Chapter 21
Hybrid Financing: Preferred Stock, Warrants, and Convertibles

21-1 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 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.

21-2 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 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.

21-3 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 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.

21-4 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 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.

21-5 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, 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.

21-6 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, the holder receives shares valued at the then-existing price, but effectively pays less than the market price for those shares.

21-7 If rights are used, they generally apply to voting securities. Although convertibles do not have voting rights, they are convertible into securities that do have the right to vote.

21-8 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 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.


21-1 First issue: 20-year straight bonds with an 8% coupon.
Second issue: 20-year bonds with 6% annual coupon with warrants. Both bonds issued at par $1,000. Value of warrants = ?

First issue: N = 20; PV = -1000, PMT = 80, FV = 1000 and solve for I = rd = 8%. (Since it sold for par, we should know that rd = 8%.)

Second issue: $1,000 = Bond + Warrants.
This bond should be evaluated at 8% (since we know the 1st issue sold 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 = 20; I = rd = 8; PMT = 60, FV = 1000, and solve for PV = $803.64.

Value of warrants = $1,000 - $803.64 = $196.36.

21-2 Convertible Bond’s Par value = $1,000; Conversion price, Pc = $40;
CR = ?

CR = = = 25 shares.

21-3 a. Expiration value = Current price - Striking price.

Current Striking Expiration
Price Price Value
$ 20 $25 -$5 or 0
25 25 0
30 25 5
100 25 75

b. No precise answers are possible, but some “reasonable” warrant prices are as follows:

Current Warrant
Stock Price Price Premium
$20 $ 2 $ 7
25 4 4
30 7 2
100 76 1

c. (1) The longer the life, the higher the warrant value.

(2) The more variable the stock price, the higher the warrant value.

(3) The higher the expected EPS growth rate, the higher the warrant price.

(4) Going from 0 to 100 percent payout would have two possible effects. First, it might affect the price of the stock causing a change in the formula value of the warrant; however, it is not at all clear that the stock price would change, let alone what the change would be. Second, and more important here, the increase in the payout ratio drastically lowers the expected growth rate. This reduces the chance of the stock going up in the future. This lowers the expected value of the warrant, hence the premium and the price of the warrant.

d. VPackage = $1,000 = = VB + 40($3)
VB = $1,000 - $150 = $850.

$850 = =
= I(7.4694) + $1,000(0.1037) = I(7.6494) + $103.70
$746.30 = I(7.4694)
I = = $99.91 » $100.

Therefore, the company would set a coupon interest rate of 10 percent, producing an annual interest payment I = $100.

21-4 a. 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.
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. There has been heavy use of 18 to 20 percent premiums in recent years.

Yes, to be able to force conversion if the market rises above the call price. If, in fact, the 10 percent growth estimate is correct, by 2008 earnings would be
$3(1.10)4 = $4.39 and, if the P/E ratio remains at 14?, the stock price will go to $4.39(14) = $61.46, making forced conversion possible even if a 30 percent premium is set.

21-5 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:

$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. 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.

At the time of issue, the value of the bond as a straight bond was $668.30, calculated as follows: N = 80, I = 8.75/2 = 4.375, PV = ?, PMT = 57.5/2 = 28.75, FV = 1000. Solving, PV = -668.296. Notice that this implies that the value of the conversion feature at the time of issue was $331.70 = $1,000 - $668.30.

If interest rates had not changed, then the value of the straight bond fifteen years after issue would have been $697.44, calculated as follows: N = 50, I = 8.75/2 = 4.375, PV = ?, PMT = 57.5/2 = 28.75, FV = 1000. Solving, PV = -697.441. To make conversion more profitable than holding the bond, the market interest rate on straight debt would have to increase to 11.68 percent, calculated as follows: N = 50, I = ?, PV = 521.91, PMT = 57.5/2 = 28.75, FV = 1000. Solving, I = 5.841, so rd = 5.841(2) = 11.682. So unless interest rates were higher than 11.68 percent, the value of the straight bond would be greater than the value of conversion, so the bond would not be converted.

d. The value of straight bond would have increased from $668.30 at the time of issue to $697.44 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.

e. Had the rate of interest fallen to 5 3/4 percent, which is the coupon rate on the bonds, then they would have had a straight bond value of $1,000. Although the value of the conversion feature would have 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.

