Chapter 20
Hybrid Financing: Preferred Stock, Warrants, and
Convertibles
ANSWERS TO BEGINNING-OF–CHAPTER QUESTIONS
20-1 Both companies and investors have different preferences regarding risks, maturities, and
20-2 Preferred dividends are not normally deductible by the issuing corporation, so they have a
higher after–tax cost than debt. Companies normally plan to pay dividends on preferred
stocks, and investors expect to collect them. However, the non-payment of preferred
20-3 A warrant is a long–term option to purchase a share of common stock. Generally, warrants
are issued with bonds and serve as “sweeteners” to induce investors to buy the bonds.
Because of the possibility of profits from the warrant, investors will buy the bond at a
coupon rate that is below the rate on straight debt of comparable risk and maturity.
20-4 A convertible is a bond or preferred stock that can be converted into common stock of the
issuing company at the holder’s option. The bond will specify a coupon rate, maturity, call
protection period, and number of shares to be received upon conversion. Investors will
expect the stock to grow at some rate, and they can use that growth rate to forecast the
20-5 See the BOC model for an illustration of Question 5. We present below verbal answers.
a. We would first use the information to find the value of the bond if it were not
convertible. We would then subtract the pure bond value from the $1,000 offering
price to get the value of the conversion option.
b. We could use the information to set up a time line of the expected cash flows, which
However, there would be a dramatic effect on the growth rate—it would fall from about
g1 = ROE(1–.25) to g2 = ROE(1–.75), assuming ROE is not affected by the dividend policy
change. Thus, if ROE = 10%, then g would decline from 10%(0.75) = 7.5% to 10%(0.25)
Answers and Solutions: 20 – 3
ANSWERS TO END-OF-CHAPTER QUESTIONS
20-1 a. Preferred stock is a hybrid security, having characteristics of both debt and equity. It
is similar to equity in that it (1) is called “stock” and is included in the equity section
b. Cumulative dividends is a protective feature on preferred stock that requires all past
preferred dividends to be paid before any common dividends can be paid. Arrearages
are the preferred dividends that have not been paid, and hence are “in arrears.”
c. A warrant is an option issued by a company to buy a stated number of shares of stock
d. A stepped–up price is a provision in a warrant that increases the striking price over time.
This provision is included to prod owners into exercising their warrants.
e. Convertible securities are bonds or preferred stocks that can be exchanged for
(converted into) common stock, under specific terms, at the option of the holder. Unlike
the exercise of warrants, conversion of a convertible security does not provide addi-
tional capital to the issuer.
Answers and Solutions: 20 – 4
20-2 Preferred stock is best thought of as being somewhere between debt (bonds) and equity
(common stock). Like debt, preferred stock imposes a fixed charge on the firm, affords its
20-3 The trend in stock prices subsequent to an issue influences whether or not a convertible
issue will be converted, but conversion itself typically does not provide a firm with
20-4 Either warrants or convertibles could be used by a firm that expects to need additional
financing in the future—warrants, because when they are exercised, additional funds will
20-5 a. The value of a warrant depends primarily on the expected growth of the underlying
stock’s price. This growth, in turn, depends in a major way on the plowback of earnings;
the higher the dividend payout, the lower the retention (or plowback) rate; hence, the
slower the growth rate. Thus, warrant values will be higher, other things held constant,
20-6 The statement is made often. It is not really true, as a convertible’s issue price reflects the
underlying stock’s present price. Further, when the bond or preferred stock is converted,
20-7 The convertible bond has an expected return which consists of an interest yield (10 percent)
plus an expected capital gain. We know the expected capital gain must be at least 4 percent,
because the total expected return on the convertible must be at least equal to that on the
SOLUTIONS TO END-OF-CHAPTER PROBLEMS
20-1 Bonds with warrants: $1,000 par value 15-year 5% coupon bonds with annual payments,
trading for $1,000.
