CHAPTER 16
CONVERTIBLE BONDS AND CONVERTIBLE PREFERRED STOCK
Teaching Guides for Questions and Problems in the Text
QUESTIONS
16-1. Convertible bonds may be exchanged at the holder’s option for a specified number of shares
of the firm’s stock. Nonconvertible debt lacks this conversion feature.
16-2. A convertible bond’s value in terms of stock depends on the number of shares into which it
may be converted and the price of the shares. This conversion value is important because it sets a
16-3. A convertible bond’s value as debt depends on the bond’s coupon rate of interest and yields
on comparable risky, nonconvertible bonds. This value sets a floor on the price of a convertible
bond. If the bond were to sell for a price that is less than its value as debt, its yield would exceed
16-4. The call feature is the means by which the firm forces the bondholder to convert the bonds.
Bonds will be called only after the price of the stock exceeds the exercise price of the bond. The
16-5. Convertible bonds are less risky than stock as they are debt instruments. The firm must meet
the terms of the bond’s indenture. These bonds are usually riskier than nonconvertible debt
16-6. As the price of the stock rises, both the conversion value of the bond as stock and the bond’s
price rise. The price of the bond approaches its value as stock (i.e., the premium over its value as
16-7. Convertible preferred stock, like convertible bonds, may be exchanged for common stock at
16-8. The advantages to the holder of convertible securities include
a. fixed income
b. possibility of price appreciation (if the price
c. less risk than common stock.
The disadvantages to the holder are
a. possibility of default
b. price fluctuations caused by changes in either the
c. loss of interest that could have been earned on
nonconvertible debt.
16-9. A put feature gives the bond’s owner the option to have the bond retired (redeemed) prior to
A call feature gives the issuer the option to repay the bond prior to maturity. The issuer may
exercise this option if interest rates decline and the firm can refinance at a favorable rate. (The
16-10. If you expect the price of the stock to rise, you are also expecting the price of any security
that may be converted into the stock to rise. In this case the put feature is irrelevant, and you
would not prefer a put bond.
A convertible-exchangeable stock’s price should appreciate with an increase in the value of the
common stock. However, the firm may force conversion of the exchangeable preferred stock even
if the price of the common stock declines because the preferred must be exchanged for the
specified security. With a convertible bond, the company can force conversion but such forced
PROBLEMS
16-1. This problem covers the important features associated with a convertible bond. It is a
straightforward problem with a modest amount of calculation.
b. Value of the bond in terms of stock:
c. Value of the stock implied by the price of the bond:
d. The premium in terms of stock: $1,040 – $864 = $176
e. Value of the bond as nonconvertible debt:
f. The premium in terms of debt: $1,040 – $817.40 = $222.60
g. If the price of the stock rises from $32 to $64, the price of the bond will not rise from $1,040 to
h. If the price of the stock declines from $32 to $16, the price of the bond will not fall from $1,040
i. Since the price of the stock is less than the exercise price of the bond, the probability of the
$1,040 while it would have to pay $1,050 if it called the bonds.)
j. Investors are willing to pay the premiums because a convertible bond offers potential for price
16-2. a. Value of the bond as nonconvertible debt:
b. Number of shares into which the bond may be converted:
c. Value of the bond in terms of stock:
d. The minimum price of the bond will be the higher of its value as stock ($1,200) or its value as
e. Short the stock for $1,200, buy the bond for $976, convert it, and cover the short with the stock
f. The price of the stock ($30) exceeds the exercise price of the bond ($25). The firm could force
g. They receive the call price: $1,040.
h. It is advantageous to convert since the bond’s value as stock ($1,200) exceeds the call price
i. In this example an increase in interest rates will not affect the value of the bond unless the
j. If the price of the stock were $10, the bond’s value as stock would be $400. The convertible bond
16-3. a. Value of the preferred stock in term of common
b. Premium paid over the preferred stock’s value as common stock is $25.00 – $17.00 = $8.00.
c. Value of the convertible preferred as nonconvertible preferred stock is $2/.10 = $20.00.
d. If the price of the common stock were to rise to $60, the convertible preferred stock would sell
for at least its value as common stock: .50 shares x $60 = $30.00.
16-4. Be certain to stress that the investor who buys Bond B forgoes some interest (7.6 percent
versus 8.0 percent) but receives the put option to sell the bond back to the company at a specified
price at a specified date in the future.
a. VA = $80 + … + $80 + $1,000
b. VA = $80 + … + $80 + $1,000
When interest rates decline, the value of both bonds rises, but the price of Bond A rises more,
because it pays the larger amount of interest for the ten years. When interest rates rise, the price of
Bond B declines less ($935.44 versus $945.64), because the holder may exercise the option after
five years. The expected maturity date is five years and not ten years, so Bond B’s price does not
decline as much as the price of the ten-year bond.
c. The implied trade-off is that Bond B offers less interest, but if interest rates were to rise, its
price declines less. Thus Bond B is safer.
d. The present value of the $4 foregone annually for ten years when the interest rate is 8 percent is
16-5. a. The value of each bond in terms of stock:
b. The premium paid over each bond’s value as stock:
Firm A: $1,100 – 920 = $180
Firm B: $1,100 – 900 = $200
c. Firm A pays no cash dividend. The bond pays $75, so the income advantage is $75. Firm B pays
d. For Firm A the income advantage takes 2.4 years ($180/$75) to offset the premium. For Firm B
the income advantage takes 4.4 years ($200/45) to offset the premium.
e. For stock A the holding period return is
($65-46)/$46 = 41.3%
The rate of return is
1.413 is the interest factor for the future value of a dollar. When this factor is located in the
interest table under four years, the rate of return is determined to be 9 percent.
