Question

Microhard has issued a bond with the following characteristics:Par: $1,000Time to maturity: 15 years Coupon rate: 7 percent Semiannual paymentsCalculate the price of this bond if the YTM is:

a. 7 percent
b. 9 percent
c. 5 percent

Answer 1

a.) $1000

b.) $837.11

c.) $1,209.30

Step-by-step explanation:

This type of bond is a coupon paying bond. Using a financial calculator, input the following for each value of YTM;

a.)

Face Value; FV = 1,000

Time to maturity of the bond; N = 15*2 = 30

Recurring coupon payment = coupon rate * Face value = (7%/2) *1000 = $35

So, coupon payment PMT = $35

Semiannual interest rate; I/Y = 7%/2 =3.5%

then compute the price of the bond; CPT PV = $1000

This bond is selling at par since the YTM = Coupon rate

b.)

The YTM in this case is higher than the coupon rate hence expect the price of the bond to be lower than the face value;

Face Value; FV = 1,000

Semiannual interest rate; I/Y = 9%/2 = 4.5%

Time to maturity of the bond; N = 30

Recurring coupon payment = coupon rate * Face value = (7%/2) *1000 = $35

So, coupon payment PMT = $35

next, compute the price of the bond; CPT PV = $837.11

This bond is selling at a Discount.

c.)

The YTM of 5% lower than the coupon rate hence expect the price of the bond to be higher than the face value;

Face Value; FV = 1,000

Semiannual interest rate; I/Y = 5%/2 = 2.5%

Time to maturity of the bond; N = 30

Recurring coupon payment = coupon rate * Face value = (7%/2) *1000 = $35

So, coupon payment PMT = $35

next, compute the price of the bond; CPT PV = $1,209.30

This bond is selling at a Premium.