A convertible bond has the following features (rounding allowed in answers): Fac
ID: 2750742 • Letter: A
Question
A convertible bond has the following features (rounding allowed in answers):
Face Value: $1,000
Maturity: 10 years
Annual coupon: $50
Conversion Price: $40
a. The bond may be converted into how many shares?
b. What is the current value of the convertible as a bond if prevailing interest rates are 6% (n=10)?
c. What is the current value of the convertible as a stock if the current stock price is $38 per share?
d. Based on (b) and (c) and assuming a market premium of $40, what should the current price of the convertible bond be?
Explanation / Answer
a. Shares = Face Value / Conversion price
= $1,000/$ 40
= 25 Shares
b. Bond matures in 10 years with a coupon rate of $ 50 and a maturity value of $1,000 the discount rate is 6%.
The PV of Cash Flow for each of the years is as follows:
Year
Annual Payment
Discount Factor @ 6%
PV of Annual Payment
1
$50.00
0.9434
$47.17
2
$50.00
0.8900
$44.50
3
$50.00
0.8396
$41.98
4
$50.00
0.7921
$39.60
5
$50.00
0.7473
$37.36
6
$50.00
0.7050
$35.25
7
$50.00
0.6651
$33.25
8
$50.00
0.6274
$31.37
9
$50.00
0.5919
$29.59
10
$1,050.00
0.5584
$586.31
Present value of Bond
$926.40
c. Current value of the Convertible Bond as a stock
= 25 Shares x $38 per share
= $950
d. Present value of Bond + Market premium
= $926.40+$40
= $966.40
Year
Annual Payment
Discount Factor @ 6%
PV of Annual Payment
1
$50.00
0.9434
$47.17
2
$50.00
0.8900
$44.50
3
$50.00
0.8396
$41.98
4
$50.00
0.7921
$39.60
5
$50.00
0.7473
$37.36
6
$50.00
0.7050
$35.25
7
$50.00
0.6651
$33.25
8
$50.00
0.6274
$31.37
9
$50.00
0.5919
$29.59
10
$1,050.00
0.5584
$586.31
Present value of Bond
$926.40
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