Question

A 20 year par value bond with semi-annual coupons at a nominal annual rate of 8% convertible semi-annually is purchased at a price of 1783.27. The bond can be called at par value X on any coupon date starting at the end of year 12 after the coupon is paid. The price guarantees a nominal annual rate of interest convertible semi-annually of at least 6%. Calculate X.

Answer 1

Answer:

3.216%

Step-by-step explanation:

This bond sells at a higher price or value, which means that its coupon is bogus of market interest rate. Therefore, the minimum yield rate that accounts for the possibility of the bond being called is calculated at the earliest possible call date. Let say exactly 15 years from the date of purchase, because that would be the most disadvantageous date for the bondholder for the call to occur.

The minimum semiannual yield:

j= i²/2

i² = 2j

which therefore satisfies the expression below for the worst possible case scenario yield:

1722.25 = 0.04*1100*$a]_30$+$\frac{1100}{(1+j)^30}$

Also, with the use of a financial calculator (making sure that the calculator is not in BGN mode)

1722.25 PV, -44 PMT, -1100 FV, 30 N, CPT 1/Y.

j can be found to be 1.608245%. The corresponding nominal annual rate compounded semiannually is (X) = i² = 2j =3.216%