Question #53059

(i) Find the price of bond with a coupon rate of 12% having 5 years to maturity. Its par value is 10,000 Br and the discount rate is 12%.

(ii) Supposing interest rates fall to 8% what will be the price of the bond?

(ii) Supposing interest rates fall to 8% what will be the price of the bond?

Expert's answer

(i) c = 12%, 5 years to maturity, F = 10,000 Br and the discount rate is r = 12%.

Cash flows on a bond with no embedded options are fairly certain and the price of bond equals the present value of future interest payments plus the present value of the face value (which is returned at maturity) based on the interest rate prevailing in the market.

Present Value of Interest Payments = c × F × (1 − (1 + r)^-t)/r + F/(1 + r)^t = 0.12*10000*(1-1.12^(-5))/0.12+10000/1.12^5 = 10,000 Br

(ii) Supposing interest rates fall to 8% the price of the bond will be:

Present Value of Interest Payments = c × F × (1 − (1 + r)^-t)/r + F/(1 + r)^t = 0.08*10000*(1-1.12^(-5))/0.12+10000/1.12^5 = 8,558.09 Br

Cash flows on a bond with no embedded options are fairly certain and the price of bond equals the present value of future interest payments plus the present value of the face value (which is returned at maturity) based on the interest rate prevailing in the market.

Present Value of Interest Payments = c × F × (1 − (1 + r)^-t)/r + F/(1 + r)^t = 0.12*10000*(1-1.12^(-5))/0.12+10000/1.12^5 = 10,000 Br

(ii) Supposing interest rates fall to 8% the price of the bond will be:

Present Value of Interest Payments = c × F × (1 − (1 + r)^-t)/r + F/(1 + r)^t = 0.08*10000*(1-1.12^(-5))/0.12+10000/1.12^5 = 8,558.09 Br

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