Straight debt: $1,000 par value 15-year bonds with 7% annual coupon, also trading for
$1,000.Value of warrants = ?
20-2 Convertible Bond’s Par value = $1,000; Conversion price, Pc = $50;
CR = ?
c
P
20-3 a. Exercise value = MAX[Current price – Strike price, 0].
Current Strike Exercise
Price Price Value
$ 20 $25 Max[-$5,0] = 0
20-4 a. A 10 percent premium results in a conversion price of $42(1.10) = $46.20, while a 30
percent premium leads to a conversion price of $42(1.30) = $54.60. Investment bankers
20-5 a. The premium of the conversion price over the stock price was 14.1 percent: $62.75/$55
– 1.0 = 0.141 = 14.1%.
b. The before-tax interest savings is calculated as follows:
Answers and Solutions: 20 – 8
d. If interest rates had not changed, then the value of the straight bond fifteen years after
issue would have been $699.25, calculated as follows: N = 25, I/YR = 8.75, PV = ?,
PMT = 57.5, FV = 1000. Solving, PV = -699.25.
Assuming that the stock had not gone above $62.75 during the fifteen years after it was
issued, the bond would not have been converted. For example, if a bondholder
e. The value of straight bond would have increased from $669.11 at the time of issue to
$699.25 fifteen years later, as calculated above, due to the fact that the bonds are closer
to maturity (because a bond’s value approaches its par value as it gets closer to
f. Had the rate of interest fallen to 5.75 percent, which is the coupon rate on the bonds,
then their straight bond value would be that of a par bond, which is $1,000. This can
also be calculated as follows: N = 25, I/YR = 5.75, PV = ?, PMT = 57.5, FV = 1000.
20-6 a. Balance Sheet
Alternative 1
Total current
Alternative 2
Total current
Alternative 3
Total current
liabilities $ 150,000
b. Original Plan 1 Plan 2 Plan 3
Number of shares 80,000 80,000 80,000 80,000
Answers and Solutions: 20 – 10
c. Original Plan 1 Plan 2 Plan 3
Total assets $ 550,000 $800,000 $800,000 $1,300,000
EBIT $ 110,000 $160,000 $160,000 $ 260,000
d. Original Plan 1 Plan 2 Plan 3
Total liabilities $400,000 $150,000 $150,000 $ 650,000
TL/TA 73% 19% 19% 50%
e. Alternative 1 results in loss of control (to 49 percent) for the firm. Under it, he loses
his majority of shares outstanding. Indicated earnings per share increase, and the debt
ratio is reduced considerably (by 54 percentage points).
The differences between these two alternatives, which are illustrated in Parts c and
d, are that the increase in earnings per share is substantially greater under Alternative
3, but so is the debt ratio. With its low debt ratio (19 percent), the firm is in a good
position for future growth under Alternative 2. However, the 50 percent ratio under 3
20-7 a.
Stock data and stock required return:
rd = 9%.
P0 = $23.
Dividend yield = 7%.g = 6%.
rs = Dividend yield + g = 7% + 6% = 13%.
Convertible bond data:
Find N (number of years) to anticipated call/conversion:
We need to find the number of years that it takes $805 to grow to $1,200 at a 6% interest
We could also calculate this as:
(CR)(P0)(1 + g)N = $1,200
At t = 0 (N = 20): N = 20, I/YR = 9, PMT = 80, FV = 1,000; solving, PV = -908.715.
Alternatively,
Repeating, we can find the straight bond value for different values of N:
V at t = 5 (N = 15): $919.39.
Conversion value:
The stock price should grow at the 6%. The conversion value at Year t is equal to the
expected stock price multiplied by the conversion ratio:
CVt = P0(1.06)N(35).
Repeating for different values of N:
CV0 = $23(35) = $805.
For the expected time of conversion (N = 7), the conversion value is:
The cash flow at the time of conversion (N = 7), is equal to the conversion value plus the
coupon payment:
Answers and Solutions: 20 – 13