# How to calculate the present value of a bond

## What is a bond?

A bond is a financial instrument that is issued for a period of time to borrow money. When the bond is issued, the holder is promised on fixed dates, usually every six months, annually, etc. until the due date and repays the main amount when due.

## Present value of a bond

Present value is an alternative bond valuation method that calculates the current value of the stream of future cash flows at a given rate of return. A bond's cash flows are fairly certain. The present value of a bond is the value that results from the discounted interest payments (interest inflows) and the discounted repayment value of the nominal value of the bond certificate. These cash flows are discounted based on the market interest rate at a given point in time.

## Calculate the present value of a bond:

### Step 1: Calculate the present value of the interest payments

The present value of the interest payments can be calculated using the following formula, where:

C = Coupon of the bond F = Nominal value of the bond R = Markett = Number of time periods until the bond matures ### Step 2: Calculate the present value of the face value of the bond

This refers to the maturity value of the bond, which can be calculated using the following formula. ### Step 3: Calculate the present value of the bond

The total present value of the bond can be presented as follows:

## Calculating the present value of a bond - example:

The following information is provided in relation to the ABC Company's bond issue.

Denomination of the bond - 2000 USD Maturity of the bond - 5 years Annual coupon - 9% Market rate - 10%

Assuming ABC Company makes annual coupon payments, calculate the present value of the bond.

Assuming the ABC Company pays its interest semi-annually, calculate the present value of the bond.

Since the company pays the interest every six months, both the coupon rate and the market interest rate must be adjusted for each period. Therefore, there are 10 maturity periods for the bond and the coupon rate and interest rate are 4.5% and 5% per period, respectively. ### Recap

A bond is a financial debt instrument. When calculating the present value of a bond, the coupon income is discounted on the basis of the market interest rate plus the nominal value of the bond at the end of the term. This value represents the current value of the future cash flows generated by this instrument. 