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G
H
Build-a-Model
2 Chapter:
20
3 Problem:
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Maggie's Magazines (MM) has straight nonconvertible bond that currently yield 9%. MM's stock sells for $22 per share,
has an expected constant growth rate of 6%, and has a dividend yield of 4$. MM plans on issuing convertible bonds
that will have a $1,000 par value, a coupon rate of 8%, a 20-year maturity, and a conversion ratio of 32 (i.e., each bond
could be convertible into 32 shares of stock). Coupon payments will be made annually. The bonds will be noncallable
for 5 years, after which they will be callable at a price of $1,90; this call price would decline by $6 per year in Year 6 and
each year thereafter. For simplicity, assume that the bonds may be called or converted only at the end of a year,
immediately after the coupon and dividend payments. Management will call the bonds when the bonds’ conversion
value exceeds 25% of the bonds’ par value (not their call price).
Inputs:
Straight bond yield
9%
Current stock price
$22.00
Expected growth rate in stock price
6%
Dividend yield
4%
Par value (and issue price) of convertible bond
$1,000.00
Coupon rate on convertible bond
8.00%
Maturity of convertible bond (years)
20
Conversion ratio
32
Call protection period (years)
5
Call price when call protection ends
$1,090.00
Call price decline per year after protection period
$6.00
Policy for call: Call when conversion value exceeds
25%
28 this percent over bond's par value.
29
30
31 a. For each year, calculate: (1) the anticipated stock price; (2) the anticipated conversion value; (3) the anticipated
32 straight-bond price; and (4) the cash flow to the investor assuming conversion occurs. At what year do you expect the
33 bonds will be forced into conversion with a call? What is the bond’s value in conversion when it is converted at this
34 time? What is the cash flow to the bondholder when it is converted at this time (Hint: the cash flow includes the
35 conversion value and the coupon payment, because the conversion is immediately after the coupon is paid.)
36
37 Will call the issue in the first year that the conversion >250
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39 Year
40
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0
1
2
3
4
5
6
7
Anticipated
stock price Conversion
at year end
Value
(1)
(2)
22.00
704.00
$23.32
746.24
24.72
791.01
26.20
838.48
27.77
888.78
29.44
942.11
31.21
998.64
33.08
1,058.56
Convert?
(Yes, no, or
already)
No
No
No
No
No
yes
Straight debt Cash flow to
value of
bondholder
convertible if converted
(3)
(4)
-$1,000.00
$80.00
$80.00
$80.00
$80.00
$80.00
$1,078.64
A
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B
35.06
37.17
39.40
41.76
44.27
46.92
49.74
52.72
55.89
59.24
62.80
66.56
70.56
C
1,122.07
1,189.39
1,260.76
1,336.40
1,416.59
1,501.58
1,591.68
1,687.18
1,788.41
1,895.71
2,009.45
2,130.02
2,257.82
Conversion year =
Value in conversion =
D
E
F
G
H
6
$
998.64
b. What is the expected rate of return (i.e., before-tax component cost) on the proposed convertible issue?
Using the RATE function:
N=
6
PMT =
$80.00
PV =
-$1,000.00
FV =
$ 998.64
Rate =
7.981%
As a check, using the IRR function and the cash flows in column F:
Expected return to bondholders
c. Assume that the convertible bondholders require a 9% rate of return. If the coupon rate remains
unchanged, then what conversion ratio will give a bond price of $1000?
Expected return required by convertible bondholders =
9%
Hint: Use Goal seek to set the difference between the convertible bondholders' current return and the
target return to zero by changing the input cell for the conversion ratio.
Current difference between bondholders' current expected return and target
return (multiplied by 1000) =
Conversion ratio (given original convertible coupon rate) that produces the
required yield (Note: after using Goal Seek, cut and paste the conversion ratio
into the yellow cell):
1
I
11/26/2018
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6 per share,
sells for $22
7 bonds
ng convertible
8
o of 32 (i.e., each bond
9
nds will be noncallable
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6 per year in Year 6 and
11
he end of a year,
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e bonds’ conversion
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(3) the anticipated
31
year do you
32 expect the
t is converted
33 at this
low includes
34 the
upon is paid.)
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Build-a-Model
Chapter:
21
Problem:
10
Start with the partial model in the file Ch17 P12 Build a Model.xlsx on the textbook’s Web site. Kasperov
Corporation has an unlevered cost of equity of 12% and is taxed at a 25% rate. The 4-year forecasts of free
cash flow and interest expenses are shown in the following table; free cash flow and interest expenses are
expected to grow at a 5% rate after Year 4. Using the compressed APV model, answer the following
questions.
INPUTS (In millions)
Year
Free cash flow
Interest expense
Projected
1
$200,0
$100,0
Long-term growth rate
Tax rate
Unlevered cost of equity
2
$280,0
$120,0
3
$320,0
$120,0
4
$340,0
$140,0
5%
25%
12,00%
a. Calculate the estimated horizon value of unlevered operations at Year 4 (i.e., immediately after the Year-4
free cash flow).
Current
1
Free cash flow
Horizon unlevered value of operations
$200,0
Projected
2
$280,0
3
$320,0
b. Calculate the current value of unlevered operations.
Current value of unlevered operations
a. Calculate the estimated horizon value of the tax shield at Year 4 (i.e., immediately after the Year-4 free
Current
Interest expense
Tax savings
Horizon unlevered value of operations
d. Calculate the current value of the tax shield.
Current value of unlevered operations
d. Calculate the current total value.
Unlevered value of operations
1
$100,0
$25,0
Projected
2
3
$120,0
$120,0
$30,0
$30,0
Value of tax shield
Total value
11/26/2018
s Web site. Kasperov
4-year forecasts of free
d interest expenses are
er the following
mediately after the Year-4
ected
4
$340,0
y after the Year-4 free
ected
4
$140,0
$35,0
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