Pricing of Bonds

Outline

Time Value of Money ConceptsValuation of Fixed Income SecuritiesPricing zero coupon bondsPrice/Yield RelationshipThe Relationship between coupon rate, required

yield, and priceRelationship between bond price and time if

interest rates are unchangedHow to account for accrued interest?

Time Value of Money

Future value of a single cash flowPresent value of a single cash flowFuture value of a series of cash flowsPresent value of a series of cash flowsPresent value of an annuity

Valuation of Fixed Income Securities

Process of determining the fair market value of a financial asset on the basis of present value of the expected cash flows

Three step process:– Estimate the expected cash flows– Determine the appropriate interest rate or interest rates

to discount the cash flows– Compute the present value of the expected cash flows

in step 1 by discounted them with interest rate(s) in step 2

Estimating Cash Flows

Holding aside the risk of default, the cash flows of fixed income securities are easy to project

• Payment of coupon/interest

• Repayment of principal

When will investors find it difficult to estimate the cash flows of a fixed-income security?

Determining the Discount Rate or Rates

What is the minimum rate that an investor should require?

How much more than the minimum interest rate should the investor require?

Should the investor require the same interest rate for each estimated cash flow or a unique interest rate for each estimated cash flow?

Discount Rate

The minimum interest rate that an investor should require is the yield available in the market place on a default-free cash flow

In the United States, this is the yield on a U.S. Treasury security, known as the base interest rate for each maturity

Premium over the base interest rate on a Treasury security that investors will require reflects the additional risks that the investor faces by acquiring a security not issued by the U.S. government

Discount Rate = Base Interest Rate + Risk Premium/Spread over Treasuries

What determines the spread?

Value of a Bond

Depends on the present value of expected cash flows from the bond

Need to estimate– Expected cash flows– The appropriate required yield/discount rate

What are the expected cash flows for a plain-vanilla bond?

Pricing Zero-Coupon Bonds

Bonds that do not pay any periodic coupon payments.

Instead the investor realizes interest as the difference between the maturity value and the purchase price of the bond

Example

Price/Yield Relationship

Price of bond changes in the opposite direction from the change in the required yield

Coupon Rate, Required Yield, and Bond Price

Par bondsDiscount bondsPremium bonds