Question

An 8% semiannual coupon bond matures in 5 years. The bond has a face value of $1,000 and a current yield of 8.21%. What are the bond’s price and YTM?

calculate using a financial calculator

Answer 1

The problem is to solve for the YTM and Price, given the following facts:

N = 5 ´ 2 = 10, PMT = 80/2 = 40, and FV = 1000. In order to solve for I/YR we need PV.

However, the current yield is equal to 8.21%. Given this information, find PV (Price).

Current yield   = Annual interest/Current price

         0.0821    = $80/PV

               PV    = $80/0.0821 = $974.42.

Now, solve for the YTM with a financial calculator:

N = 10, PV = -974.42, PMT = 40, and FV = 1000. Solve for I/YR = YTM = 4.32%. However, this is a periodic rate so the nominal YTM = 4.32%(2) = 8.64%.