Your next significant task as financial manager of the Alpha-Beta Group (ABG) is
ID: 2728759 • Letter: Y
Question
Your next significant task as financial manager of the Alpha-Beta Group (ABG) is to price several types of bonds considering various market conditions for your Chief Executive Officer. You must utilize your extensive knowledge of finance and make bond decisions for the boss and answer the following scenarios provided for your firm.
Coupon Issue
Zero Coupon
Perpetual
Convertible
Maturity
5 years
5 years
Infinity
5 years
Coupon rate
6 percent
Zero
6 percent
5 percent
Show your calculations!
a. If the market yield is 7 percent, what are the values of the three first bonds (assume a face value of $1,000)?
b. Why are the values of the bonds lower than their face value?
c. Why is the coupon rate for the convertible bond lower than that for the non-convertible coupon issue?
d. Given that the convertible bond is trading at $1,040, what is the value of the option to convert?
e. Suppose that the market yield rises to 7.5 percent. What are the bond values at that yield?
Coupon Issue
Zero Coupon
Perpetual
Convertible
Maturity
5 years
5 years
Infinity
5 years
Coupon rate
6 percent
Zero
6 percent
5 percent
Explanation / Answer
(a)
(i) Annual coupon of coupon bond = $1,000 x 6% = $60
Value of coupon bond ($) = 60 x PVIFA(7%, 5) + 1,000 x PVIF(7%, 5) = 60 x 4.1002 + 1,000 x 0.713
= 246.01 + 713 = 959.01
(ii) If value of zero-coupon bond be V, then
V x (1.07)5 = $1,000
V x 1.4026 = $1,000
V = $1,000 / 1.4026 = $712.99
(iii) Annual coupon = $1,000 x 6% = $60
Value of perpetual bond = $60 / 0.07 = $857.14
(b)
Values are lower than face value because market yield is higher than their coupon rate. Therefore, bondholders are earning lower than market-going rate and so, bonds are priced at a discount.
(c)
Convertibility of a bond is an option which is favorable to the bond-holder and unfavorable to the bond-issuer, therefore it has a lower coupon rate than a non-convertible similar bond.
(d)
Value of conversion option = Value of convertible bond - Value of non-convertible bond
= $(1,040 - 959.01) = $80.99
Note: First 4 sub-parts are answered.
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