# How to calculate value of a bond

The value of the bond or debenture is the “FAIR (INTRINSIC / ECOCOMIC) VALUE” which requires that all the future expected cash flows of the bond be discounted to its present value.

## Formula

Valuation of bond is actually the practical application of time value of money i.e. discounting the future values to present values.

The bond valuation formula is:

 Value of bond  = Present value of annuity of interest payments + Present value of principal amount

OR

 V  = C * 1 – (1 + r) -t + F r (1 +r) t

Where
V = Value of the bond
C = Coupon or interest rate payable on bond in regular intervals
r = required rate of return of investor. This is minimum interest rate required to attract the investor
F = Face or Par value of the bond which is payable on bond maturity
t = is the time / tenure of the bond remaining in maturity

## Stepwise process of valuation of bond

The formula can best be explained with the help of steps involved in valuation of bonds and debentures.

#### Step 1: Determine the future cash flows

Bonds and debentures future cash flows consist of two components:

• Principal amount: This the Par / Face value written on the instrument of the bond. This amount is receivable at maturity therefore will be discounted back to present value using the simple interest formula as shown above.

• Interest amount: Besides principal amount bond holder is entitled to receive coupon / interest payments at regular intervals until the bond matures e.g. annually or semi annually. A better approach for discounting interest payments is to use annuity formula because these interest payments fulfill the definition of annuity i.e. equal amount of payments at regular intervals of time.

#### Step 2: Determine the discount rate

Determine the rate “r” for discounting the cash flows determined in step 1. This discount rate is called investor’s required rate of return. This rate is necessary to attract the investor otherwise he will invest in the bonds of similar risk having better required rate of return. The method of calculating the required rate of return is explained here.

#### Step3: Discounting the expected cash flows

Once expected cash flows of bond / debenture and the required rate of return to discount them is determined. The next step is simple application of time value of money.

• Discount the principal amount using simple interest formula.
• Discount the interest payments using annuity formula.

## Example

Suppose, a 7% bond with face value of \$100 pays interest annually and will mature in 5 years. The required rate of return of investor is 8%. Calculate the value of the bond.

Solution
Step 1: Determine the expected cash flows:

• Principal amount is equal to face value which will be received at maturity i.e. \$100.
• Interest payments are equal to 7% * \$ 100 = \$ 7 per year. Since maturity is 5 years total amount receivable will be \$ 7 * 5 = \$35.

Step 2: Determine the discount rate:
Discount rate is the required rate of return of investor which is given in this case i.e. 8%. Otherwise we have to calculate this rate as well.

Step 3: Discount the expected cash flows:
Now using all the information in the formula:

 V  = C * 1 – (1 + r) -t + F r (1 +r) t
 V  = 7 * 1 – (1 + 0.08) -5 + 100 0.08 (1 +0.08) 5

 V  = 27.95 + 68.05

 V  = \$ 96