Question

Suppose a seven-year, $1,000 bond with a 4.04% coupon rate and semiannual coupons is trading with a yield to maturity of 1.65%.

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

b. If the yield to maturity of the bond rises to 1.73% (APR with semiannual compounding), at what price will the bond trade?

Answer 1

a.Information provided:

Par value = Future value= $1,000

Coupon rate= 4.04% / 2= 2.02%

Coupon payment = 0.0202*$1,000 = $20.20 per semi-annual period

Time= 7 years*2= 14 semi-annual periods

Yield to maturity = 1.65%/2 = 0.8250% per semi-annual period

The price of the bond is calculated first.

The present value is calculated by entering the below in a financial calculator:

FV= 1,000

PMT= 20.20

I/Y= 0.8250

N= 14

Press the CPT key and PV to compute the present value.

The value obtained is 1,157.39.

Therefore, the price of the bond is $1,157.39.

The bond is trading at premium since it is trading above par value.

b.The price of the bond is calculated by computing the present value.

The present value is calculated by entering the below in a financial calculator:

FV= 1,000

PMT= 20.20

I/Y= 1.73/2= 0.8650

N= 14

Press the CPT key and PV to compute the present value.

The value obtained is 1,151.68.

Therefore, the price of the bond is $1,151.68.