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%.
Maturity of bond (years) 20
Time to expiration of warrants (years) 10
Value per warrant $5.00
Par (face) value of bond $1,000.00
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A B C D E F G H I
12/10/2012
Inputs (Note: All values are in millions, except per share data.)
Value of operations $500.00
Number of shares outstanding 20
Data for Bonds with Warrants (Note: All values are in millions, except per share data.)
Warrants per bond 27
Strike price $25.00
First, find the value of the embedded straight bond.
Chapter 20. Mini Case for Hybrid Financing: Preferred Stock, Warrants, and Convertibles
b. What is a call option? How can a knowledge of call options help a financial manager to better understand
warrants and convertibles? Answer: See Chapter 20 Mini Case Show
(1) What coupon rate should be set on the bond with warrants if the total package is to sell for $1,000?
c. Mr. Duncan has decided to eliminate preferred stock as one of the alternatives and focus on the others.
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.
Paul Duncan, financial manager of EduSoft Inc., is facing a dilemma. The firm was founded 5 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 an industry shakeout is imminent. To survive, EduSoft must
grab market share now, and this will require a large infusion of new capital.
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: See Chapter 20 Mini Case Show
As Duncan’s assistant, you have been asked to help in the decision process by answering the following
questions:
The following data apply to all three alternatives:
Expected growth rate of FCF 8.00%
Current stock price $20.00
Tax rate 40.00%
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packages. Use the corporate valuation model to estimate the expected stock price in 10 years. Assume that
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A B C D E F G H I
Value of warrants per bond = (Warrant per bond) x (Value per warrant)
Value of warrants per bond = $135.00
Value Package =
Value
Bonds + Value warrants = $1,000
N20
I/YR 10%
Number of warrants (in millions) = 2.70
Strike price of each warrant = $25.00
Cash received from exercise of warrants = $67.50
Number of shares before exercise (in millions) = 20.00
Number of shares from exercise of warrants (in millions) = 2.70
Total shares after exercise (in millions) = 22.7
(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).
(2) When would you expect the warrants to be exercised? What is a stepped-up-exercise price? Answer: See
Chapter 20 Mini Case Show
Use the required payment to determine the required coupon rate.
Find the payment such that the bond with warrant is issued at par.
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expected growth rate.
Value of operations $500
Coupon rate 8.40%
PMT $84
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A B C D E F G H I
Current valuation analysis
Required inputs:
Initial Vop $500
Initial value of debt = Number of bonds x Iissue price $100
Number of shares outstanding 20
Intrinsic price per share $20.00
Valuation analysis in 10 years when warrants expire
Required inputs:
Number of years until expiration = 10
Expected V10 = Vop *(1 + g)10
N10
Price = $901.69
Number of bonds (in millions) 0.10
Total bond value (in millions) = $90.169
Intrinsic stock price in at expiration
Value of operations $1,079.46
How much will the bonds be worth in 10 years? (There will be 10 years remaining to maturity.)
Begin by estimating the required return on the debt, rd, and the required return on the warrants, rw. To find the
overall cost of capital for the convertible bond, rc, comine the cost of straight debt with the cost of the warrant,
weighting them by the percentages they comprise of the bond-with-warrants package.
To find the cost of warrants, we will find the expected profit of the warrant holders and the expected return. If
the warrants are very likely to be in the money at expiration, then we can approximate the expected profit by
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Profit per warrant after exercise = $21.55
Number of warrants per bond = 27.00
Profit per bond from exercising warrants = $581.98
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PV = Intitial cost of warrants = -$135.00
PMT = zero = 0
FV = Cash flow at exercise = $581.98
RATE = Component cost of warrants per bond = 15.73%
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Coupon on convertible debt = 8.40%
Required return on straight debt = 10.00%
Required return on equity = Dividend yield + g = 13.40%
Required return on warrant = 15.73%
(6) If the corporate tax rate is 40%, what is the after-tax cost of the bond with warrants?
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A B C D E F G H I
Intrinsic value of equity $1,056.79
Estimating the expected return to the warrant-holders
Intrinsic stock price per share after exercise = $46.55
Strike price of each warrant = $25.00
N = Number of years until exercise = 10
% straight bond in bond with warrants = 86.50%
% warrants in bond with warrants = 13.50%
Component cost of straight debt = 10.00%
Component cost of warrants = 15.73%
Pre-tax component cost of bond with warrants = 10.77%
(5) How would you expect the cost of the bond with warrants to compare with the cost of straight debt? With
The per warrant profit to the warrant-holder is equal to the stock price minus the strike price. The total profit
per bond is equal to the total number warrants per bond multiplied by the profit per warrant.
The component cost per warrant is the IRR of an investment in warrants at time 0 and a cash flow from
exercising.
The pre-tax component cost of the bond with warrants is the weighted average of the pre-tax component costs
of the straight bond and the warrants.
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2$933.12
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A B C D E F G H I
AT rd =I/YR = 6.24%
After-tax component cost of bond with warrants = 7.52%
Required inputs:
Par value of convertible bond = $1,000.00
Coupon rate on convertible bond = 8.50%
Conversion ratio = 40
Maturity (in years) of convertible bond = 20
Inputs:
N = 20
I/YR = 10%
Conversion value = CVt = CR(P0)(1 + g)t.
t Conversion value
0$800.00
1$864.00
(2) What is the convertible’s straight-debt value? What is the implied value of the convertibility feature?
(1) What conversion price is built into the bond?
(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?
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
into 40 shares of EduSoft stock at the owner’s option.
conversion, the bondholder will also receive the conversion value. We can find the return using the RATE
FV = Conversion value = $1,269.50
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A B C D E F G H I
The floor value is the higher of the straight debt value and the conversion value.
Straight-debt value =
t
0$800.00 $723.65 $800.00
1$864.00 $711.02 $864.00
I/YR = g = 8%
N = Number of years until conversion = 6
PV = Intitial cost of bond = -$1,000.00
PMT = coupon payment = $85.00
Recall that the bond can be called only on an anniversary date, so we must round the number of years that we
just found up to the next integer. Also, we must verify that the year is at least as great as the number of years
the bond is protected from calls.
The bondholder will receive the coupon each year until conversion (including the year of the conversion). At
Conversion
Value
Floor
value
(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?
(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.)
A convertible will generally sell above its floor value prior to maturity because convertibility constitutes a call
option that has value.
Notice that the conversion value grows at the same rate as the stock. So the first step is to find the number of
years until the initial conversion value grows to the value at which it will be called.
(6) What is the expected return on the convertible to EduSoft? Does this cost appear to be consistent with the
convertible bond’s risk?
2$933.12 $697.12 $933.12
PV = Intitial cost of bond = -$1,000.00
PMT = coupon payment = $51.00
FV = Conversion value = $1,269.50
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2. Convertible conversion brings in no new funds.
3. In either case, new lower debt ratio can support more financial leverage.
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A B C D E F G H I
For consistency, need rd < rc < rs.
N = Number of years until conversion = 6
1. Exercise of warrants brings in new equity capital.
Does the firm want to commit to 20 years of debt?
1. Convertible conversion removes debt, while the exercise of warrants does not.
f. How do convertible bonds help reduce agency costs?
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?
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
(7) What is the after-tax cost of the convertible bond?
Use the after-tax coupon payment, then find the rate of return.
The firm’s future needs for equity capital:
Since rc is between rd and rs, the costs are consistent with the risks.