Question

1. There’s a bond with par value of $1,000, sells for $950, matures in 15 years, has a 8% annual coupon rate, and pays coupons semiannually. Calculate the realized compounded holding period annual yield assuming you held the bond for 5-years. Assume the reinvestment rate during the five years after you bought the bond is 10%, and the market interest rate at the time you sold the bond was exactly 8%.

2. Assume that a callable bond was issued at par. Who holds the call option on the bond and whether the coupon would be higher or lower than an otherwise identical bond, also issued at par, but without the call option?

Answer 1

Part (1):

Given,

Face value= $1,000 and coupon rate=8%

Therefore, annual coupon payment= 1000*8% = $80

Period of holding (n)= 5 years. Reinvestment rate= 10%

Therefore, future value of coupon payments in 5 years= 80*FVIFA(10%,5)

=80*6.1051= $488.41

Also given, YTM after 5 years= 8% (equal to coupon rate)

Therefore, sale price is equal to face value, ie., $1,000

Total value at the end of investment horizon (F) = $1000+$488.408= $1,488.408

Given, purchase price (P)= $950

Realized compounded annual yield= (F/P)^(1/n)-1

=(1488.408/950)^(1/5)-1 = 9.39556%

Part 2:

If there is call option, issuer of the bond will hold the call option.

Since the call option is not beneficial for the investor, coupon rate on such bonds will be higher, given all other features similar to other bonds.