For example, if the Project Company A issues a bond with a face value of INR 1000, time to maturity of 10 years, and coupon of INR 56 per year. If the prevailing interest rate is 5.6%, then the present value of the face value is the sum of the present value of the face value and present values of the coupons.
Present value of face value = 1000/(1+0.056)10 = 579.91
Present value of coupons = 56 x (1-1/1.05610)/0.056 = 56 x (1-1/1.7244)/0.056
= 56 x 7.5016 = 420.09
The value of bond is 1000 (579.91 + 420.09). The bond sells at its face value.
For the same bond, in case after a year if the interest rate goes up and the prevailing interest rate is 7.6% instead of 5.6%, the impact of the interest rate on the value of the bond can be determined by calculating the present value of bond.
Present value of face value = 1000/(1+0.076)9 = 517.25
And, the present value of the coupon is:
Present value of coupons = 56 x (1-1/1.076 9)/0.076 = 56 x (1-1/1.9333)/0.076
= 56 x 6.3520 = 355.71
The value of the bond is the sum of the present values of face value and coupons, i.e. 517.25 + 355.71 = 872.96. The bond should sell at INR 872.96.
It can be seen that the value of the bond and interest rates always move in opposite directions. When interest rate rises the bond's value declines. When interest rates are above the bond's coupon rate, the bond sells at a discount. On the other hand, when the interest rate falls bond's value rises. Interest rates below the bond coupon rate cause the bond to sell at a premium.