Chapter 20
Hybrid Financing: Preferred Stock, Warrants, and Convertibles
ANSWERS TO END-OF-CHAPTER QUESTIONS
20-1a.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 of a firm’s balance sheet, (2) has no maturity date, and (3) has payments which are considered dividends--thus, they are not legally required and are not tax deductible. However, it is also similar to debt in that it (1) sets a fixed rate for dividends, (2) affords its holders no voting rights, and (3) has priority over common shareholders in the event of bankruptcy.
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 at a specified price. Warrants are generally distributed with debt, or preferred stock, to induce investors to buy those securities at lower cost. A detachable warrant is one that can be detached and traded separately from the underlying security. Most warrants are detachable.
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 additional capital to the issuer.
f.The conversion ratio is the number of shares of common stock received upon conversion of one convertible security. The conversion price is the effective price per share of stock if conversion occurs. Thus, the conversion price is the par value of the convertible security divided by the conversion ratio. The conversion value is the value of the stock that the investor would receive if conversion occurred. Thus, the conversion value is the market price per share times the conversion ratio.
g.A “sweetener” is a feature that makes a security more attractive to some investors, thereby inducing them to accept a lower current yield. Convertible features and warrants are examples of sweeteners.
20-2Preferred 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 holders no voting rights, and has priority over common stock in the event of bankruptcy. However, like equity, its payments are considered dividends from both legal and tax standpoints, it has no maturity date, and it is carried on the firm’s balance sheet in the equity section. From a creditor’s viewpoint, preferred stock is more like common stock, but from a common stockholder’s standpoint, preferred stock is more like debt.
20-3The 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 additional funds. Indirectly, however, conversion may make it easier for a firm to get additional funds by lowering the debt ratio, thus making it easier for the firm to borrow. In the case of warrants, on the other hand, if the price of the stock goes up sufficiently, the warrants are likely to be exercised and thus to bring in additional funds directly.
20-4Either 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 be brought into the firm directly; convertibles, because when they are converted, the equity base is expanded and debt can be sold more easily. However, a firm that does not have additional funds requirements would not want to use warrants.
20-5a.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, the smaller the firm’s dividend payout ratio. This effect is more pronounced for long-term than for short-term warrants.
b.The same general arguments as in Part a hold for convertibles. If a convertible is selling above its conversion value, raising the dividend will lower growth prospects, and, at the same time, increase the “cost” of holding convertibles (or warrants) in terms of forgone cash returns. Thus, raising the dividend payout rate before a convertible’s conversion value exceeds its call price will lower the probability of eventual conversion, but raising the dividend after a convertible’s conversion value exceeds its call price raises the probability that it will be converted soon.
c.The same arguments as in Part b apply to warrants.
20-6The 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, the holder receives shares valued at the then-existing price, but effectively pays less than the market price for those shares.
20-7The 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 nonconvertible bond, 14 percent. In all likelihood, the expected return on the convertible would be higher than that on the straight bond, because a capital gains yield is riskier than an interest yield. The convertible would, therefore, probably be regarded as riskier than the straight bond, and rc would exceed rd. However, the convertible, with its interest yield, would probably be regarded as less risky than common stock. Therefore, rd < rc < rs.
SOLUTIONS TO END-OF-CHAPTER PROBLEMS
20-1Bonds 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 = ?
Straight debt yield = coupon rate = 5% since these bonds are trading at par. Note: if the bonds were not trading at par you’d need to calculate the yield to maturity.
Bonds with warrants: $1,000 = Bond + Warrants.
This bond should be evaluated at 7% (since we know the straight debt trades at par) to determine its present value. Then the value of the warrants can be determined as the difference between $1,000 and the bond’s present value.
N = 15; I/YR = rd = 7; PMT = 50, FV = 1000, and solve for PV = $817.84.
Value of warrants = $1,000 - $817.84 = $182.16.
20-2 Convertible Bond’s Par value = $1,000; Conversion price, Pc = $50;
CR = ?
CR = = = 20 shares.
20-3a.Exercise value = MAX[Current price - Strike price, 0].
Current Strike Exercise
Price Price Value
$ 20 $25 Max[-$5,0] = 0
25 25 0
30 25 5
100 25 75
b.VPackage = $1,000 = = VB + 50($3)
VB= $1,000 - $150 = $850.
$850 = =
With a financial calculator, N = 20; I/YR = 12; PV = −850; FV = 1000; solve for PMT = 99.92 $100. Therefore, the company would set a coupon interest rate of 10 percent, producing an annual interest payment I = $100.
