Amortization is the method of reducing the value of an intangible asset like a bond. Therefore, the value of an amortized bond will be adjusted against its amortized interest at a given point.

The fair market value of a bond is the price investors are willing to pay for a bond at any time. It is theoretically the present value of the future cash flows arising from the bond.

With their key differences, let us discuss the amortization cost and fair value of a bond.

**What is the Fair Value of a Bond?**

The fair value of a bond is equal to the sum of the present value of its future interest payments and its book value at maturity.

The book value or face value of a bond remains fixed. The interest payments on a bond can change as the market interest rates change. Most bonds are issued with a fixed interest rate.

However, investors expect an adjusted bond yield when the market interest rate changes. It can be achieved by either adjusting the bond’s market price (premium or discount) or adjusting the bond’s interest rate.

A change in the fair value of a bond is described in terms of its par or face value. When it is trading at a higher price than its par value, it’s called trading above par and below par when its current price is lower.

**How to Calculate the Fair Value of a Bond?**

Theoretically, the fair value of a bond requires calculating the present value of the future cash flows or the interest payments of a bond.

If a bond does not pay interest (zero-coupon bonds), then the bond’s fair value will only be adjusted for its par value.

The fair value of a bond = PV of Coupons + PV of Face Value

PV of Coupons = Σ C/(1+r) ^{t} PV of Face Value = P/(1+r) ^{T}

In practice, several other factors affect a bond’s fair value or market price.

**Interest Rate**

Bond prices and interest rates are inversely related. It means the bond price falls when the interest rate increases and vice versa.

It happens because investors can invest in a newly issued bond with favorable interest rates. So, if the market offers more with an increased interest rate, the bond price must fall to compensate the investors as its interest rate is fixed.

**Time to Maturity**

Bonds with longer maturity periods tend to be riskier. Therefore, investors would demand more compensation for investing in these bonds.

However, it also means that the interest rates can change in the coming years.

**Coupon Rate**

If a bond offers coupon payments, it will be more attractive to investors as compared to a similar bond without coupons.

Therefore, the coupon rate of a bond also influences its pricing.

**Credit Rating of the Issuer**

A major factor affecting a bond’s fair value is its issuer’s credit rating. Credit rating agencies can change the issuer’s rating depending on several factors.

**Example**

Suppose a corporate bond with a face value of $1,000 comes with an annual interest rate of 5% annual coupons for 4 years and the YTM is 1.5%.

We can calculate the fair value of the bond by using the formula:

Fair value of a bond = PV of Coupons + PV of Face Value

PV of Coupons = Σ C/(1+r) ^{t} PV of Face Value = P/(1+r) ^{T}

PV of Coupons = 50 / (1.015)^{1} + 50 / (1.015)^{2} + 50 / (1.015)^{3} + 50 / (1.015)^{4 }= 192.74

PV of Face Value = 1000/ (1.015) ^4 = 942.15

**Fair value of the bond = $ 1134.89**

**What is the Amortization Cost of a Bond?**

The amortization of a bond is the process of repaying the price in regular intervals until its maturity.

An amortized bond means paying the principal and interest costs for a fixed period. The carrying value of the bond is equal to the face value of the bond plus the unamortized value of the bond.

The price of an amortized bond changes as it pays more through its amortization schedule. As time passes, the credit default risk of the bond reduces.

It also reduces the interest rate risk of the bond. These two factors play a major role in determining the value of an amortized bond.

The amortization of the bond can be calculated by the straight-line method or the effective interest rate method.

**How to Calculate the Amortization Cost of a Bond?**

There are two options to calculate the value of an amortized bond.

You can add the value of unamortized interest to the face value of the bond or deduct the amortized interest from the face value of the bond. Both options will provide the same result.

If you need to use the effective interest rate method, you’ll need the bond’s interest rate, its time to maturity, and its par value.

Using these values, we can determine whether the bond is trading at a discount or premium.

When the market interest rate is equal to the bond’s interest rate, it sells at par. If the interest rate is higher than the bond rate, it sells at a discount.

A bond sells at a premium when its interest rate is higher than the market rate.

**Example**

Suppose ABC Corporation issues a bond with a face value of $1000 and a maturity period of 10 years. Let’s assume that the bond was sold at a premium for $ 1,150.

Let’s calculate the value of the amortized bond after 4 years.

Amortized amount per year = Premium amount/Bond Term

Amortized amount per year = (1,150 – 1,000)/10 = $15

Total amortized premium for 4 years = $15 * 4 = $60

Unamortized Premium = $150 – $60 = $90

Carrying Value of the bond = Face Value + Unamortized Premium

Carrying value of the bond = $1,000 + 90 = $ 1,090.

**Amortization Bond Cost v Fair Value of a Bond – Key Differences**

The amortized cost only gives the carrying value of the bond. It is a way to analyze how much of a bond’s interest payment has been amortized at a certain point.

It does not include the market effects on the price of a bond. In other words, it calculated the theoretical carrying price of a bond at a given point.

As explained in our example, as the bond nears maturity, the carrying value moves closer to the bond’s par value.

The bond’s fair value includes several other factors like the demand-supply relationship of the bond. It includes comparing the market interest rate against the bond’s interest rate.

The bond’s fair value can be different from the carrying value of an amortized bond as investors may be willing to take risks in anticipation of higher returns in the future.

Also, the credit rating of a bond issuer has no impact on the carrying value of an amortized bond. However, it directly affects the fair market value of a bond.