Question

Consider a bond that pays annual coupons and matures in 5.5 years from today when the last coupon is paid. The principal is $100 and the annual coupon is $10 and the yield to maturity (compounded annually with a 30/360 daycount) is 10%. Find the flat price of the bond today.

Answer 1

Following is the given information about Bond in the question:

Principal Price   : $100

Annual Coupon: $10

YTM                  : 10%

Maturity Period : 5.5 Years

Now, Flat price of a bond is:

Coupon Amount + Coupon Amount + ………… + Maturity Amount

   (1+ YTM)¹                  (1+ YTM)²                                  (1+ YTM)ⁿ

=       10        +    10    +       10 +    10 +     10 + 5 +      100       

     (1+.10)¹        (1+.10)²          (1+.10)³        (1+.10)⁴     (1+.10)⁵   (1+.10)^5.5 (1+.10)^5.5

= 10 × 0.9091 + 10 × 0.82645 + 10 × 0.75131 + 10 × 0.68301 + 10 × 0.62092 + 5 × 0.59135 + 100 × 0.59135

= $100

Therefore, the flat price of the bond as on today is $100.