Pricing of Bonds
Outline
 Time Value of Money Concepts
 Valuation of Fixed Income Securities
 Pricing zero coupon bonds
 Price/Yield Relationship
 The Relationship between coupon rate, required
yield, and price
 Relationship between bond price and time if
interest rates are unchanged
 How to account for accrued interest?
Time Value of Money
Future value of a single cash flow
Present value of a single cash flow
Future value of a series of cash flows
Present value of a series of cash flows
Present 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 bonds
Discount bonds
Premium bonds