20-4a.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 often use the rule of thumb that the premium over the present price should be in the range of 10 to 30 percent. If the firm’s growth rate is low, the premium would be closer to 10 percent, while a high growth rate firm would command a premium closer to 30 percent.
- Yes, to be able to force conversion if the market rises above the call price.
20-5a.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:
$400,000,000(0.0875 - 0.0575) = $12 million per year.
However, the after-tax interest savings would be more relevant to the firm and would be calculated as $12,000,000(1 - T).
c.At the time of issue, the value of the bond as a straight bond was $669.11, calculated as follows: N = 40, I/YR = 8.75, PV = ?, PMT = 57.5, FV = 1000. Solving, PV = -669.11. Notice that this implies that the value of the conversion feature at the time of issue was $331.89 = $1,000 - $669.11.
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 converted the bond, the bondholder would receive about 15.9 shares of stock per bond, calculated as follows:
Conversion ratio = CR = $1,000/$62.75 = 15.936255 shares.
If the stock price is $32.75, then the value of the bond in conversion is
15.936255($32.75) = $521.91.
Because the value in conversion is less than the value as a bond, investors would not wish to convert the bond.
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 maturity). However, the value of the conversion feature would have fallen sharply, for two reasons. First, the stock price fell from $55 to $32.75, and a decrease in stock price hurts the value of an option. Second, the time until maturity for the conversion fell from 40 years to 25 years, and a reduction in the remaining time to exercise an option hurts its value. Therefore, the bonds probably would have fallen below the $1,000 issue price.
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. Solving, PV = -1,000.
The value of the bond in conversion is 15.936255($32.75) = $521.91.
Although the value of the conversion feature wouldhave dropped in value due to the decline in stock price and the decrease in the remaining time for the conversion to be exercised, the value of the conversion feature would still have a positive value (because an option value can never be zero or below). Therefore, the bonds would probably have a price slightly above their par value of $1,000.
20-6a.Balance Sheet
Alternative 1
Total current
liabilities$150,000
Long-term debt--
Common stock, par $1162,500
Paid-in capital437,500
Retained earnings 50,000
Total assets$800,000Total claims$800,000
Alternative 2
Total current
liabilities$ 150,000
Long-term debt--
Common stock, par $1150,000
Paid-in capital450,000
Retained earnings50,000
Total assets$ 800,000Total claims$ 800,000
Alternative 3
Total current
liabilities$ 150,000
Long-term debt (8%)500,000
Common stock, par $1150,000
Paid-in capital450,000
Retained earnings50,000
Total assets$1,300,000Total claims$1,300,000
b. Original Plan 1 Plan 2 Plan 3
Number of shares 80,000 80,000 80,000 80,000
Total shares 100,000 162,500 150,000 150,000
Percent ownership 80% 49% 53% 53%
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
Interest 20,000 0 0 40,000
EBT $ 90,000 $160,000 $160,000 $ 220,000
Taxes (40%) 36,000 64,000 64,000 88,000
Net income $ 54,000 $ 96,000 $ 96,000 $ 132,000
Number of shares 100,000 162,500 150,000 150,000
Earnings per share $0.54 $0.59 $0.64 $0.88
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).
Alternative 2 results in maintaining control (53 percent) for the firm. Earnings per share increase, while a reduction in the debt ratio like that in Alternative 1 occurs.
Under Alternative 3 there is also maintenance of control (53 percent) for the firm. This plan results in the highest earnings per share (88 cents), which is an increase of 63 percent on the original earnings per share. The debt ratio is reduced to 50 percent.
Conclusions. If the assumptions of the problem are borne out in fact, Alternative 1 is inferior to 2, since the loss of control is avoided. The debt-to-equity ratio (after conversion) is the same in both cases. Thus, the analysis must center on the choice between 2 and 3.
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 is not prohibitive and is a great improvement over the original situation. The combination of increased earnings per share and reduced debt ratios indicates favorable stock price movements in both cases, particularly under Alternative 3. There is the remote chance that the firm could lose its commercial bank financing under 3, since it was the bank which initiated the permanent financing suggestion. The additional funds, especially under 3, may enable the firm to become more current on its trade credit. Also, the bonds will no doubt be subordinated debentures.
Both Alternatives 2 and 3 are favorable alternatives. If the principal owner is willing to assume the risk of higher leverage, then 3 is slightly more attractive than 2. The actual attractiveness of Alternative 3 depends, of course, on the assumption that funds can be invested to yield 20 percent before interest and taxes. It is this fact that makes the additional leverage favorable and raises the earnings per share.
20-7a.
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:
Par = $1,000, 20-year.
Coupon = 8%.
Conversion ratio = CR = 35 shares.
