April 3, 2019

B-268 SOLUTIONS

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 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

Value of a right = $81.00 – 79.82 = $1.18

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 $53. 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 = $40,000,000/$48 = 833,333 shares

CHAPTER 15 B-269

c. A shareholder can buy 4.92 rights on shares for:

4.92($53) = $260.76

The shareholder can exercise these rights for $48, at a total cost of:

$260.76 + 48 = $308.76

The investor will then have:

Ex-rights shares = 1 + 4.92

Ex-rights shares = 5.92

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 = $74.80 = [N($81) + $40]/(N + 1)

N = 5.613

The number of new shares is the amount raised divided by the per-share subscription price, so:

B-270 SOLUTIONS

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

Profit = 1,000($7) – 1,000($5) = $2,000

5. Using X to stand for the required sale proceeds, the equation to calculate the total sale proceeds,

including floatation costs is:

X(1 – .09) = $60,000,000

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 – .09) = ($60,000,000 + 900,00)

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 = (10,000,000 shares)($18.20) – 900,000 – 320,000 = $180,780,000

The company received $180,780,000 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 $20 per share, and the company received $18.20 per share. The difference, which is

the underwriters spread, is also a direct cost. The total direct costs were:

Total direct costs = $900,000 + ($20 – 18.20)(10,000,000 shares) = $18,900,000

We are given part of the indirect costs in the problem. Another indirect cost is the immediate price

appreciation. The total indirect costs were:

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

Number of rights needed = 120,000 old shares/25,000 new shares = 4.8 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:

P

X = [NPRO + PS]/(N + 1)

a. P

X = [4.8($94) + $94]/(4.80 + 1) = $94.00; No change.

b. PX = [4.8($94) + $90]/(4.80 + 1) = $93.31; Price drops by $0.69 per share.

c. PX = [4.8($94) + $85]/(4.80 + 1) = $92.45; Price drops by $1.55 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 = 8,000,000 + $35,000,000/$50 = 8,700,000

Since the book value per share is $18, the old book value of the shares is the current number of

shares outstanding times 18. 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 = [8,000,000($18) + 700,000($50)]/8,700,000 = $23.53

The current EPS for the company is:

EPS0 = NI0/Shares0 = $17,000,000/8,000,000 shares = $2.13 per share

And the current P/E is:

10. The total equity of the company is total assets minus total liabilities, or:

Equity = $8,000,000 – 3,400,000

Equity = $4,600,000

So, the current ROE of the company is:

ROE0 = NI0/TE0 = $900,000/$4,600,000 = .1957 or 19.57%

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

NI1 = (ROE0)(TE1) = .1957($4,600,000 + 850,000) = $1,066,304

The company’s current earnings per share are:

EPS0 = NI0/Shares outstanding0 = $900,000/30,000 shares = $30.00

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 = $850,000/$84 = 10,119

CHAPTER 15 B-273

11. Using the P/E ratio to find the necessary EPS after the stock issue, we get:

P

1 = $84 = 2.800(EPS1)

EPS1 = $30.00

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

NI = $30(10,119 shares) = $303,571

And the new ROE is:

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

Number of new shares = $60,000,000/$PS

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

N = Old shares outstanding/New shares outstanding

N = 19,000,000/($60,000,000/$PS)

N = 0.03167PS

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:

P

X = [NPRO + PS]/(N + 1)

And the equation for the value of a right is:

CHAPTER 15 B-275

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 = $23(1 – .06) = $21.62 per share

So, to raise the required funds, the company must sell:

New shares offered = $5,600,000/$21.62 = 259,019

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

P

X = [NPRO + PS]/(N + 1)

P

X = [4($60) + $35]/(4 + 1) = $55

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

Value of a right = PRO – PX

Value of a right = $60 – 53 = $7