Question

A company is issuing a 3-year maturity bond that is expected to pay $40 every six month and a lump sum of $1000 at the end of three years from now. If bond investors require 5% annual nominal interest rate (APR), how much is the price of this bond today? Please show your formula in your answer and explain step-by-step calculation to arrive to your final answer.

Answer 1

The price is computed as follows:

= cash flow in 6 months / (1 + interest rate)¹ + cash flow in 1 year / (1 + interest rate)² + cash flow in 1.5 years / (1 + interest rate)³ + cash flow in 2 years / (1 + interest rate)⁴ + cash flow in 2.5 years / (1 + interest rate)⁵ + cash flow in 3 years / (1 + interest rate)⁶ + lump sum cash flow in 3 year / (1 + interest rate)⁶

Interest rate will be as follows:

= 5% / 2

= 2.5% or 0.025

So, the price will be as follows:

= $ 40 / 1.025¹ + $ 40 / 1.025² + $ 40 / 1.025³ + $ 40 / 1.025⁴ + $ 40 / 1.025⁵ + $ 40 / 1.025⁶ + $ 1,000 / 1.025⁶

= $ 1,082.62 Approximately