# Present Value of Bonds

15th February 2020The method for valuation of bonds involves three steps as follows:

Step 1: Estimate the expected cash flows

Step 2: Determine the appropriate interest rate that should be used to discount the cash flows.

& Step 3: Calculate the present value of the expected cash flows (step-1) using appropriate interest rate (step- 2) i.e. discounting the expected cash flows

**STEP 1: Estimating cash flows**

Cash flow is the cash that is estimated to be received in future from investment in a bond. There are only two types of cash flows that can be received from investment in bonds i.e. coupon payments and principal payment at maturity.

The usual cash flow cycle of the bond is coupon payments are received at regular intervals as per the bond agreement, and final coupon plus principle payment is received at the maturity. There are some instances when bonds don’t follow these regular patterns. Unusual patterns maybe a result of the different type of bond such as zero-coupon bonds, in which there are no coupon payments. Considering such factors, it is important for an analyst to estimate accurate cash flow for the purpose of bond valuation.

**STEP 2: Determine the appropriate interest rate to discount the cash flows**

Once the cash flow for the bond is estimated, the next step is to determine the appropriate interest rate to discount cash flows. The minimum interest rate that an investor should require is the interest available in the marketplace for default-free cash flow. Default-free cash flows are cash flows from debt security which are completely safe and has zero chances default. Such securities are usually issued by the central bank of a country, for example, in the USA it is bonds by U.S. Treasury Security.

Consider a situation where an investor wants to invest in bonds. If he is considering to invest corporate bonds, he is expecting to earn higher return from these corporate bond compared to rate of returns of U.S. Treasury Security bonds. This is because chances are that a corporate bond might default, whereas the U.S. Security Treasury bond is never going to default. As he is taking a higher risk by investing in corporate bonds, he expects a higher return.

One may use single interest rate or multiple interest rates for valuation.

**STEP 3: Discounting the expected cash flows**

Now that we already have values of expected future cash flows and interest rate used to discount the cash flow, it is time to find the present value of cash flows. Present Value of a cash flow is the amount of money that must be invested today to generate a specific future value. The present value of a cash flow is more commonly known as discounted value.

The present value of a cash flow depends on two determinants:

- When a cash flow will be received i.e. timing of a cash flow
- The required interest rate, more widely known as Discount Rate (rate as per Step-2)

First, we calculate the present value of each expected cash flow. Then we add all the individual present values and the resultant sum is the value of the bond.

The formula to find the present value of one cash flow is:

**PRESENT VALUE FORMULA FOR BOND VALUATION**

Present Value _{n} = Expected cash flow in the period n/ (1+i) ^{n}

Here,

i = rate of return/discount rate on bond

n = expected time to receive the cash flow

By this formula, we will get the present value of each individual cash flow t years from now. The next step is to add all individual cash flows.

Bond Value = Present Value _{1} + Present Value _{2} + ……. + Present Value _{n}