1
2
3
4
5
6
7
8
9
Expected growth rate of FCF 8.00%
Current stock price $20.00
Tax rate 25.00%
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
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%.
17
18
19
20
21
22
23
29
30
31
32
33
34
35
36
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
Number of bonds issued 0.10
45
46
47
48
49
56
57
58
59
60
61
62
A B C D E F G H I
11/23/2018
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.
Value of warrants per bond = (Warrant per bond) x (Value per warrant)
Value of warrants per bond = $135.00
Chapter 20. Mini Case for Hybrid Financing: Preferred Stock, Warrants, and Convertibles
(1) What coupon rate should be set on the bond with warrants if the total package is to sell for $1,000?
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:
bonds with warrants; or (3) convertible bonds.
63
75
76
68
69
70
71
77
78
79
80
82
83
84
85
86
to 30% above the current stock price when the warrants are issued.
99
Strike price of each warrant = $25.00
87
88
89
94
95
96
Number of shares from exercise of warrants (in millions) = 2.70
101
102
103
104
110
weighting them by the percentages they comprise of the bond-with-warrants package.
111
112
113
114
115
A B C D E F G H I
N20
Number of shares before exercise (in millions) = 20.00
(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 much cash will the firm receive when the warrants are exercised?
How many shares of stock will there be after the warrants are exercised?
(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.
67
122
123
124
Coupon rate 8.40%
PMT $84
Number of bonds (in millions) 0.10
125
126
127
128
129
130
131
132
140
141
142
143
144
145
146
147
148
149
150
155
156
157
158
159
Intrinsic value of equity $1,056.79
÷ Number of shares $22.70
Intrinsic price per share $46.55
170
171
172
179
180
181
182
A B C D E F G H I
The cost of debt debt is the cost of straight debt = rd = 10%
Current valuation analysis
Required inputs:
Total intrinsic value of firm $500
− Debt $100
Intrinsic value of equity $400
÷ Number of shares 20
Intrinsic price per share $20.00
Valuation analysis in 10 years when warrants expire
Required inputs:
Number of years until expiration = 10
N10
I10%
Intrinsic stock price in at expiration
Value of operations $1,079.46
Estimating the expected return to the warrant-holders
How much will the bonds be worth in 10 years? (There will be 10 years remaining to maturity.)
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
first estimating the expected stock price at expiration. We begin by performing a current valuation analysis and
then we repeat the analysis assuming 10 years have passed and the value of operations has grown at it
expected growth rate.
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.
Initial value of debt = Number of bonds x Iissue price $100
Value of operations $500
183
184
185
PV = Intitial cost of warrants = -$135.00
PMT = zero = 0
FV = Cash flow at exercise = $581.98
193
194
195
196
197
198
Component cost of straight debt = 10.00%
Component cost of warrants = 15.73%
204
205
206
207
208
209
210
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%
217
218
219
225
226
227
228
229
240
241
242
243
244
A B C D E F G H I
Intrinsic stock price per share after exercise = $46.55
N = Number of years until exercise = 10
% straight bond in bond with warrants = 86.50%
% warrants in bond with warrants = 13.50%
(5) How would you expect the cost of the bond with warrants to compare with the cost of straight debt? With
(6) If the corporate tax rate is 25%, what is the after-tax cost of the bond with warrants?
Because the bond portion of the package was issued at a discount (its value was only $865, not $1,000), its
after-tax cost of debt is not equal to rd(1-T). You must find the rate of return given the after-tax coupon.
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.
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
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.
Strike price of each warrant = $25.00
Number of warrants per bond = 27.00
245
246
247
248
249
250
251
252
258
259
264
265
266
2$933.12
276
277
278
279
280
281
282
283
284
294
295
296
297
298
299
300
A B C D E F G H I
Required inputs:
Inputs:
N = 20
Conversion value = CVt = CR(P0)(1 + g)t.
t Conversion value
0$800.00
1$864.00
The floor value is the higher of the straight debt value and the conversion value.
Straight-debt value =
(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?
(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?
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
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.
314
315
316
317
318
319
320
321
322
323
324
325
332
333
334
335
336
337
338
339
340
341
342
343
344
PV = Intitial cost of bond = -$1,000.00
PMT = coupon payment = $85.00
FV = Conversion value = $1,269.50
345
346
347
348
Since rc is between rd and rs, the costs are consistent with the risks.
354
355
356
357
358
359
362
363
364
365
366
367
A B C D E F G H I
Bond will be called (and converted) in year: 6
N = Number of years until conversion = 6
For consistency, need rd < rc < rs.
10.00%
rc = 11.83%
rs = 13.40%
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, the bondholder will also receive the conversion value. We can find the return using the RATE
function.
rd =
(7) What is the after-tax cost of the convertible bond?
Use the after-tax coupon payment, then find the rate of return.
(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?
368
369
377
378
379
380
381
382
A B C D E F G H I
Pre-tax coupon payment = $85.00
After-tax coupon payment = $63.75
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: See
Chapter 20 Mini Case Show