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Homework answers / question archive / Suppose a seven-year, $1,000 bond with an 8

Suppose a seven-year, $1,000 bond with an 8

Finance

Suppose a seven-year, $1,000 bond with an 8.2% coupon rate and semiannual coupons is trading with a yield to maturity of 6.32% 

a) Is this bond currently trading at a discount, at par, or at a premium? Explain (Select the best choice below ) 
A) Because the yield to maturity is greater than the coupon rate, the bond is trading at a premium.

B) Because the yield to maturity is less than the coupon rate, the bond is trading at a premium.

C) Because the yield to maturity is greater than the coupon rate, the bond is trading at par.

D) Because the yield to maturity is less than the coupon rate, the bond is trading at a discount.
b) If the yield to maturity of the band rises to 7.38% (APR with semiannual compounding), what price will the bond trade for? 
 

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a) We can calculate the price of bond by using the following formula in excel:-

=-pv(rate,nper,pmt,fv)

Here,

PV = Price of bond

Rate = 6.32%/2 = 3.16% (semiannual)

Nper = 7*2 = 14 periods (semiannual)

Pmt = Coupon payment = $1,000*8.2%/2 = $41

FV = $1,000

Substituting the values in formula:

= -pv(3.16%,14,41,1000)

= $1,105.03

Correct option is B)

The bond is trading at premium because the yield to maturity is less than the coupon rate. (6.32%<8.2%)

 

b) We can calculate the price of bond by using the following formula in excel:-

=-pv(rate,nper,pmt,fv)

Here,

PV = Price of bond

Rate = 7.38%/2 = 3.69% (semiannual)

Nper = 7*2 = 14 periods (semiannual)

Pmt = Coupon payment = $1,000*8.2%/2 = $41

FV = $1,000

Substituting the values in formula:

= -pv(3.69%,14,41,1000)

= $1,044.21

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