21-6 a. Balance Sheet
Alternative 1

Total current
liabilities $150,000
Long-term debt --
Common stock, par $1 162,500
Paid-in capital 437,500
Retained earnings 50,000
Total assets $800,000 Total claims $800,000

Alternative 2

Total current
liabilities $ 150,000
Long-term debt --
Common stock, par $1 150,000
Paid-in capital 450,000
Retained earnings 50,000
Total assets $ 800,000 Total claims $ 800,000

Alternative 3

Total current
liabilities $ 150,000
Long-term debt (8%) 500,000
Common stock, par $1 150,000
Paid-in capital 450,000
Retained earnings 50,000
Total assets $1,300,000 Total 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 debt $400,000 $150,000 $150,000 $ 650,000
Debt/assets ratio 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.

21-7 Facts and analysis in the problem:

rd = 14%.
rs = $2.18/$30.00 + 9% = 16.27%.
P0 = $30.
D0 = $2.
g = 9%.


Par = $1,000, 20-year.
Coupon = 10%.
R = 20 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:

(P0)(R)(1 + g)n = $1,200
($30)(20)(1 + 0.09)n = $1,200
$600(1.09)n = $1,200.

We need to find the number of years that it takes $600 to grow to $1,200 at a 9 percent interest rate. Using a financial calculator, the answer is n ? 8 years (note that if you are using an HP-12C, the number calculated for n is always rounded up, the solution using an HP-12C is n = 9). Note that we could also solve for n as follows:

(1.09)n = $1,200/$600 = 2
n ln(1.09) = ln(2)
n(0.08618) = 0.69315
n = 0.69315/0.08618 = 8.04 ? 8.

Straight-debt value of the convertible at t = 0:
(Assumes annual payment of coupon)

At t = 0 (n = 20):

V =
= $100(6.6231) + $1,000(0.0728) = $735.

V at t = 5 (n = 15): $754.
V at t = 10 (n = 10): $791.
V at t = 15 (n = 5): $863.
V at t = 20 (n = 0): $1,000.

Conversion value:

Cvt = P0(1.09)n(20).
CV0 = $30(20) = $600.
CV5 = $30(1.09)5(20) = $923.
CV8 = $30(1.09)8(20) = $1,196.
CV10 = $30(1.09)10(20) = $1,420.


b. $1,000 = .

Using a financial calculator, we find rc = 11.65%.

c. rs = + 0.09 = 16.27%. rd = 11.65%.

Generally, to clear the market at par value, the rate on the convertible bond should be between the cost of straight debt and the required return on equity, or in this case, between 14 percent and 16.27 percent. This reflects the fact that convertibles are more risky than straight debentures due to the less certain cash flows, but less risky than equity due to the floor on potential capital loss.
Several changes could be made to improve the return on the convertible:
Reduce Pc (or increase R). This would raise the Ct line (shift left) and move up the probable time of conversion. Discounting the cash flows over a shorter time period would raise the yield, holding the purchase price and cash flows constant.

Increase the coupon yield. Higher annual payments would increase the yields, holding the time period constant.

Use some combination of changes in R and the coupon to produce 14% < rd < 16.27%.

d. P2 = $30(1.09)2 = $35.643 = .

P3 = $2.38/0.1627 = $14.628 = .

Percentage decline in stock price = 59%.

