Question

What is the price of a $1,000 par value, semi-annual coupon bond with 5 years to maturity, a coupon rate of 09.70% and a yield-to-maturity of 04.40%?

Please show formula and solve using excel.

Answer 1

$Bond\, price=Coupon\times \left ( \frac{1-\left ( 1+i \right )^{-n}}{i} \right )+\frac{Face\, value}{\left ( 1+i \right )^{n}}$

Coupon payment is (1,000*0.097/2) = 48.5.

Semi-annual interest rate is (0.044/2) = 0.022.

$Bond\, price=48.5\times \left ( \frac{1-\left ( 1+0.022 \right )^{-10}}{0.022} \right )+\frac{1,000}{\left ( 1+0.022 \right )^{10}}$

$Bond\, price=48.5\times \left ( \frac{1-0.8044351557}{0.022} \right )+\frac{1,000}{1.243108277}$

$Bond\, price=48.5\times 8.889311106+804.435$

Using excel,

1 Future value 2 Semi-annual coupon rate 3 Semi-annual yield to maturity 4. Number of interest payments 5 Bond price 1000 =9.7%/2 =4.4%/2 =2*5 --PV(B3,B4,B1*B2,B1,0)

Results is shown below:

A 1 Future value 2 Semi-annual coupon rate 3 Semi-annual yield to maturity 4 Number of interest payments 5 Bond price 1,000 0.0485 0.022 10 1235.57