Question

Bond X is noncallable and has 20 years to maturity, a 8% annual coupon, and a $1,000 par value. Your required return on Bond X is 12%; if you buy it, you plan to hold it for 5 years. You (and the market) have expectations that in 5 years, the yield to maturity on a 15-year bond with similar risk will be 10%. How much should you be willing to pay for Bond X today? (Hint: You will need to know how much the bond will be worth at the end of 5 years.) Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

First, the price of the bond at the end of the 15th year is calculated.

Information provided:

Par value = Future value= $1,000

Time= 15 years

Coupon rate= 8%

Coupon payment= 0.08*1,000= $80

Yield to maturity = 12%

The price of the bond is computed by calculating the present value.

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

FV= 1,000

N= 15

I/Y= 12

PMT= 80

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

The value obtained is 757.57.

Therefore, the the price of the bond at the end of the 15th year  is $757.57

Next, the price of the bond at the end of the 5th year is calculated.

Information provided:

Par value = Future value= $757.57

Time= 5 years

Coupon rate= 8%

Coupon payment= 0.08*1,000= $80

Yield to maturity = 12%

The price of the bond is computed by calculating the present value.

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

FV= 757.57

N= 15

I/Y= 12

PMT= 80

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

The value obtained is 683.27.

Therefore, the the price of the bond at the end of the 5th year is $683.27.

In case of any query, kindly comment on the solution.