# Bond Valuation

## What Is Bond Valuation?

Bond valuation is a technique for determining the hypothetical fair value of a particular bond. Bond valuation incorporates working out the current value of a bond's future interest payments, otherwise called its cash flow, and the bond's value upon maturity, otherwise called its face value or par value. Since a bond's par value and interest payments are fixed, an investor utilizes bond valuation to determine what rate of return is required for a bond investment to be worthwhile.

## Figuring out Bond Valuation

A bond is a debt instrument that turns out a consistent revenue stream to the investor as coupon payments. At the maturity date, the full face value of the bond is repaid to the bondholder. The qualities of a normal bond include:

**Coupon rate**: Some bonds have an interest rate, otherwise called the coupon rate, which is paid to bondholders semi-annually. The coupon rate is the fixed return that an investor earns periodically until it matures.**Maturity date**: All bonds have maturity dates, some short-term, others long-term. At the point when a bond matures, the bond issuer reimburses the investor the full face value of the bond. For corporate bonds, the face value of a bond is generally $1,000 and for government bonds, the face value is $10,000. The face value isn't really the invested principal or purchase price of the bond.**Current price**: Depending on the level of interest rate in the environment, the investor might purchase a bond at par, below par, or better than expected. For instance, on the off chance that interest rates increase, the value of a bond will diminish since the coupon rate will be lower than the interest rate in the economy. At the point when this happens, the bond will trade at a discount, that is, below par. Notwithstanding, the bondholder will be paid the full face value of the bond at maturity even however he purchased it for not exactly the par value.

## Bond Valuation in Practice

Since bonds are an essential part of the capital markets, investors and analysts try to comprehend how the various elements of a bond cooperate to determine its intrinsic value. Like a stock, the value of a bond determines whether it is a suitable investment for a portfolio and consequently, is a vital step in bond investing.

Bond valuation, in effect, is computing the present value of a bond's expected future coupon payments. The hypothetical fair value of a bond is calculated by discounting the future value of its coupon payments by a fitting discount rate. The discount rate utilized is the yield to maturity, which is the rate of return that an investor will get if they reinvested each coupon payment from the bond at a fixed interest rate until the bond matures. It considers the price of a bond, par value, coupon rate, and time to maturity.

## $3.9 trillion

The size of the U.S. municipal bond market, or the total amount of debt outstanding, toward the finish of 2018, as indicated by the Securities Industry and Financial Markets Association (SIFMA), an industry group.

## Coupon Bond Valuation

Working out the value of a coupon bond factors in the annual or semi-annual coupon payment and the par value of the bond.

The current value of expected cash flows is added to the current value of the face value of the bond as found in the accompanying formula:

$\begin &V_{\text}=\sum\frac{(1+r)^t}\ &V_{\text}=\frac{(1+r)^T}\ &\textbf\ &C=\text{future cash flows, that is, coupon payments}\ &r=\text{discount rate, that is, yield to maturity}\ &F=\text\ &t=\text\ &T=\text \end$

For instance, we should find the value of a corporate bond with an annual interest rate of 5%, making semi-annual interest payments for a very long time, after which the bond matures and the principal must be repaid. Assume a YTM of 3%:

- F = $1,000 for corporate bond
- Coupon rate
_{annual}= 5%, hence, Coupon rate_{semi-annual}= 5%/2 = 2.5% - C = 2.5% x $1000 = $25 per period
- t = 2 years x 2 = 4 periods for semi-annual coupon payments
- T = 4 periods
- r = YTM of 3%/2 for semi-annual compounding = 1.5%

- Present value of semi-annual payments = 25/(1.015)
^{1}+ 25/(1.015)^{2}+ 25/(1.015)^{3}+ 25/(1.015)^{4}= 96.36 - Present value of face value = 1000/(1.015)
^{4}= 942.18

In this manner, the value of the bond is $1,038.54.

## Zero-Coupon Bond Valuation

A zero-coupon bond makes no annual or semi-annual coupon payments as long as necessary. All things being equal, it is sold at a deep discount to par when issued. The difference between the purchase price and par value is the investor's interest earned on the bond. To compute the value of a zero-coupon bond, we just have to find the current value of the face value. Carrying over from the model over, the value of a zero-coupon bond with a face value of $1,000, YTM of 3% and 2 years to maturity would be $1,000/(1.03)^{2}, or $942.59.

## Features

- It includes working out the current value of a bond's expected future coupon payments, or cash flow, and the bond's value upon maturity, or face value.
- Bond valuation is a method for determining the hypothetical fair value (or par value) of a particular bond.
- As a bond's par value and interest payments are set, bond valuation assists investors with sorting out what rate of return would make a bond investment worth the cost.

## FAQ

### What Is Duration and How Does That Affect Bond Valuation?

Bond valuation takes a gander at discounted cash flows at their net present value whenever held to maturity. Duration rather measures a bond's price sensitivity to a 1% change in interest rates. Longer-term bonds have a higher duration, all else equivalent. Longer-term bonds will likewise have a bigger number of future cash flows to discount, thus a change to the discount rate will greaterly affect the NPV of longer-maturity bonds too.

### Why Is the Price of My Bond Different From Its Face Value?

A bond's face or par value will frequently contrast from its market value. This has to do with several factors including changes to interest rates, an organization's credit rating, time to maturity, whether there are any call provisions or other embedded options, and in the event that the bond is secured or unsecured. A bond will continuously mature at its face value when the principal initially lent is returned.

### Why Are Bond Prices Inversely Related to Interest Rates?

A bond that pays a fixed coupon will see its price differ contrarily with interest rates. This is on the grounds that getting a fixed interest rate, of say 5% isn't exceptionally alluring assuming winning interest rates are 6%, and become even less attractive on the off chance that rates can earn 7%. For that bond paying 5% to become equivalent to another bond paying 7%, it must trade at a discounted price. Moreover, assuming that interest rates drop to 4% or 3%, that 5% coupon turns out to be very alluring thus that bond will trade at a premium to recently issued bonds that offer a lower coupon.

### How Are Convertible Bonds Valued?

A convertible bond is a debt instrument that has an embedded option that permits investors to change over the bonds into shares of the organization's common stock. Convertible bond valuations consider a huge number of factors, remembering the variance for underlying stock price, the conversion ratio, and interest rates that could influence the stocks that such bonds could eventually turn into. At its most fundamental, the convertible is priced as the sum of the straight bond and the value of the embedded option to change over.

### Are Bonds Valued the Same As Stocks?

Not precisely. The two stocks and bonds are generally valued utilizing discounted cash flow investigation — which takes the net present value of future cash flows that are owed by a security. Not at all like stocks, bonds are made out of an interest (coupon) part and a principal part that is returned when the bond matures. Bond valuation takes the current value of every part and adds them together.