1.08) = $40,000

**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:

P_{X} = $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) = 2,352,273

**4.** If you receive 1,000 shares of each, the profit is:

Profit = 1,000($11) – 1,000($6) = $5,000

Since you will only receive one-half of the shares of the oversubscribed issue, your profit will be:

Expected profit = 500($11) – 1,000($6) = –$500

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 floatation costs is:

X(1 – .08) = $25M

X = $27,173,913 required total proceeds from sale.

So the number of shares offered is the total amount raised divided by the offer price, which is:

Number of shares offered = $27,173,913/$35 = 776,398

**6.** This is basically 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:

X(1 – .08) = $25.9M

X = $28,152,174 required total proceeds from sale.

Number of shares offered = $28,152,174/$35 = 804,348

**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 = (5M shares)($19.75) – 800,000 – 250,000 = $97.7M

The company received $97.7 million from the stock offering. Now we can calculate the direct costs. Part of the direct costs are given in the problem, but the company also had to pay the underwriters. The stock was offered at $21 per share, and the company received $19.75 per share. The difference, which is the underwriters spread, is also a direct cost. The total direct costs were:

Total direct costs = $800,000 + ($21 – 19.75)(5M shares) = $7.05M

We are given part of the indirect costs in the problem. Another indirect cost is the immediate price appreciation. The total indirect costs were:

Total indirect costs = $250,000 + ($26 – 21)(5M shares) = $25.25M

This makes the total costs:

Total costs = $7.05M + 25.25M = $32.3M

The floatation costs as a percentage of the amount raised is the total cost divided by the amount raised, so:

Flotation cost percentage = $32.3M/$97.7M = .3306 or 33.06%

**8.** The number of rights needed per new share is:

Number of rights needed = 100,000 old shares/20,000 new shares = 5 rights per new share.

Using P_{RO} as the rights-on price, and P_{S} as the subscription price, we can express the price per share of the stock ex-rights as:

P_{X} = [NP_{RO} + P_{S}]/(N + 1)

*a.* P_{X} = [5($90) + $90]/6 = $90.00; No change.

*b*. P_{X} = [5($90) + $85]/6 = $89.17; Price drops by $0.83 per share.

*c*. P_{X} = [5($90) + $70]/6 = $86.67; Price drops by $3.33 per share.

* 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:

Number of shares after offering = 10M + $35M/$50 = 10.7M

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 700,000 shares, and these will have a book value of $50 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 = [10M($40) + .7M($50)]/10.7M = $40.65

The current EPS for the company is:

EPS_{0} = NI_{0}/Shares_{0} = $15M/10M shares = $1.50 per share

And the current P/E is:

(P/E)_{0} = $50/$1.50 = 33.33

If the net income increases by $500,000, the new EPS will be:

EPS_{1} = NI_{1}/shares_{1} = $15.5M/10.7M shares = $1.45 per share

Assuming the P/E remains constant, the new share price will be:

P_{1} = (P/E)_{0}(EPS1) = 33.33($1.45) = $48.29

The current market-to-book ratio is:

Current market-to-book = $50/$40 = 1.25

Using the new share price and book value per share, the new market-to-book ratio will be:

New market-to-book = $48.29/$40.65 = 1.1877

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 $35 million. The NPV of the project is the new market value of the firm minus the current market value of the firm, or:

NPV = –$35M + [10.7M($48.29) – 10M($50)] = –$18,333,333

*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:

NI_{1} = (10.7M shares)($1.50 per share) = $16.05M

**10.** The current ROE of the company is:

ROE_{0} = NI_{0}/TE_{0} = $630,000/$3,600,000 = .1750 or 17.50%

The new net income will be the ROE times the new total equity, or:

NI_{1} = (ROE_{0})(TE_{1}) = .1750($3,600,000 + 1,100,000) = $822,500

The company’s current earnings per share are:

EPS_{0} = NI_{0}/Shares outstanding_{0} = $630,000/14,000 shares = $45.00

The number of shares the company will offer is the cost of the investment divided by the current share price, so:

Number of new shares = $1,100,000/$98 = 11,224

The earnings per share after the stock offer will be:

EPS_{1} =$822,500/25,224 shares = $32.61

The current P/E ratio is:

(P/E)_{0} = $98/$45.00 = 2.178

Assuming the P/E remains constant, the new stock price will be:

P_{1} = 2.178($32.61) = $71.01

The current book value per share and the new book value per share are:

BVPS_{0} = TE_{0}/shares_{0} = $3,600,000/14,000 shares = $257.14 per share

BVPS_{1} = TE_{1}/shares_{1} = ($3,600,000 + 1,100,000)/25,224 shares = $186.33 per share

So the current and new market-to-book ratios are:

Market-to-book_{0} = $98/$257.14 = 0.38

Market-to-book_{1} = $71.01/$186.33 = 0.38

The NPV of the project is the new market value of the firm minus the current market value of the firm, or:

NPV = –$1,100,000 + [$71.01(25,224) – $98(14,000)] = –$680,778

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:

P_{1} = $98 = 2.178(EPS_{1})

EPS_{1} = $45.00

The additional net income level must be the EPS times the new shares outstanding, so:

NI = $45(11,224 shares) = $505,102

And the new ROE is:

ROE_{1} = $505,102/$1,100,000 = .4592

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:

NPV = –$1,100,000 + [$98(25,224) – $98(14,000)] = $0

Accounting dilution still takes place, as BVPS still falls from $257.14 to $186.33, but no market dilution takes place because the firm is investing in a zero NPV project.

**12.** The number of new shares is the amount raised divided by the subscription price, so:

Number of new shares = $60M/$P_{S}

And the ex-rights number of shares (N) is equal to:

N = Old shares outstanding/New shares outstanding

N = 5M/($60M/$P_{S})

N = 0.0833P_{S}

We know the equation for the ex-rights stock price is:

P_{X} = [NP_{RO} + P_{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:

P_{X} = $52 = [N($55) + $P_{S}]/(N + 1)

$52 = [55(0.0833P_{S}) + P_{S}]/(0.0833P_{S} + 1)

$52 = 5.58P_{S}/(1 + 0.0833P_{S})

P_{S} = $41.60

**13.** Using P_{RO} as the rights-on price, and P_{S} as the subscription price, we can express the price per share of the stock ex-rights as:

P_{X} = [NP_{RO} + P_{S}]/(N + 1)

And the equation for the value of a right is:

Value of a right = P_{RO} – P_{X}

Substituting the ex-rights price equation into the equation for the value of a right and rearranging, we get:

Value of a right = P_{RO} – {[NP_{RO} + P_{S}]/(N + 1)}

Value of a right = [(N + 1)P_{RO} – NP_{RO} – P_{S}]/(N+1)

Value of a right = [P_{RO} – P_{S}]/(N + 1)

**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 = $22(1 – .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:

P_{X} = [NP_{RO} + P_{S}]/(N + 1)

P_{X} = [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) = $12,711.13

**15.** Using the equation for valuing a stock ex-rights, we find:

P_{X} = [NP_{RO} + P_{S}]/(N + 1)

P_{X} = [4($80) + $40]/5 = $72

The stock is correctly priced. Calculating the value of a right, we find:

Value of a right = P_{RO} – P_{X}

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.