Bond valuation

Bonds are listed on a exchange at a price or a bond value. A bond 's value is affected by time and the effective interest rate for the bond.

Bond valuation involves calculating the present value of the payments that the bond gives. Coupon bonds provides continuous interest coupons and a payment of the face value at the maturity day. A zero coupon bond has no periodic coupons, but only a nominal value paid at maturity. As interest rates changes every day there is also changes of bond values every day.

Bond valuation, coupon bond, 5 years to maturity:
5 year goverment bond, nominal amount 1 000 000, coupon rate of 10 % (100 000), the effective five-year market rate is 15%. The periodic payments are discounted using the market rate.

100000/1.15 + 100000/1.15^2 + 100000/1.15^3 + 100000/1.15^4 + 1100000/1.15^5 = 832 392

Value = 832 392
Rate = 83.23 %

Bond valuation, coupon bond, 4.5 years to maturity:
5 year government bond, face value 1 000 000, coupon rate of 10 % (100 000), the effective five-year market rate is 10%. The periodic payments are discounted using the market rate. Accrued coupon of 50 000, the seller's share of the next coupon.

Value after 180 days: (100000 + 100000/1.10^1 + 100000/1.10^2 + 100000/1.10^3 + 1100000/1.10^4) = 1 100 000
Value today: 1100000/1.1^(180/360) = 1 048 809
Subtract the accrued coupon: 1048809 - ((180/360) * 100 000) = 998 809

Value = 1 048 809 (What we pay for the bond)
Price = 998 809 (excluding accrued coupon)
Rate = 99.88 % (excluding accrued coupon)

Bond valuation, zero coupon bond five year to maturity:
5 year government bond, nominal amount 1 000 000, the effective five-year market rate is 15%. The face value is discounted by the market rate.

1000000/1.15^5 = 497 176

Value = 497 176
Rate = 49.70%

Bond valuation, zero coupon bond 4.5 years to maturity:
5 year government bond, face value 1 000 000, the effective five-year market rate is 15%. The nominal amount is discounted by the market rate.

Value after 180 days: 1000000/1.15^4 = 571 753
Value today: 571 753/(1.15^(180/360)) = 533 162
Rate = 53.31 %