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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%.
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
The 27 warrants each have an estimated value of $5, so
Therefore, the bonds must carry a coupon rate that will cause each bond to sell for $865. The
straight-debt rate is rd = 10%, so if the coupon were set at 10 percent, the bonds would sell at par, not at
$865. The coupon must therefore be below 10 percent, and it is found by solving for PMT
Therefore, the required coupon rate is $84/$1,000 = 8.4%. With an 8.4% coupon,
c. 2. When would you expect the warrants to be exercised? What is a
stepped-up-exercise price?
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
However, note that in order to force warrant holders to exercise and thus to bring
in equity capital, some warrants contain step-up provisions, whereby the strike price
Mini Case: 20 - 1
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website, in whole or in part.
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
c. 3. Will the warrants bring in additional capital when exercised? If EduSoft issues
100,000 bond-with-warrant packages, how much cash will EduSoft receive when
the warrants are exercised? How many shares of stock will be outstanding after
the warrants are exercised? (EduSoft currently has 20 million shares
outstanding).
Answer: When exercised, each warrant will bring in an amount equal to the strike price, which
in this case means $25 of equity capital, and holders will receive one share of
Data:
Number of warrants/bond = 27
Shares before exercise = 20 million.
New shares = (Number of warrants/bond) x (Number of bonds)
Mini Case: 20 - 2
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website, in whole or in part.
c. 4. Because the presence of warrants causes a lower coupon rate on the
accompanying debt issue, shouldn’t all debt be issued with warrants? To answer
this, estimate the expected stock price in 10 years when the warrants are
expected to be exercised, then estimate the return to the holders of the
bond-with- warrants packages. Use the corporate valuation model to estimate
the expected stock price in 10 years. Assume that EduSoft’s current value of
operations is $500 million and it is expected to grow at 8% per year.
Answer: Even though the 8.4 percent coupon rate on the bond is below the 10 percent coupon
Steps to estimate the cost of the bond with warrants.
1.Estimate the percentages of the “package” that are due to straight debt and
warrants.
The value of operations (currently Vop,0 = $500 million) is expected to grow at a rate
of 8% per year.
For each bond: N = 10; I/YR = 10; PMT = 84; FV = 1000. Solve for PV = −
Find the payoff to the warrant-holder at the time of exercise:
For each warrant:
+$46.55 for value of each share
For each bond:
Payoff = (Payoff/warrant) x (Warrants/Bond)
To find the expected return to the warrant-holder, consider the amount paid for the
initial value of warrants in bond and the amount received as the net payoff at exercise:
To find the expected return on the bond with warrants, find the combined expected
return on the bonds and the warrants in each of the bond-with-warrants packages.
c. 5. 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 (which is 13.4%)?
Mini Case: 20 - 4
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website, in whole or in part.
c. 6. If the corporate tax rate is 40%, what is the after-tax cost of the bond with
warrants?
Answer: Because the bond portion of the package was issued at a discount (its value was only
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, 8.5
percent annual coupon, callable convertible bond for its $1,000 par value, whereas a
straight-debt issue would require a 10 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 $1.00, and the dividend is
expected to grow at a constant 8 percent rate. The convertible could be converted
into 40 shares of Edusoft stock at the owner’s option.
1. What conversion price is built into the bond?
Answer: Conversion Price = PC =
received Shares #
Par value
=
40
000,1$
= $25.
The conversion price is similar to a warrant’s strike 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.
Mini Case: 20 - 5
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website, in whole or in part.
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 10 percent, the value of
an 8.5 percent annual coupon bond is $872.30:
Alternatively, using a financial calculator, enter N = 20, I = 10,
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
And, hence, for year 0 and year 10, we have the following:
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?
Mini Case: 20 - 6
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website, in whole or in part.
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 $872.30 while the conversion value is
$800, and hence the floor value is $872.30. At year 10, the conversion value of
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
Mini Case: 20 - 7
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website, in whole or in part.
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 $85 for 6
years, and then would issue stock worth 40($20)(1.08)6 = $1,269.50. Thus, the cash
flow stream would look like this:
0 1 2 3 4 5 6
| | | | | | |
The IRR of this stream, which is the cost of the convertible issue, is 11.84 percent.
Note that Edusoft’s cost of straight debt is 10 percent, while its cost of equity is
13.4 percent:
0
0
P
)g1(D
20$
)08.1(00.1$
The firm’s convertible bond has risk which is a blend of the cost of debt and the cost
d. 7. What is the after-tax cost of the convertible bond?
Answer: Use the after-tax coupon payment, then find the rate of return.
N = Number of years until conversion = 6
Mini Case: 20 - 8
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website, in whole or in part.
e. 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
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.
f. 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
Information asymmetry occurs when a company knows its future prospects better
than outside investors. Outside investors think the company will issue new stock only
Mini Case: 20 - 9
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website, in whole or in part.
