1
2
3
4
5
6
7
A B C D E F G H I
does not think it would be wise to issue new common stock at this time. On the other hand, interest rates are
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
61
62
63
64
Bonds
66
67
Find the payment such that the bond with warrant is issued at par.
73
74
75
76
77
78
79
80
81
82
86
87
88
89
90
91
92
to 30% above the current stock price when the warrants are issued.
How much cash will the firm receive when the warrants are exercised?
98
99
100
101
102
Number of shares before exercise (in millions) = 20.00
Number of shares from exercise of warrants (in millions) = 2.70
106
107
109
110
111
112
113
114
115
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?
118
119
120
121
122
123
124
125
128
129
Current valuation analysis
131
132
133
134
135
136
Value of operations $500
Total intrinsic value of firm $500
142
143
144
145
146
147
Required inputs:
Number of years until expiration = 10
153
154
155
156
157
163
Coupon rate 8.40%
PMT $84
164
165
166
167
168
169
170
171
172
174
175
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.
176
177
178
179
180
181
182
187
Intrinsic stock price per share after exercise = $46.55
Strike price of each warrant = $25.00
188
189
190
191
192
194
195
198
199
200
201
202
203
209
210
211
212
213
214
215
Pre-tax component cost of bond with warrants = 10.77%
221
222
223
224
225
232
233
234
235
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
236
237
238
239
240
241
242
243
244
245
246
250
251
252
253
254
Conversion ratio = 40
Maturity (in years) of convertible bond = 20
(1) What conversion price is built into the bond?
261
262
263
264
265
into 40 shares of EduSoft stock at the owner’s option.
271
272
273
274
275
276
278
279
280
281
282
283
284
285
286
287
5$1,175.46
6$1,269.50
7$1,371.06
8$1,480.74
9$1,599.20
294
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?
295
296
297
298
299
300
301
302
304
305
306
307
308
309
7$1,371.06 $603.79 $1,371.06
8$1,480.74 $579.16 $1,480.74
9$1,599.20 $552.08 $1,599.20
315
316
317
318
319
320
to be called? (Hint: Recall that the call must be made on an anniversary date of the issue.)
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.
326
327
328
329
330
331
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.
337
338
339
340
341
342
conversion, the bondholder will also receive the conversion value. We can find the return using the RATE
348
349
350
351
0$800.00 $723.65 $800.00
352
353
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?
Straight-
Debt Value
Floor
value
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
378
379
380
381
382
383
389
390
391
392
393
394
400
A B C D E F G H I
decision based on other factors. What are some of the factors which he should consider?
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 =