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A B C D E F G H I
10/28/2015
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
Chapter 20. Mini Case for Hybrid Financing: Preferred Stock, Warrants, and Convertibles
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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
Value
$1,000 - $135
$865
PV $865
FV $1,000
PMT = $84.14 = rounding to the nearest dollar is = $84.00
Coupon Rate 8.414% = rounding to the thousandths = 8.40%
Strike price of each warrant = $25.00
Cash received from exercise of warrants = $67.50
Total shares after exercise (in millions) = 22.7
Use the required payment to determine the required coupon rate.
When exercised, each warrant will bring in an amount equal to the strike price, $25; this is equity capital.
Warant-holders will receive one share of common stock per warrant. The strike price is typically set some 20%
Value Bonds =
Value Bonds =
(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).
(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.
How many shares of stock will there be after the warrants are exercised?
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A B C D E F G H I
The cost of debt debt is the cost of straight debt = rd = 10%
Required inputs:
Initial Vop $500
Initial value of debt = Number of bonds x Iissue price $100
Number of shares outstanding 20
Intrinsic value of equity $400
÷ Number of shares 20
Intrinsic price per share $20.00
Valuation analysis in 10 years when warrants expire
Expected V10 =$500 * 2.159
Expected V10 =$1,079.46
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
Total intrinsic value of firm $1,146.96
− Debt $90.17
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
expected growth rate.
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A B C D E F G H I
Intrinsic value of equity $1,056.79
÷ Number of shares $22.70
Intrinsic price per share $46.55
Estimating the expected return to the warrant-holders
Profit per warrant after exercise = $21.55
Number of warrants per bond = 27.00
Profit per bond from exercising warrants = $581.98
N = Number of years until exercise = 10
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%
% 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%
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%
After-tax PMT $50.40
PV $865
FV $1,000
The per warrant profit to the warrant-holder is equal to the stock price minus the strike price. The total profit
The component cost per warrant is the IRR of an investment in warrants at time 0 and a cash flow from
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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%
Pc = Par Value /# Shares
Pc = $1,000.00 /40
Pc = $25.00
Straight-debt value = PV = $872.30
Implied value of convertibility = Issue price - straight-debt value
Implied convertible value = $127.70
Conversion value = CVt = CR(P0)(1 + g)t.
t Conversion value
0$800.00
1$864.00
2$933.12
3$1,007.77
4$1,088.39
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
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
(2) What is the convertible's straight-debt value? What is the implied value of the convertibility feature?
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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
1$864.00 $711.02 $864.00
2$933.12 $697.12 $933.12
3$1,007.77 $681.83 $1,007.77
4$1,088.39 $665.02 $1,088.39
5$1,175.46 $646.52 $1,175.46
6$1,269.50 $626.17 $1,269.50
I/YR = g = 8%
PMT = $0.00
PV = -$800.00
FV = $1,200.00
N = 5.268
Bond will be called (and converted) in year: 6
N = Number of years until conversion = 6
PV = Intitial cost of bond = -$1,000.00
PMT = coupon payment = $85.00
FV = Conversion value = $1,269.50
RATE = rc = 11.83%
(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
A convertible will generally sell above its floor value prior to maturity because convertibility constitutes a call
option that has value.
(6) What is the expected return on the convertible to EduSoft? Does this cost appear to be consistent with the
convertible bond's risk?
Conversion
Value
Straight-
Debt Value
Floor
value
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A B C D E F G H I
For consistency, need rd < rc < rs.
10.00%
rc = 11.83%
rs = 13.40%
Since rc is between rd and rs, the costs are consistent with the risks.
N = Number of years until conversion = 6
PV = Intitial cost of bond = -$1,000.00
PMT = coupon payment = $51.00
FV = Conversion value = $1,269.50
RATE = rc = 8.71%
1. Exercise of warrants brings in new equity capital.
2. Convertible conversion brings in no new funds.
3. In either case, new lower debt ratio can support more financial leverage.
f. How do convertible bonds help reduce agency costs?
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
converted into equity, which is what the company wants to issue.
(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:
rd =