Assuming zero future growth, the value of the stock will not increase, and the value of the convertible will depend only upon its value as a straight bond. Since the firm’s interest payments are relatively low compared to what they would have been had straight debt been issued originally, the firm is unlikely to call the bond issue. Therefore, it would be valued according to its coupon, the current market rate on debt of that risk, and years remaining to maturity (18):

VBond = = $741.

Prior to the change in expected growth from 9 to 0 percent, the market value would have been above the straight bond value: According to the graph, the bond would sell for about $1,025. Thus, there would be a percentage decline of 28 percent in the value of the convertible, about half the 59 percent loss on the stock.


21-8 The detailed solution for the problem is available both on the instructor’s resource CD-ROM (in the file Solution to FM11 Ch 21 P08 Build a Model.xls) and on the instructor’s side of the textbook’s web site,

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 two securities: (1) bonds with warrants or (2) 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. One of the firm’s alternatives is to issue a bond with warrants attached. Edusoft’s current stock price is $20, and its investment banker estimates that the cost of a 20-year, annual coupon bond without warrants would be 12 percent. The bankers suggest attaching 50 warrants, each with an exercise price of $25, to each $1,000 bond. It is estimated that each warrant, when detached and traded separately, would have a value of $3.

1. What coupon rate should be set on the bond with warrants if the total package is to sell for $1,000?

Answer: If the entire package is to sell for $1,000, then

Vpackage = Vbond + Vwarrants = $1,000.

The 50 warrants each have an estimated value of $3, so

Vwarrants = 50($3) = $150.

thus, Vbond + $150 = $1,000 = $850.

Therefore, the bonds must carry a coupon rate that will cause each bond to sell for $850. The straight-debt rate is rd = 12%, so if the coupon were set at 12 percent, the bonds would sell at par, not at $850. The coupon must therefore be below 12 percent, and it is found by solving for INT in this equation:

$850 = INT(PVIFA12%,20) + $1,000(PVIF12%,20)
INT ? $100.

Alternatively, using a financial calculator, enter N = 20, I = 12,
PV = -850, and FV = 1,000 to solve for PMT = $100.

Therefore, the required coupon rate is 10%. With a 10 percent coupon, the bonds would have a value of $850, and hence the package of one bond plus 50 warrants would be worth $1,000.

c. 2. Suppose the bonds were issued and the warrants immediately traded on the open market for $5 each. What would this imply about the terms of the issue? Did the company “win” or “lose”?

Answer: If the warrants traded for $5 immediately after issue, then the company would have set the terms of the bonds with warrants improperly, its stockholders would have been “losers,” and the purchasers of the bonds with warrants would have been “winners.” The 50 warrants would be worth 50($5) = $250, and the package would actually be worth $850 + $250 = $1,100. Selling something worth $1,100 for $1,000 would impose an unnecessary cost of $100 per bond on Edusoft’s shareholders. Because the package could have been sold with a lower coupon rate, the firm could have had lower future interest payments whose present value would be smaller by $100.

c. 3. When would you expect the warrants to be exercised? Assume they have a 10-year life; that is, they expire 10 years after issue.

Answer: Generally, a warrant will sell in the open market at a premium above its expiration value, which is the value of the warrant if exercised. Thus, prior to expiration, an investor who wanted cash would sell his or her warrants in the marketplace rather than exercise them. Therefore, warrants tend not to be exercised until just before they expire.
However, note that in order to force warrant holders to exercise and thus to bring in equity capital, some warrants contain exercise price step-up provisions, whereby the exercise price increases in steps over the life of the warrant. Since the value of the warrant falls when the exercise price is increased, step-up provisions encourage holders of in-the-money warrants to exercise just prior to the timing of a step-up.
Finally, note that warrant holders will tend to exercise voluntarily if the dividend on the stock rises enough. No dividend is earned on a warrant, and high dividends increase the attractiveness of stocks over warrants. The expiration value of the warrant will fall if the stock price falls, and stock prices fall when the stock goes ex dividend. If the dividend is large, warrant holders can avoid recurring large losses by exercising.

c. 4. Will the warrants bring in additional capital when exercised? If so, how much, and what type of capital?

