# How does one calculate the present value of a bond?

##### 1 Answer

The present value of a bond is its price.

#### Explanation:

A traditional bond is made up of two kinds of cash flows: a lump sum received at maturity (the face value) and annual (or semi-annual) interest payments. The value of the bond is the present value of these cash flows. In words: the present value of a bond is the present value of the lump sum payment plus the present value of the annual cash flows.

**Consider this example.**

A 10-year bond with a face (maturity) value of $1,000 and a coupon rate of 5%. Calculation of the present value involves two steps.

**1. Present value of the face value.**

We will use the formula that calculates the present value of a lump sum.

Where,

FV = the maturity value

r = the discount rate

n = the number of years to maturity.

We know that FV = $1,000 and n = 10, but what does r = ? First, it is not the coupon rate. It is the rate of return an investor demands when buying the bond - the going market rate. Let us assume that it is 4%.

PV = $677 (rounded)

**2. Present value of the annual interest payments.**

For this calculation, we have to use the formula for a present value of an annuity.

Where,

A = the yearly coupon payment of $50 (.05 * 1,000)

PV = $405

When we add the two present values together we get $1,082.

This is the present value of the bond and the price at which it should sell.