Chapter 19: Convertibles, Warrants, and Derivatives
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)
21. Earnings per share with convertibles (LO19-5) Myers Drugs Inc. has 1.20 million shares
of stock outstanding. Earnings after taxes are $9 million. Myers also has warrants
outstanding that allow the holder to buy 100,000 shares of stock at $15 per share. The stock
is currently selling for $50 per share.
a. Compute basic earnings per share.
b. Compute diluted earnings per share considering the possible impact of the warrants.
Use the following formula:
Earnings after taxes
Shares outstanding + Assumed net increase in shares from the warrants
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Chapter 19: Convertibles, Warrants, and Derivatives
19-21. Solution:
Myers Drugs Inc.
a. Basic earnings per share
Earnings $9,000,000 $7.50
Shares 1, 200,000
= = =
b. Diluted earnings per share
Earnings after taxes
Shares outstanding + Assumed net increase in shares from the warrants
$9,000,000 $7.09
1, 270,000
= =
2. Reduction in shares from cash proceeds
Assumed reduction in shares outstanding from
purchase of shares with cash received
22. Conversion value and changing pure bond value (LO19-3) Tulsa Drilling Company has
$1.3 million in 12 percent convertible bonds outstanding. Each bond has a $1,000 par value.
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Chapter 19: Convertibles, Warrants, and Derivatives
The conversion ratio is 40, the stock price is $36, and the bonds mature in 10 years. The bonds
are currently selling at a conversion premium of $60 over the conversion value.
a. Today, one year later, the price of Tulsa Drilling Company common stock has risen to
$46. What would your rate of return be if you had purchased the convertible bond one
year ago and sold it today? Assume that on the date of sale, the conversion premium has
shrunk from $60 to $10. (Hint: Don’t forget to include the interest payment for the first
year)
b. Assume the yield on similar nonconvertible bonds has fallen to 8 percent at the time of
sale. What would the pure bond value be at that point? (Use semiannual analysis.)
Would the pure bond value have a significant effect on valuation then?
19-22. Solution:
Tulsa Drilling Company
a. First find the price of the convertible bond. The conversion
value is $1,440 ($36 × 40). The conversion value, $1,440,
$46 stock price × 40 shares = $1,840 conversion value
total return
b. Pure bond value after one year (nine years remaining).
Answer: $1,253.19
N I/Y PV PMT FV
No, because the pure bond value of $1,253.54 is still well below
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Chapter 19: Convertibles, Warrants, and Derivatives
23. Falling stock prices and pure bond value (LO19-3) Manpower Electric Company has
6 percent convertible bonds outstanding. Each bond has a $1,000 par value. The conversion
ratio is 20, the stock price $36, and the bonds mature in 16 years.
a. What is the conversion value of the bond?
b. Assume after one year that the common stock price falls to $30.50. What is the
conversion value of the bond?
c. Also assume that after one year interest rates go up to 10 percent on similar bonds.
There are 15 years left to maturity. What is the pure value of the bond? Use semiannual
analysis.
d. Will the conversion value of the bond (part b) or the pure value of the bond (part c)
have a stronger influence on its price in the market?
e. If the bond trades in the market at its pure bond value, what would be the conversion
premium (stated as a percentage of the conversion value)?
19-23. Solution:
a. 20 shares × $36 per share = $720 conversion value
Answer: $692.55
N I/Y PV PMT FV
d. For the time being, the pure bond value ($692.55) will have
the stronger influence than the stock price. The conversion
e. Market price of bond = Pure bond value = $692.55
Conversion value = –610.00
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Chapter 19: Convertibles, Warrants, and Derivatives
COMPREHENSIVE PROBLEM
Comprehensive Problem 1.
Fondren Exploration Ltd. (rates of return on convertible bond investments) (LO19-1)
Fondren Exploration Ltd. has 1,000 convertible bonds ($1,000 par value) outstanding, each of
which may be converted to 50 shares of stock. The $1 million worth of bonds has 25 years to
maturity. The current price of the stock is $26 per share. The firm’s net income in the most recent
fiscal year was $270,000. The bonds pay 12 percent interest. The corporation has 150,000 shares
of common stock outstanding. Current market rates on long-term nonconvertible bonds of equal
quality are 14 percent. A 35 percent tax rate is assumed.
a. Compute diluted earnings per share.
b. Assume the bonds currently sell at a 5 percent conversion premium over conversion value
(based on a stock price of $26). However, as the price of the stock increases from $26 to $37
due to new events, there will be an increase in the bond price, and a zero conversion
premium. Under these circumstances, determine the rate of return on a convertible bond
investment that is part of this price change, based on the appreciation in value.
c. Now assume the stock price is $16 per share because a competitor introduced a new
product. Would the conversion value be greater than the pure bond value, based on the
interest rates stated here? (See Table 16-3 in Chapter 16 to get the bond value without
having to go through the actual computation.)
d. Referring to part c, if the convertible traded at a 15 percent premium over the
conversion value, would the convertible be priced above the pure bond value?
e. If long-term interest rates in the market go down to 10 percent while the stock price is
at $23, with a 6 percent conversion premium, what would the difference be between the
market price of the convertible bond and the pure bond value? Assume 25 years to
maturity, and once again use Table 16-3 for part of your answer.
CP 19-1. Solution:
Fondren Exploration Limited
a. Diluted earnings per share
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Chapter 19: Convertibles, Warrants, and Derivatives
Adjusted earnings after taxes = $270,000 actual earnings +
b. Current conversion value = 50 × $26 = $ 1,300
Chapter 19: Convertibles, Warrants, and Derivatives
Comprehensive Problem 2.
United Technology Corp. (a call decision with convertible bonds) (LO19-1) United Technology
Corporation (UTC) has $40 million of convertible bonds outstanding (40,000 bonds at $1,000 par
value) with a coupon rate of 11 percent. Interest rates are currently 8 percent for bonds of equal risk.
The bonds have 15 years left to maturity. The bonds may be called at a 9 percent premium over par.
They are convertible into 30 shares of common stock. The tax rate for the company is 25 percent.
The firm’s common stock is currently selling for $41, and it pays a dividend of $3.50 per
share. The expected income for the company is $38 million with 6 million shares outstanding.
Thoroughly analyze the bonds and determine whether the firm should call the bond at the
9 percent call premium. In your analysis, consider the following:
a. The impact of the call on basic and diluted earnings per share (assume the call forces
conversion).
b. The consequences of your decision on financing flexibility.
c. The net change in cash outflows to the company as a result of the call and conversion.
CP 19-2. Solution:
United Technology Corporation (UTC)
a. If the bond is called, it will be converted because the
conversion value is greater than the call price ($1,230 >
$1,090).
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Chapter 19: Convertibles, Warrants, and Derivatives
Adjusted earnings after taxes
Shares outstanding New shares issued
=+
$38,000,000 + $4,400,000 (1 .25)
6,000,000 + 1,200,000
–
=
$38,000,000 + $3,300,000
7,200,000
$41,300,000 $5.74
7, 200, 000
=
= =
b. With the elimination of the convertible bond, UTC has
reduced its debt and increased its equity financing. This
provides more flexibility in the way of debt issues for the
Chapter 19: Convertibles, Warrants, and Derivatives
c. Aftertax dividend expense = 1,200,000 × $3.50 =
$4,200,000
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