Question

Suppose a​ ten-year, $ 1 000 bond with an 8.3 % coupon rate and semiannual coupons is trading for $ 1035.26.

a. What is the​ bond's yield to maturity​ (expressed as an APR with semiannual​ compounding)?

b. If the​ bond's yield to maturity changes to 9.3 % ​APR, what will be the​ bond's price?

Answer 1

Part A: YTM is the Rate at which PV of Cash Inflows are equal to Bond Price

YTM = Rate at which least +ve NPV + [ NPV at thta rate / change in NPV due to 0.5% inc in rate ] * 0.5%

= 3.5% + [ 57.12 / 72.00 ] * 0.5%

= 3.5% + 0.40%

= 3.90%

YTM per Six Months = 3.90%

YTM per anum = 3.90% * 12/6

= 7.80%

Part B:

Value of Bond = PV of Cash Inflows discounted at YTM