Answer: When exercised, each warrant will bring in the exercise price, which in this case means $25 of equity capital, and holders will receive one share of common stock per warrant. Note that the exercise price is typically set at 10 to 30 percent above the current stock price on the issue date. A high-growth firm would set the exercise price towards the high end of the range, and a low-growth firm would set the price towards the bottom end.

c. 5. Since warrants lower the cost of the accompanying debt issue, shouldn’t all debt be issued with warrants? What is the expected return to the holders of the bond with warrants (or the expected cost to the company) if the warrants are expected to be exercised in five years, when Edusoft’s stock price is expected to be $36.75? How would you expect the cost of the bond with warrants to compare with the cost of straight debt? With the cost of common stock?

Answer: Even though the 10 percent coupon rate on the bond is below the 12 percent coupon on straight bonds, the overall cost of a bond-with-warrants issue is generally higher than that of a straight-debt issue. Some of the return to investors (the debt portion) is contractual in nature, but their expected return on the warrant is related to stock price movements, and hence the warrant is riskier and has a much higher cost to the firm than debt. The overall risk of the issue is a weighted average of the bond yield and the required return on the warrant, and this weighted average cost is greater than the straight-debt cost.
If the warrants are exercised in 5 years, when p = $36.75, then Edusoft would be exchanging stock worth $36.75 for 1 warrant plus $25. The cost/rate of return situation can be analyzed either from an investor’s viewpoint or from the company’s viewpoint--the same result, on a pre-tax basis, is produced in each case. The firm would incur an opportunity cost of $36.75 - $25.00 = $11.75 on each warrant, and investors would obtain that amount of profit. Since each bond has 50 warrants, the total loss to the company (or profit to the warrant holders) per bond would be $587.50. Edusoft must also make the interest payments over the bond’s 20-year life, as well as repay the principal after 20 years. Combining these flows, we have the following situation:

0 1 4 5 6 19 20
| | · · · | | | · · · | |
1,000 -100 -100 -100 -100 -100 -100
-587.50 -1,000
-687.50. -1,100

The IRR of this cash flow stream, 14.65 percent, is the pre-tax cost of the bond-with-warrants issue. This cost is higher than the 12 percent cost of straight debt because, from the investors’ standpoint, the issue is riskier than straight debt. It is lower, though, than the cost of equity because part of the return is fixed by contract.

d. As an alternative to the bond with warrants, Mr. Duncan is considering convertible bonds. The firm’s investment bankers estimate that Edusoft could sell a 20-year, 10.5 percent annual coupon, callable convertible bond for its $1,000 par value, whereas a straight-debt issue would require a 12 percent coupon. The convertibles would be call protected for 5 years, the call price would be $1,100, and the company would probably call the bonds as soon as possible after their conversion value exceeds $1,200. Note, though, that the call must occur on an issue date anniversary. Edusoft’s current stock price is $20, its last dividend was $1.48, and the dividend is expected to grow at a constant 8 percent rate. The convertible could be converted into 40 shares of Edusoft stock at the owner’s option.

1. What conversion price is built into the bond?

Answer: Conversion Price = PC = = = $25.

The conversion price is similar to a warrant’s exercise price, and, as with warrants, the conversion price is typically set at between 10 and 30 percent above the stock price on the issue date.

d. 2. What is the convertible’s straight-debt value? What is the implied value of the convertibility feature?

Answer: Since the required rate of return on a 20-year straight bond is 12 percent, the value of a 10.5 percent annual coupon bond is $887.96:

V = $105(PVIFA12%,20) + $1,000(PVIF12%,20) = $887.96.

