19-10. Solution:
Reynolds Technology
b. Pure bond value $763.57
N I/Y PV PMT FV
11. Pure bond value and change in interest rates (LO19-3) Pittsburgh Steel Company has a
convertible bond outstanding, trading in the marketplace at $960. The par value is $1,000,
the coupon rate is 10 percent, and the bond matures in 20 years. The conversion price is
$55 and the company’s common stock is selling for $48 per share. Interest is paid
semiannually. If non-convertible bonds of similar risk are currently yielding 12 percent,
what will be the pure bond value of the Pittsburgh Steel Company bonds? (Use semiannual
analysis.)
19-11. Solution:
Pittsburgh Steel Company
Pure bond value $849.54
N I/Y PV PMT FV
12. Current yield on a convertible bond (LO19-1) The Olsen Mining Company has been
very successful in the last five years. Its $1,000 par value convertible bonds have a
conversion ratio of 32. The bonds have a quoted interest rate of 7 percent a year. The firm’s
common stock is currently selling for $41.30 per share. The current bond price has a
conversion premium of $10 over the conversion value.
a. What is the current price of the bond?
b. What is the current yield on the bond (annual interest divided by the bond’s market
price)?
c. If the common stock price goes down to $23.40 and the conversion premium goes up
to $100, what will be the new current yield on the bond?
19-12. Solution:
Olsen Mining Company
a. $41.30 stock price × 32 shares =
$1,321.60 conversion value
b. 7% × $1,000 = $70 annual interest
Annual interest $70 5.26%
Bond price $1,331.60
= =
c. $23.40 stock price × 32 shares =
$748.80 conversion value
+100.00 conversion premium
$848.80 bond price
Annual interest $70 8.25%
Bond price $848.80
= =
13. Conversion value versus pure bond value (LO19-1) Standard Olive Company of
California has a convertible bond outstanding with a coupon rate of 5 percent and a
maturity date of 20 years. It is rated Aa, and competitive, nonconvertible bonds of the same
risk class carry a 10 percent return. The conversion ratio is 15. Currently the common stock
is selling for $35 per share on the New York Stock Exchange.
a. What is the conversion price?
b. What is the conversion value?
c. Compute the pure bond value. (Use semiannual analysis.)
d. Draw a graph that includes the pure bond value and the conversion value but not the
convertible bond price. For the stock price on the horizontal axis, use 10, 20, 30, 40, 50, and
60.
e. Calculate the crossover point at which the pure bond value equals conversion value.
19-13. Solution:
Standard Olive Company of California
a. $1,000 par/15 conversion ratio = $66.67 conversion price
b. $ 35 Stock price
× 15 Conversion ratio
$ 525 Conversion value
c.
N I/Y PV PMT FV
d.
Conversion Value
Pure bond Value
19-13. (Continued)
e. At a stock price of $35 per share, the price of the bond will
be influenced more by the pure bond value (floor price) of
$570.98. If interest rates move up, the pure bond value will
14. Call feature with a convertible bond (LO19-1) Defense Systems Inc. has convertible
bonds outstanding that are callable at $1,070.
The bonds are convertible into 33 shares of common stock. The stock is currently selling
for $39.25 per share.
a. If the firm announces it is going to call the bonds at $1,070, what action are
bondholders likely to take and why?
b. Assume that instead of the call feature, the firm has the right to drop the conversion
ratio from 33 down to 30 after 5 years and down to 27 after 10 years. If the bonds have
been outstanding for four years and 11 months, what will the price of the bonds be if
the stock price is $40? Assume the bonds carry no conversion premium.
c. Further assume that you anticipate that the common stock price will be up to $42.50 in
two months. Considering the conversion feature, should you convert now or continue to
hold the bond for at least two more months?
19-14. Solution:
Defense Systems Inc.
a. They will probably convert the bonds to common stock.
With a conversion ratio of 33 shares and a common stock
b. Bond price = Stock price × Conversion ratio
c. Bond price in two months = Stock price × Conversion ratio
$42.50 × 30 = $1,275
15. Convertible bond and rates of return (LO19-2) Vernon Glass Company has $15 million
in 10 percent convertible bonds outstanding. The conversion ratio is 40, the stock price is
$17, and the bond matures in 10 years. The bonds are currently selling at a conversion
premium of $45 over their conversion value.
If the price of the common stock rises to $23 on this date next year, what would your
rate of return be if you bought a convertible bond today and sold it in one year? Assume on
this date next year, the conversion premium has shrunk from $45 to $20.
19-15. Solution:
Vernon Glass Company
First, find the price of the convertible bond. The conversion
value is $680 ($17 × 40). The conversion value of $680,
plus the conversion premium of $45, equals $725, the
current market price of the convertible bond.
