Question

New Homes has a bond issue with a coupon rate of 5.5 percent that matures in 8.5 years. The bonds have a par value of $1,000 and a market price of $1,122. Interest is paid semiannually. What is the yield to maturity?

Answer 1

Face Value = $1000

Semi-annual Coupon rate = 5.5%

Semi-annual Coupon payment = $1000*5.5%*1/2 = $27.5

Price of bond = $ 1,122

Maturity = 8.5 years

n = 8.5years*2 = 17

Calculating YTM of the bond:

Taking YTM as 4%:

Semi-annual YTM = 4%/2 = 2%

Price = $ 393.03 + $ 714.16

Price = $ 1107.19

Now, Since, At YTM 4% price is closer to Originla price, taking another YTM at 3%

Semi-annual YTM = 3%/2 = 1.5%

Price = $ 409.96 + $ 776.39

Price = $ 1186.35

Now, calculating YTM:

YTM = 3.81%

So, Yield to maturity is 3.81%

If you need any clarification, you can ask in comments.

If you like my answer, then please up-vote as it will be motivating