Alternatively, using a financial calculator, enter N = 20, I = 12,
PMT = 105, and FV = 1,000 to solve for PV = $887.96. However, the convertible would sell for $1,000, so the implied value of the convertible feature is $1,000 - $887.96 = $112.04. The convertibility value is analogous to the premium on a warrant.

d. 3. What is the formula for the bond’s expected conversion value in any year? What is its conversion value at year 0? At year 10?

Answer: The conversion value in any year is simply the value of the stock one would receive upon converting. Since Edusoft is a constant growth stock, its price is expected to increase by g each year, and hence the expected stock price is Pt = P0(1 + g)t. The value of converting at any year is CR(Pt), where CR is the number of shares received (the conversion ratio). Thus, the expected conversion value in any year is:

CVt = CR(Pt) = CR(P0)(1 + g)t = 40($20)(1.08)t,

And, hence, for year 0 and year 10, we have the following:

Year 0: CV0 = 40($20)(1.08)0 = $800.

Year 10: CV10 = 40($20)(1.08)10 = $1,727.14.

d. 4. What is meant by the “floor value” of a convertible? What is the convertible’s expected floor value at year 0? At year 10?

Answer: The floor value is simply the higher of the straight-debt value and the conversion value. At year 0, the straight-debt value is $887.96 while the conversion value is $800, and hence the floor value is $887.96. At year 10, the conversion value of $1,727 is clearly higher than the straight-debt value, and hence the conversion value sets the floor price for that year. The convertible, however, will generally sell above its floor value prior to maturity because the convertibility option carries additional value. (As discussed below, the price of the convertible can fall to the floor value if the dividends paid on the stock that would be received in conversion greatly exceed the interest paid on the bond.)

d. 5. Assume that Edusoft intends to force conversion by calling the bond as soon as possible after its conversion value exceeds 20 percent above its par value, or 1.2($1,000) = $1,200. When is the issue expected to be called? (Hint: recall that the call must be made on an anniversary date of the issue.)

Answer: The easiest way to find the year conversion is expected is by recognizing that the conversion value begins at $800, grows at the rate of 8% per year, and must rise to $1,200. Then, simply input into a financial calculator, I = 8, PV = 800 (or -800), and FV = 1200, and then press the n button to find the year. It is 5.27, and since the call must occur on an anniversary date, we would round up to 6, so the bond should be called after 6 years. (Note: some calculators automatically round up; the HP-12c is one. However, the HP-17b gives the unrounded answer 5.27.)

d. 6. What is the expected cost of capital for the convertible to Edusoft? Does this cost appear to be consistent with the riskiness of the issue?

Answer: The firm would receive $1,000 now, would make coupon payments of $105 for 6 years, and then would issue stock worth 40($20)(1.08)6 = $1,269.50. Thus, the cash flow stream would look like this:

0 1 2 3 4 5 6
| | | | | | |
1,000 -105 -105 -105 -105 -105 -105.00

The IRR of this stream, which is the cost of the convertible issue, is 13.68 percent.
Note that Edusoft’s cost of straight debt is 12 percent, while its cost of equity is 16.0 percent:

rs = + g = + 8% = 16.0%.

The firm’s convertible bond has risk which is a blend of the cost of debt and the cost of equity, so rc should fall between the cost of debt and equity. Thus, a 13.68 percent cost appears reasonable. Note, though, that the cost of the convertible’s capital is below the 14.65% estimated cost for the bonds with warrants.

e. Edusoft’s market value capital structure is as follows (in millions of dollars):

Debt $ 50
Equity 50

If the company raises $20 million in additional capital by selling (1) convertibles or (2) bonds with warrants, what would its WACC be, and how would those figures compare with its current WACC? Edusoft’s tax rate is 40 percent.

Answer: It is necessary to find the after-tax cost of the convertible, as follows:

0 1 2 3 4 5 6
| | | | | | |
1,000 -63* -63 -63 -63 -63 -63.00

*INT(1 - T) = 105(0.6) = 63.
The Solution Value Is rc(At) = 9.81%.
The After-Tax Cost Of Straight Debt Is 0.6(12%) = 7.2%.

