Question

Suppose a​ ten-year, $1,000 bond with an 8.4% coupon rate and semiannual coupons is trading for $1,034.17.

a. What is the​ bond's yield to maturity​ (expressed as an APR with semiannual​ compounding)?

b. If the​ bond's yield to maturity changes to 9.7% APR, what will be the​ bond's price?

Suppose a​ five-year, $1,000 bond with annual coupons has a price of $896.48 and a yield to maturity of

6.3%.

c. What is the​ bond's coupon​ rate?

Answer 1

a.Information provided:

Face value= future value= $1,000

Market price= present value= $1,034.17

Time= 10 years*2= 20 semi-annual periods

Coupon rate= 8.4%/2= 4.2%

Coupon payment= 0.042*1,000= $42

The yield to maturity is calculated by entering the below in a financial calculator:

FV= 1,000

PV= -1,034.17

N= 20

PMT= 42

Press the CPT key and I/Y to compute the yield to maturity.

The value obtained is 3.9497

Therefore, the yield to maturity is 3.9497%*2= 7.8994% 7.90%.

b.Information provided:

Face value= future value= $1,000

Market price= present value= $1,034.17

Time= 10 years*2= 20 semi-annual periods

Coupon rate= 8.4%/2= 4.2%

Coupon payment= 0.042*1,000= $42 per semi-annual period

Yield to maturity = 9.7% /2 = 4.85% per semi-annual period

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

Enter the below in a financial calculator to compute the present value:

FV= 1,000

N= 20

PMT= 42

I/Y = 4.85

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

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

The value obtained is 917.96.

Therefore, the price of the bond is $917.96.

c.Information provided:

Par value= future value= $1,000

Market price= present value= $896.48

Time= 5 years

Yield to maturity = 6.3%

The coupon rate is computed by first calculating the coupon payment.

The coupon payment is calculated by entering the below in a financial calculator:

FV= 1,000

PV = -896.48

N= 5

I/Y = 6.3

Press the CPT key and PMT to compute the coupon payment.

The value obtained is 38.2238.

Therefore, the coupon payment is $38.2238.

Coupon rate = Annual coupon payment / Par value

= $38.2238 / $1,000

= 0.0382*100

= 3.82%.