Question

Clapper Corp. issued 12-year bonds 2 years ago at a coupon rate of 7.8 percent. The bonds make semiannual payments. If these bonds currently sell for 108 percent of par value, what is the YTM?

Par Value = $1,000

Using Method One: the equation

Bond price = par value * (1+r)^-n + coupon * (1 - (1+r)^-n)/r

Please show all work

Answer 1

Current price=108%*1000=1080.00

Bond price = par value * (1+r)^-n + coupon * (1 - (1+r)^-n)/r=1000*(1+r/2)^(-10*2)+(1000*7.8%/2)*(1-(1+r/2)^(-10*2))/(r/2)

THis has to be trial and error as we have to use equations

As price is more than par, yield will be less than coupon rate

Start with yield of 6% and see what is the price predicted using above equation. If it is less than current price of 1080.00 then we decrease yield otherwise increase yield

Step 1: Yield of 6%
=1000*(1+6%/2)^(-10*2)+(1000*7.8%/2)*(1-(1+6%/2)^(-10*2))/(6%/2)=1133.897

As this is more than 1080.00, we increase yield

Step 2: Yield of 6.5%
=1000*(1+6.5%/2)^(-10*2)+(1000*7.8%/2)*(1-(1+6.5%/2)^(-10*2))/(6.5%/2)=1094.506

As this is more than 1080.00, we increase yield

Step 3: Yield of 6.8%
=1000*(1+6.8%/2)^(-10*2)+(1000*7.8%/2)*(1-(1+6.8%/2)^(-10*2))/(6.8%/2)
=1071.709

As this is less than 1080.00, we decrease yield

Step 4: Yield of 6.7%
=1000*(1+6.7%/2)^(-10*2)+(1000*7.8%/2)*(1-(1+6.7%/2)^(-10*2))/(6.7%/2)
=1079.240

As this is less than 1080.00, we decrease yield

We go on till we So, yield is 6.69%