The capital structure, with the convertibles added, would be as follows:

Straight Debt $ 50 41.67% ? 40%
Convertibles 20 16.67 ? 20%
Equity 50 41.67 ? 40%
$120 100.00% 100%


WACC (W/Convertibles) = 0.4(7.2%) + 0.2(9.81%) + 0.4(16%) = 11.24%.

WACC (Current) = 0.5(7.2%) + 0.5(16%) = 11.6%.

The convertibles would lower the WACC slightly, because the convertibles have a cost (9.81%) that is less than the current overall cost of capital to the firm (11.6%). This assumes, though, that the cost of equity would not be affected by the addition of convertible debt. In fact, this debt would increase somewhat the riskiness of the equity (and the other debt), but people would expect it to eventually be converted, at which point the equity ratio would increase, and the risk of leverage would decline. Again, this demonstrates the difficulty of obtaining precise cost of capital estimates, and the necessity of using judgment in determining the cost of capital.

We assume that the warrants are converted in year 5, as described in part c(5) above.

The after-tax cost of the warrants would be:

0 1 4 5 6 19 20
| | · · · | | | · · · | |
1,000 -60* -60 -60 -60 -60 -60
-587.50** -1,000
-647.50. -1,060

*INT(1 - T) = 100(0.6) = 60.
**#Warrants(Opportunity Loss/Warrant) = 50(11.75) = 587.50.
The IRR of this stream is 10.32%.

The capital structure, with the bond with warrants added, would be as follows:

Straight Debt $ 50 41.67% ? 40%
Bond With Warrants 20 16.67 ? 20%
Equity 50 41.67 ? 40%
$120 100.00% 100%


WACC(W/Bond With Warrants) = 0.4(7.2%) + 0.2(10.32%) + 0.4(16%)
= 11.34%.

As you remember, the WACC without the bond with warrants was 11.6%, so the use of warrants decreases the cost of capital, since the cost of the bond with warrants is lower than the prior WACC. The WACC is higher than if convertibles were used because the cost of warrants is higher, apparently because investors think they are more risky. Also note that we assumed conversion in year 5 at an estimated stock price, so the cost of the bond with warrants is determined very arbitrarily.

f. Mr. Duncan believes that the costs of both the bond with warrants and the convertible bond are close enough to one another to call them even, and also consistent with the risks involved. Thus, he will make his decision based on other factors. What are some of the factors which he should consider?

Answer: One factor that should be considered is the firm’s future needs for capital. If Edusoft anticipates a continuing need for capital, then warrants may be favored, because their exercise will bring in additional equity capital without the need to retire the accompanying low-coupon debt issue. Conversely, the convertible issue brings in no new funds at conversion, and the low-coupon debt will be gone when the bonds are converted.
Another factor is whether Edusoft wants to commit to 20 years of debt at this time. Conversion will remove the debt issue, while the exercise of warrants does not. Of course, if Edusoft’s stock price does not rise over time, then neither the warrants nor the convertibles would be exercised, and the debt would remain outstanding in both cases.
g. How do convertible bonds help reduce agency costs?
Answer: Agency costs can arise due to conflicts between shareholders and bondholders, in the form of asset substitution (or bait-and-switch.) This happens when the firm issues low cost straight debt, then invests in risky projects. Bondholders suspect this, so they charge high interest rates. Convertible debt allows bondholders to share in upside potential, so it has low rate. Thus, convertible debt helps reduce this agency cost.
Information asymmetry occurs when a company knows its future prospects better than outside investors. Outside investors think the company will issue new stock only if future prospects are not as good as market anticipates, so issuing new stock send negative signal to market, causing the stock price to fall. A company with good future prospects can issue stock “through the back door” by issuing convertible bonds. This avoids the negative signal of issuing stock directly. Since prospects are good, bonds will likely be converted into equity, which is what the company wants to issue.