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Chapter 19: Convertibles, Warrants, and Derivatives
19-20
$600,000 $49,000*
100,000 28,000**
+
=
+
$649,400 $5.07
128,000
==
*interest savings × (1 – tax rate)
21. Earnings per share with convertibles (LO5) Myers Drugs, Inc., has 2 million shares of
stock outstanding. Earnings after taxes are $6 million. Myers also has warrants outstanding
which 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
19-21. Solution:
Myers Drugs, Inc.
a. Basic earnings per share
Earnings $6,000,000 $3.00
Shares 2,000,000
= = =
b. Diluted earnings per share
Chapter 19: Convertibles, Warrants, and Derivatives
19-21
Earnings after taxes
Shares outstanding + Assumed net increase in shares from the warrants
=
$6,000,000
2,000,000 70,000*
=
+
$6,000,000 $2.90
2,070,000
==
19-21. (Continued)
* 1. New shares created 100,000
2. Reduction in shares from cash proceeds
(computed below) 30,000
22. Conversion value and changing pure bond value (LO3) Tulsa Drilling Company has $1
million in 11 percent convertible bonds outstanding. Each bond has a $1,000 par value. The
conversion ratio is 40, the stock price is $32, and the bonds mature in 10 years. The bonds are
currently selling at a conversion premium of $70 over the conversion value.
a. If the price of Tulsa Drilling Company common stock rises to $42 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 that on this date next year, the conversion premium has shrunk
from $70 to $20.
Chapter 19: Convertibles, Warrants, and Derivatives
19-22
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 $1,280 ($32 × 40). The conversion value, $1,280,
b. Pure bond value after one year (nine years remaining).
n = 18 and i = 4%
The stock price is the major factor determining the
convertible bond price.
23. Falling stock prices and pure bond value (LO3) Manpower Electric Company has
7 percent convertible bonds outstanding. Each bond has a $1,000 par value. The conversion
ratio is 25, the stock price $38, and the bonds mature in 16 years.
Chapter 19: Convertibles, Warrants, and Derivatives
19-23
a. What is the conversion value of the bond?
b. Assume after one year, the common stock price falls to $27.50. What is the conversion
value of the bond?
c. Also, assume 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. 25 shares × $38 per share = $950 conversion value
c. n = 30 (2 ×15) i = 5% (10%/2)
d. For the time being, the pure bond value ($769.02) will have
the stronger influence than the stock price. The conversion
e. Market price of bond = pure bond value = $769.02
Chapter 19: Convertibles, Warrants, and Derivatives
19-24
COMPREHENSIVE PROBLEM
Comprehensive Problem 1.
Fondren Exploration, Ltd. (rates of return on convertible bond investments) (LO1) 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 above? (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
adjusted earnings after taxes = $270,000 actual earnings +
Chapter 19: Convertibles, Warrants, and Derivatives
= $348,000 adj. earnings aftertax
b. Current conversion value = 50 × $26 = $ 1,300
Chapter 19: Convertibles, Warrants, and Derivatives
19-26
f. Common stock
$ 26 price
× 50,000 shares
Convertibles
1,000 convertible bonds
× 1,000 par value
requirement on the stock (dividends + growth).
Comprehensive Problem 2.
United Technology Corp. (a call decision with convertible bonds) (LO1) 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.
Chapter 19: Convertibles, Warrants, and Derivatives
19-27
CP 19-2. Solution:
United Technology Corporation (UTC)
Interest expense 11% × $40 million = $4,400,000 million
Shares created from conversion = 30 × 40,000 bonds
$1,090).
The convertibles are not included in basic earnings per
share.
CP 19-2. (Continued)
Basic EPS before conversion = NI/shares outstanding
conversion
Adjusted earnings after taxes
Shares outstanding New Shares issued
=
+
Chapter 19: Convertibles, Warrants, and Derivatives
19-28
$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
=
==
of common stock in the open market. This would serve the
purpose of a partial refunding which would result in a lower
outlay for interest and dividends. Flexibility is improved.
c. Aftertax dividend expense = 1,200,000 × $3.50 = $4,200,000
Aftertax interest expense = $4,400,000 (1 – .25) = $3,300,000
Aftertax net cash loss $ 900,000
