Question

Suppose a​ seven-year, $1,000 bond with an 8.3% coupon rate and semiannual coupons is trading with a yield to maturity of 6.37%.

a. Is this bond currently trading at a​ discount, at​ par, or at a​ premium? Explain.

b. If the yield to maturity of the bond rises to 7.42% ​(APR with semiannual​ compounding), what price will the bond trade​ for?

Answer 1

Face/Par Value of bond = $1000

Semi-Annual Coupon Bond = $1000*8.3%*1/2

= $41.5

No of coupon payment(n) = 7 years*2 = 14

Semi-annual YTM = 6.37%/2 = 3.185%

a). Calculating the Market price of Bond:-

Price = $462.929 + $644.715

Price of Bond = $1107.64

- As the price of Bond is higher than the face Value, the Bond is trading at Premium

The Bond's YTM is lower than the coupon rate and due to inverse relationhip that exist between YTM and trading price, when YTM is lower than coupon rate the Price is traded at premium (i.e, higher than face value)

b). Yield to maturity of the bond rises to 7.42% ​(APR with semiannual​ compounding)

Semi-annual YTM = 7.42%/2 = 3.71%

Calculating the Market price of Bond:-

Price = $446.883 + $600.497

Price of Bond = $1047.38

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