Question

You purchased a 20-year par value bond with semiannual coupons at a nominal annual rate of 8% convertible semiannually at a price of 1722.25. The bond can be called at par value X on any coupon date starting at the end of year 15 after the coupon is paid. The price guarantees that you will receive a nominal annual rate of interest convertible semiannually of at least 6%. Calculate X.
a. 1400
b. 1420
c. 1440
d. 1400
e. 1480

Answer 1

Answer:

1400

Explanation:

The concept par value bond refers to a bond that may be redeemed for its face value.  From the coupon nominal annual rate of 8%, it means the coupon is 4% for half of the year is higher than the effective yield of 3% for 6 month period. As such, the bond sells at a higher premium price.

As a result, the minimum yield rate that contributes to the potential of the bond being called is computed at the initial conceivable call date, which is precisely 15 years after the date of purchase, because it is the most unfavorable period for the bondholder if the call occurs. As a result, the par value X fulfills the following condition:

$1722.25 = 0.04*X*a_{|30|3\%|}+\dfrac{X}{1.03^{30}}$

Making X the subject:

$X = \dfrac{1722.25}{0.04*a_{|30|3\%|}+1.03^{-30}}$

Using financial Calculator:

X = 1400.01

X ≅ 1400