(PV = -46; N = 4; PMT = 0; FV = 65; I = ? = 9.03.)
An alternative calculation is
For the bond the holding period return is
The rate of return is
(The $1,300 is the conversion value of the bond: $65 x 20 shares = $1,300.) Once again this
problem is an illustration of the calculation of the rate of return given a cash outflow (the cost of
the bond) and various cash inflows (the interest payments and the terminal value of the bond).
The equation may be solved by trial and error or using a financial calculator. Using a financial
calculator, the answer is PV -1100, N = 4; PMT = 75; FV = 1300; I = ? = 10.7.
Using the present value tables determines the following:
Thus, the return falls between 10 and 12 percent.
Since the return on the stock was only 9 percent, the investment in the bond proved to be superior.
The interest more than offset the premium paid for the bond.
16-6. a. Number of shares into which the bond may be converted:
c. Bond’s income advantage: $70 – (15.5 X 2) = $39
d. Time necessary to overcome the premium:
e. The conversion price ($64.516) exceeds the price of the stock ($60), so the probability of the
bond being called is nil.
f. The price of the bond must rise to at least
g. Holding period return on the bond:
h. The holding period return is misleading because it does not express the return on an annual
basis.
i. The annualized rates of return are
j. The conversion features are adjusted for the stock split, so that a two for one split would result
k. If the bond is held to maturity, the investor receives$1,000. Since the bond was purchased for
l. If the price of the stock rises to $90, the bond is worth 15.5 X $90 = $1,395. Even though
interest rates rose to 12 percent, that increase would have no affect on the price of the bond, which
would now sell for its value as stock.
16-7. a. Value of the bond as nonconvertible debt:
(If interest is compounded semi-annual, the value of the bond is N = 24; I = 4.5; PMT = 25; FV =
1000; PV = ? = -710.)
The premium over the bond’s value as debt is
b. The income advantage is $50 – ($0.50)30 = $35.
The bond’s value as stock is $25 x 30 = $750.
The bond’s premium over its value as stock is
The breakeven time is $250/$35 = 7.14 years.
c. If interest rates remain the same, the price of the bond should not fall below $714, its value as
debt.
d. If the price of the stock rises from $25 to $40, the value of the bond must be at least worth its
e. The terms of convertible bonds adjust the conversion prices (and the number of shares) for
f. The investor receives the $1,000 principal. Since the bond is currently selling for $1,000, the
g. Since the price of the stock ($25) is less then the conversion price ($33.34), no bondholders
h. If the bond is called and the bondholders do not convert, they receive the $1,000 principal and
any call penalty. In this example, the bondholders would receive $1,000 + $50 = $1,050.
16-8. a. Since the convertible preferred stock may be exchanged
for 2 shares, it is worth $80 in terms of stock
($40 x 2).
e. The value of the preferred stock as common stock at various prices of the common stock:
Price of the Number of shares Value of the
common stock into which the preferred stock
preferred may be
exchanged
$10 6.0 $60
f. The return on the stock:
$40(1 + r)4 = $75
(1 + r)4 = $75/$40 = 1.875
1.875 is the interest factor for the future value of a dollar. When this factor is located in the
interest table under four years, the rate of return is determined to be in excess of 16 percent. (PV =
-40; N = 4; PMT = 0; FV = 75; I = ? = 17.02.)
An alternative calculation is
(The $120 is the exchange value of the preferred stock.) Once again this problem is an illustration
of the calculation of the rate of return given a cash outflow (the cost of the exchangeable preferred
stock) and various cash inflows (the dividend payments and the terminal value).
The return on the stock exceeded the return on the convertible exchange stock. Even though the
preferred stock paid the dividend, the adjustment to the number of shares received limits the
upside potential.
g. If the price of the stock is $45, the preferred is worth $90 ($45 x 2).
The return on the stock:
1.125 is the interest factor for the future value of a dollar.
When this factor is located in the interest table under four years, the rate of return is determined to
be approximately 3 percent. (PV = -40; N = 4; PMT = 0; FV = 45; I = ? = 2.99.)
For the exchangeable preferred stock, the return is
The equation may be solved by trial and error or with a financial calculator. If interest tables are
used and 7 percent is selected, the present value of the cash inflows is
h. If the price of the stock is $25, the preferred is worth $60 since the number of shares is adjusted
to obtain $60 worth of common stock.
Since the stock is now selling for $25, the investor sustained an approximate annualized loss of 11
percent on the stock.
