Question

Suppose a​ seven-year, $ 1 comma 000$1,000 bond with aa 7.7 %7.7% coupon rate and semiannual coupons is trading with a yield to maturity of 6.45 %6.45%. 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 7.36 %7.36% ​(APR with semiannual​ compounding), what price will the bond trade​ for?

Answer 1

a. Premium

b. $1,018.34

Step-by-step explanation:

a. For computing the present value we need to apply the formula which is shown in the attachment below:

Given that,

Future value = $1,000

Rate of interest = 6.45% ÷ 2 = 3.225%

NPER = 7 years × 2 = 14 years

PMT = $1,000 × 7.7% ÷2 = $38.50

The formula is shown below:

= -PV(Rate;NPER;PMT;FV;type)

So, after applying the above formula, the present value is $1,069.53

Since the present value is more than the face value so the bond is currently sold at a premium

b. For computing the present value we need to apply the formula which is shown in the attachment below:

Given that,

Future value = $1,000

Rate of interest = 7.36% ÷ 2 = 3.68%

NPER = 7 years × 2 = 14 years

PMT = $1,000 × 7.7% ÷2 = $38.50

The formula is shown below:

= -PV(Rate;NPER;PMT;FV;type)

So, after applying the above formula, the present value is $1,018.34