# How to Calculate the Present Value of a Bond

by Eric Bank ; Updated July 27, 2017Bonds are financial instruments that corporations and government entities issue as a way of borrowing money from investors. Bonds carry a **face value**, which is the amount the issuer will have to pay back when the bond becomes due, or **matures**. Regular bonds also pay a fixed amount of interest, called the **coupon**, on a regular basis. Present value is a technique to figure how much all the bond's cash flows -- return of face value plus coupon payments -- would be worth if they were all paid today, a process called **discounting**. Investors calculate the present value of a bond and use it as the price they'd be willing to fork over to buy or sell the bond.

## Concept of Discounting

Discounting **lowers the value** of future cash flows. It's based on the idea that the money in your pocket today is worth more than the promise of receiving the money at a later date, because of:

- The risk that the money won't be received when expected.
- The interest you can earn by having the money now instead of waiting for it.
- The effect of inflation, which lowers the purchasing power of money over time, and makes future cash flows less valuable.

A **discount factor** is applied to each cash flow to figure its value in today's dollars. The sum of these discounted cash flows is the present value of the bond. Normally, this is also considered the fair price for the bond. Bond investors select a discount factor that represents the **required rate** they would demand to buy the bond, which might or might not coincide with the bond's stated interest rate.

## Discount, Par and Premium

Bonds are issued with a stated interest rate that is paid out via the periodic coupons. If the stated interest rate is equal to the required rate, the bond will sell for its face value, or **par**. If the required rate is higher than the stated rate, the bond will sell at a **discount** -- less than par. A **premium** bond sells for more than par and results from a stated rate higher than the required rate. The required rate typically rises during times of rising inflation and tightening credit. The market of bond buyers and sellers can have differing views on the required rate, which creates different discount factors, present values and bond prices. The prevailing interest rate represents the most popular required rate at a moment in time.

## Bond Value

Four factors are used to evaluate a bond:

- Face Value (Fv): an amount to be paid on the day the bond matures.
- Coupon Payment (Pmt): the amount of interest received in each coupon period. Bonds typically have coupon periods of 3, 6 or 12 months.
- Number of Periods (Nper): the number of periods remaining until the bond matures. The final period usually coincides with the maturity date.
- Required Rate (Rate): the interest rate per coupon period demanded by investors.

The formula for determining the value of a bond uses each of the four factors, and is expressed as:

Bond Present Value = Pmt/(1+Rate) + Pmt/(1+Rate)^{2}+ ... +Pmt/(1+Rate)^{Nper}+ Fv/(1+Rate)^{Nper}

### Solving in Excel

An Excel spreadsheet makes short work of the messy-looking equation. Select the present value function, PV, from the Formulas menu and enter each of the four factors. The result is the bond's present value. You may have to use more elaborate methods if you want to figure the PV for a date other than a coupon payment date. The PV method is good for "what-if" forecasting to estimate a bond's value should the required rate change. This method won't work if the coupon amount or frequency can change over time.