16. Price appreciation with a warrant (LO19-4) Assume you can buy a warrant for $6 that
gives you the option to buy one share of common stock at $14 per share. The stock is
currently selling at $18 per share.
a. What is the intrinsic value of the warrant?
b. What is the speculative premium on the warrant?
c. If the stock rises to $29 per share and the warrant sells at its theoretical value without a
premium, what will be the percentage increase in the stock price and the warrant price
if you buy the stock and the warrant at the prices stated here? Explain this relationship.
19-16. Solution:
a. ($18 stock price – $14 exercise price) × 1 share per
warrant = $4 intrinsic value
c. Percentage change if stock is purchased at $18
$29 $18 $11 61.11% increase in stock price
$18 $18
–= =
17. Profit potential with a warrant (LO19-4) The Redford Investment Company bought 100
Cinema Corp. warrants one year ago and would like to exercise them today. The warrants
were purchased at $24 each, and they expire when trading ends today (assume there is no
speculative premium left). Cinema Corp. common stock is selling today for $50 per share.
The exercise price is $30 and each warrant entitles the holder to purchase two shares of
stock, each at the exercise price.
a. If the warrants are exercised today, what would the Redford Investment Company’s
dollar profit or loss be?
b. What is the Redford Investment Company’s percentage rate of return?
19-17. Solution:
The Redford Investment Company
a. Intrinsic value of a warrant = (Market value of common
stock – Exercise price of warrant) × No. of shares each
warrant entitles holder to purchase.
b. $1,600/$2,400 = 66.7% return
18. Comparing returns on warrants and common stock (LO19-4) The Gifford Investment
Company bought 90 Cable Corporation warrants one year ago and would like to exercise
them today. The warrants were purchased at $25 each, and they expire when trading ends
today. (Assume there is no speculative premium left.) Cable Corporation common stock
was selling for $49 per share when Gifford Investment Company bought the warrants. The
exercise price is $41, and each warrant entitles the holder to purchase two shares of stock,
each at the exercise price.
a. What was the intrinsic value of a warrant at that time?
b. What was the speculative premium per warrant when the warrants were purchased?
The purchase price, as indicated earlier, was $25.
c. What would Gifford’s total dollar profit or loss have been had they invested the $2,250
directly in Cable Corporation’s common stock one year ago at $49 per share? Cable
Corporation common stock is selling today for $59 per share.
d. What would the percentage rate of return be on this common stock investment?
Compare this to the rate of return on the warrant computed when the common stock was
selling for $59 per share.
19-18. Solution:
Gifford Investment Company (Continued)
a. ($49 stock price – $41 exercise price) × 2 shares = $16
intrinsic value
c. $2,250 investment / $49 per share = 46 shares
46 shares × ($59 – $49) = $460
d. Intrinsic value of a warrant = (Market value of common
stock – Exercise price of warrant) × No. of shares each
warrant entitles holder to purchase
19. Return calculations with warrants (LO19-4) Mr. John Hailey has $1,000 to invest in the
market. He is considering the purchase of 50 shares of Comet Airlines at $20 per share. His
broker suggests that he may wish to consider purchasing warrants instead. The warrants are
selling for $10, and each warrant allows him to purchase one share of Comet Airlines
common stock at $18 per share.
a. How many warrants can Mr. Hailey purchase for the same $1,000?
b. If the price of the stock goes to $40, what would be his total dollar and percentage
return on the stock?
c. At the time the stock goes to $40, the speculative premium on the warrant goes to 0
(though the market value of the warrant goes up). What would be Mr. Hailey’s total
dollar and percentage returns on the warrant?
d. Assuming that the speculative premium remains $3.50 over the intrinsic value, how far
would the price of the stock have to fall from $40 before the warrant has no value?
19-19. Solution:
Comet Airlines
a.
$1,000 100 warrants
$10 =
b. $ 40 New price
– 20 Old price
$ 20 Gain
d. With an $18 exercise price, at a stock price of $14.50, the
warrant would have a negative intrinsic value of $3.50.
20. Earnings per share with warrants (LO19-5) Online Network Inc. has a net income of
$650,000 in the current fiscal year. There are 100,000 shares of common stock outstanding,
along with convertible bonds, which have a total face value of $1.6 million. The $1.6
million is represented by 1,600 different $1,000 bonds. Each $1,000 bond pays 6 percent
interest. The conversion ratio is 10. The firm is in a 30 percent tax bracket.
a. Compute basic earnings per share.
b. Compute diluted earnings per share.
19-20. Solution:
Online Network Inc.
a. Basic earnings per share
Earnings $650,000 $6.50
Shares 100,000
= = =
b. Diluted earnings per share
Adjusted earnings after taxes
Shares outstanding + All convertible securities
=
$650,000 $67, 200*
100,000 16,000**
+
=+
$717, 200 $6.18
116,000
= =
*Interest savings × (1 – Tax rate)
= $96,000 (1 – .30)
= $96,000 (.70) = $67,200 in reduced aftertax interest exp.
**= 16,000 in additional shares from conversion
1,600 convertible bonds × 10 conversion ratio