The loss is -0.92%. The return on the convertible exchange stock exceeds the return on the stock.
While the investor did sustain a loss, the adjustment in the number of shares limits the downside
potential loss.
Teaching Guides for the Financial Advisor’s Case: The Pros and Cons of Investing in a
Convertible Bond
The situation in this problem is essentially the conflict between a husband and wife concerning the
amount of risk they are willing to take to accumulate assets to finance their children’s education.
1. If the bonds were not convertible, they would sell as non- convertible bonds with a yield to
maturity of 10 percent. Since the bonds have an 8 percent coupon, they would have to sell for a
2. The value of the bonds as stock: $8.50 x 100 shares = $850
3. If the price of the stock rose to $15, the bond’s value as stock would rise to $15 x 100 = $1,500.
4. If the price of the stock declined to $5, the price of the bond would fall to its value as debt. If
5. If the money were invested in non-convertible bonds, changes in the price of the stock would
6. If the price of the stock rose, the holder does not have to convert as long as the bond is not
7. The bonds may be sold, as there is a secondary market in convertible bonds. However, the
8. If the firm were to fail, the bonds would go into default. There is little assurance that
9. The bonds do offer the safety associated with debt and the potential for growth if the value of
10. The convertibles offer more interest and the potential for growth that is not available through a
11. If the bonds were placed in the children’s names with Mrs. Roussel as custodian for the
Money managers and financial planners need to perceive their clients’ risk tolerance. Such
professionals may be liable for investing clients’ funds in a vehicle that is viewed as inappropriate.
Since Mrs. Roussel asks several questions concerning the possibility of loss on the bonds, you
could read into the questions that such securities are not appropriate. However, just because an
individual bond may be inappropriate does not mean that other alternatives may not increase the
Teaching Guides for the Comprehensive Financial Advisor’s Comprehensive Investment Case: The
Variety of Bonds and Their Impact on Investment Decision Making
This case reviews the features that differentiate various types of corporate bonds. All five bonds
are issued by the same company, mature at the same time, and initially sell for their principal
amount.
1. The first question concerns quality. Presumably the mortgage bond would have the highest
rating since it is secured. The subordinated debenture should have the lowest rating since it is
unsecured and subordinated to the other bonds.
2. The differences in yields depend on the features of each bond and its relative position in case of
default. The mortgage bond has a lower interest rate (6.0%) than the debenture, which has a lower
rate (7.0%) than the subordinated debenture (8.0%). The convertible bond has the lowest rate
(4.0%) since it offers the investor the option to convert the bond into stock. The put bond also has
3. The duration of each bond is as follows:
a. 4.0% convertible bond 14.13 years
b. 8.0% subordinated debenture 10.60
c. 6.0 mortgage bond 12.16
d. 7.0% callable debenture 11.34
e. 6.5% put bond 11.73
The calculations of duration assume that each bond will be outstanding for the entire 20 years.
This assumption may not hold for the convertible bond and the put bond. The assumption may not
hold for the bonds with a call feature and a call penalty. In addition, the sinking funds will retire
4. If interest do not change and the price of the stock remains $8.50, the prices of the bonds
5. If interest rates rise after five years, the prices of the bonds should fall. However, the amount of
a. 4.0% convertible bond $806
This price, however, is less than the value of the bond as stock (100 x $8.50 = $850), so the bond’s
price cannot fall to $806. Its value as stock ($850) sets a minimum price on the bond.
b. 8.0% subordinated debenture $848
c. 6.0 mortgage bond $829
d. 7.0% callable debenture $839
e. 6.5% put bond $921
The increase in interest rates suggests that investors will exercise the option, so the number of
years the bond will be outstanding is 5 and not 15.
6. If interest rates fall after ten years, the prices of the bonds should rise. However, the amount of
the increases will differ since the bonds’ features differ. Possible prices and the assumptions use to
determine them as follows:
a. 4.0% convertible bond $2,367 ($1,180)
The price of the stock also rises by 9 percent (if it moves with the market), so new price of the
b. 8.0% subordinated debenture $1,147
c. 6.0 mortgage bond $1,162
d. 7.0% callable debenture $1,154
e. 6.5% put bond $1,158
The decline in interest rates suggests that investors will not exercise the option, so the number of
years the bond will be outstanding remains 10.
7. If the prices in part 6 are used, the annualized returns (derived using a financial calculator) for
each bond are as follows:
a. 4.0% convertible bond 11.84%
Since the price of the stock rose which caused the value of the bond s stock to rise, the value as
stock is used to determine the return on the initial $1,000 investment.
b. 8.0% subordinated debenture 8.96%
c. 6.0 mortgage bond 7.16%
d. 7.0% callable debenture 8.06%
The 7% debenture is also callable, but there is no call penalty. If the bond were called, the return
on the investment is 7%.
Since the price of the stock rose, the value of the convertible bond also rose and produced the
highest return. The anticipation of the price of the stock rising argues for the convertible. Lower
interest rates, however, favor the bond with the highest coupon (the 8.0% subordinated debenture).