Call = Five-year deferment.
Call price = $1,075 in Year 5, declines by $5 per year.
Will be called when Ct = 1.2(Par) = $1,200.
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 rate. Using a financial calculator, I/YR = 6, PV = 805, PMT = 0, FV = -1200; solving, N = 6.852. So the call will be at the first year end after this, or at Year 7.
We could also calculate this as:
(CR)(P0)(1 + g)N= $1,200
($23)(35)(1 + 0.06)N= $1,200
$805(1.06)N= $1,200.
(1.06)N= $1,200/$805 = 1.49
N ln(1.06)= ln(1.49)
N(0.05827)= 0.39878
N= 0.39878/0.05827 = 6.84 ≈ 7.
Straight-debt value of the convertible at t = 0:
(Assumes annual payment of coupon)
At t = 0 (N = 20): N = 20, I/YR = 9, PMT = 80, FV = 1,000; solving, PV = -908.715. Alternatively,
V=
= $908.715.
Repeating, we can find the straight bond value for different values of N:
V at t = 5 (N = 15): $919.39.
V at t = 10 (N = 10): $935.82.
V at t = 15 (N = 5): $961.10
V at t = 20 (N = 0): $1,000.
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.
CV5 = $23(1.06)5(35) = $1,077.
CV8 = $23(1.06)8(35) = $1,283.
CV10 = $23(1.06)10(35) = $1,442.
For the expected time of conversion (N = 7), the conversion value is:
CV7 = $23(1.06)7(35) = $1,210.422.
The cash flow at the time of conversion (N = 7), is equal to the conversion value plus the coupon payment:
CF7 = $1,210.422 + $80 = $1,290.422.
b.$1,000 = .
Using a financial calculator, N =7, PV = -1000, PMT = 80, FV = 1210.42; solving, we find I/YR = rc = 10.20%.
SOLUTION TO SPREADSHEET PROBLEM
20-8The detailed solution for the spreadsheet problem, Ch20 P08 Build a Model Solution.xls,is available on the textbook’s web site.
Answers and Solutions: 20 - 1
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MINI CASE
Paul Duncan, financial manager of Edusoft Inc., is facing a dilemma. The firm was founded five years ago to provide educational software for the rapidly expanding primary and secondary school markets. Although Edusoft has done well, the firm’s founder believes that an industry shakeout is imminent. To survive, Edusoft must grab market share now, and this will require a large infusion of new capital.
Because he expects earnings to continue rising sharply and looks for the stock price to follow suit, Mr. Duncan does not think it would be wise to issue new common stock at this time. On the other hand, interest rates are currently high by historical standards, and with the firm’s B rating, the interest payments on a new debt issue would be prohibitive. Thus, he has narrowed his choice of financing alternatives to: (1) preferred stock; (2) bonds with warrants; or (3) convertible bonds.
As Duncan’s assistant, you have been asked to help in the decision process by answering the following questions:
a.How does preferred stock differ from both common equity and debt? Is preferred stock more risky than common stock? What is floating rate preferred stock?
Answer:Preferred stock is a hybrid--it contains some features that are similar to debt and some features that are similar to common equity. Like debt, preferred payments to investors are contractually fixed, but like common equity, preferred dividends can be omitted without putting the company into default and thus into bankruptcy. Note, however, that the provisions of most preferred stock issues prevent a firm from paying common dividends when the preferred dividend has not been paid. Further, preferred dividends are generally cumulative; that is, dividends that are omitted accumulate (without interest) and must be paid before any common dividends can be paid. Finally, preferred stockholders can normally elect several directors if preferred dividends are omitted for some period, generally three consecutive quarters. Thus, preferred stock lies somewhere between common equity and debt in the risk/return spectrum. Floating rate preferred stock has a dividend payment that is indexed to the rate on treasury securities, so it almost always trades at par.
b.What is a call option? How can knowledge of call options help a financial manager to better understand warrants and convertibles?
Answer:A call option is a contract which gives the holder the right, but not the obligation, to buy some defined asset, say a stock, at a specified price within some specified period of time. A warrant is a long-term option, and a convertible has built into it an implied call option. If financial managers understand how call options are valued, they can make better decisions regarding the structuring of warrant and convertible issues.
c.Mr. Duncan has decided to eliminate preferred stock as one of the alternatives and focus on the others. EduSoft’s investment banker estimates that EduSoft could issue a bond-with-warrants package consisting of a 20-year bond and 27 warrants. Each warrant would have a strike price of $25 and 10 years until expiration. It is estimated that each warrant, when detached and traded separately, would have a value of $5.The coupon on a similar bond but without warrants would be 10%.