Understanding the Valuation of Bonds

(This article explains the method of calculating the value of a coupon bond factors in the annual or semi-annual coupon payment and the par value of the bond.)

Bond valuation is the process by which an investor estimates the theoretical fair value, or intrinsic worth, of a bond. Like any security or capital investment, a bond’s fair value is calculated as the present value of its expected future cash flows.

Purpose of Bond Valuation

Investors use bond valuation to determine whether to buy, sell, or hold a bond. This analysis helps them assess the required rate of return for a bond investment to be worthwhile.

How Bond Valuation is calculated

The value of a bond is derived by calculating the present value of all its expected future cash flows. This involves considering the bond’s face value, coupon rate, discount rate, and maturity date.

Discount face value is the price paid for an item after a discount is applied to its original price, or face value.

Explanation

Face value: The original price of an item

Discount: The amount by which the original price is reduced

Formula for Discount face value: The price paid for an item after the discount is applied : Face Value ÷ (1 + r)^t

Steps to Calculate Bond Valuation:

1. Calculate Expected Cash Flows
   Use the bond’s face value, annual coupon rate, and maturity date to determine the cash flows.
   Formula:
   Annual Cash Flow = Coupon Rate × Face Value
2. Discount Expected Cash Flows to Present Value
   Discount each expected cash flow to its present value using the formula:
   Formula:
   Present Value of Cash Flow = Cash Flow ÷ (1 + r)^t
   Where:
   1. r = discount rate (interest rate)
   1. t = year of the cash flow
3. Value Individual Cash Flows and Final Face Value Payment
   Sum the present values of all coupon payments and the bond’s face value.
   Formula for Cash Flows value is sum of cash flow for number of coupon payments, that is;
   Cash Flow Value = [Cash Flow ÷ (1 + r)^1] + [Cash Flow ÷ (1 + r)^2] + … + [Cash Flow ÷ (1 + r)^t]   …………….      Call it as A
   Formula for Final Payment:
   Final Face Value Payment = Face Value ÷ (1 + r)^t  ………  Call it as B

(B=DISCOUNTED FACE VALUE)

4. Calculate Total Bond Value: Formula:
Bond Value = Sum of Discounted Cash Flows + Discounted Face Value

              i.e. Add the present values of all coupon payments and the discounted face value

             And you’ve successfully calculated the value of your bond: (A+B)

By following these steps, investors can accurately estimate a bond’s intrinsic value and make informed investment decisions.

Calculation for Semi-annual payments

There is not much difference in calculation method for valuation of annual and semiannual coupon bonds. The only difference between the formulas for annual and semi-annual coupon bonds is the timing and amount of interest payments. The formula for semi-annual coupon bonds involves dividing the annual coupon rate by two.

For example, let’s find the value of a corporate bond of face value ₹ with an annual interest rate of 5%, making semi-annual interest payments for two years, after which the bond matures and the principal must be repaid. Let us assume an YTM of 3%:

• Face Value =  ₹ 1,000 for corporate bond
• Coupon rate(annual) = 5%,
• therefore, Coupon rate for Semi-annual= 5% / 2 = 2.5%
• Cash-flow = 2.5% x  ₹ 1000 =  ₹ 25 per period
• t = 2 years x 2 = 4 periods for semi-annual coupon paymentsT = 4 periods
• r = YTM of 3% / 2 for semi-annual compounding = 1.5% or 1.5/100=0.015
• Formula for Cash Flows value is sum of cash flow for number of coupon payments, that is;
  Cash Flow Value = [Cash Flow ÷ (1 + r)^1] + [Cash Flow ÷ (1 + r)^2] + … + [Cash Flow ÷ (1 + r)^t] 
  Formula for Final Payment:
  Final Face Value Payment = Face Value ÷ (1 + r)^t 

1. Present value of semi-annual payments = 25 / (1.015)¹ + 25 / (1.015)² + 25 / (1.015)³ + 25 / (1.015)⁴ = 96.36
2. Present value of face value = ₹ 1000 / (1.015)⁴ = 942.18
3. Therefore, the value of the bond is ₹ 1,038.54.