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Money & Banking ­ MGT411
VU
Lesson 13
BONDS & BONDS PRICING
Bond & Bond pricing
Zero Coupon Bond
Fixed Payment Loan
Coupon Bonds
Consols
Bond Yield
Yield to Maturity
Current Yield
Bonds
Virtually any financial arrangement involving the current transfer of resources from a lender to
a borrower, with a transfer back at some time in the future, is a form of bond.
Car loans, home mortgages, even credit card balances all create a loan from a financial
intermediary to an individual making a purchase
Governments and large corporations sell bonds when they need to borrow
The ease with which individuals, corporations, and governments borrow is essential to the
functioning of our economic system.
Without this free flow of resources through the bond markets, the economy would grind to a
halt.
Historically, we can trace the concept of using bonds to borrow to monarchs' almost insatiable
appetite for resources.
The Dutch invented modern bonds to finance their lengthy war of independence
The British refined the use of bonds to finance government activities.
The practice was soon popular among other countries
A standard bond specifies the fixed amount to be paid and the exact dates of the payments
How much should you be paying for a bond?
The answer depends on bond's characteristics
Bond Prices
Zero-coupon bonds
Promise a single future payment, such as a Treasury bill.
Fixed payment loans
Conventional mortgages.
Car loans
Coupon Bonds
Make periodic interest payments and repay the principal at maturity.
Treasury Bonds and most corporate bonds are coupon bonds.
Consols
Make periodic interest payments forever, never repaying the principal that was borrowed.
Zero-Coupon Bonds
These are pure discount bonds since they sell at a price below their face value
The difference between the selling price and the face value represents the interest on the bond
The price of such a bond, like a Treasury bill (called "T-bill"), is the present value of the future
payment
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Money & Banking ­ MGT411
VU
Price of a $100 face value zero-coupon bond
$ 100
=
(1 + i )
n
Where
i is the interest rate in decimal form and
n is time until the payment is made in the same time units as the interest rate
Given n, the price of a bond and the interest rate move in opposite directions
The most common maturity of a T-bill is 6 months; the Treasury does not issue them with a
maturity greater than 1 year
The shorter the time until the payment is made the higher the price of the bond, so 6 month T-
bills have a higher price that a one-year T-bill
Examples: Assume i=4%
Price of a One-Year Treasury bill
100
=
= $ 96 . 15
(1 + 0 . 04 )
Price of a Six-Month Treasury bill
100
=
= $ 98 . 06
(1 + 0 . 04 )
1/ 2
The interest rate and the price for the T-bill move inversely.
If we know the face value and the price then we can solve for the interest rate
Fixed Payment Loans
They promise a fixed number of equal payments at regular intervals
Home mortgages and car loans are examples of fixed payment loans;
These loans are amortized, meaning that the borrower pays off the principal along with the
interest over the life of the loan.
Each payment includes both interest and some portion of the principal
The price of the loan is the present value of all the payments
Value of a Fixed Payment Loan =
FixedPayme t + FixedPayme t +  ... + FixedPayment
n
n
(1 + i)
(1 + i)
(1 + i)
2
n
Coupon Bond
The value of a coupon bond is the present value of the periodic interest payments plus the present value
of the principal repayment at maturity
CouponPayment  CouponPayment
CouponPayment  FaceValue
PCB = ⎢
+
+ ...... +
⎥ +  (1 + i)n
(1 + i)1
(1 + i)2
(1 + i)n
The latter part, the repayment of the principal, is just like a zero-coupon bond.
41
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Money & Banking ­ MGT411
VU
Consols
A consol offers only periodic interest payments; the borrower never repays the principal
There are no privately issued consols because only governments can credibly promise to make
payments forever
The price of a consol is the present value of all the future interest payments, which is a bit
complicated because there are an infinite number of payments
Bond Yields
Now that we know how to price a bond while interest rate is known; we now move to other
direction and calculate the interest rate or return to an investor
So combining information about the promised payments with the price to obtain what is called
the yield ­ a measure of cost of borrowing or reward for lending.
Interest rate and yield are used interchangeably
Yield to Maturity
The most useful measure of the return on holding a bond is called the yield to maturity (YTM).
This is the yield bondholders receive if they hold the bond to its maturity when the final
principal payment is made
It can be calculated from the present value formula
Price of One-Year 5 percent Coupon Bond =
$5
$100
+
(1 + i )  (1 + i )
The value of i that solves this equation is the yield to maturity
If the price of the bond is $100, then the yield to maturity equals the coupon rate.
Since the price rises as the yield falls, when the price is above $100, the yield to maturity must
be below the coupon rate.
Since the price falls as the yield rises, when the price is below $100, the yield to maturity must
be above the coupon rate.
Yield to Maturity
Considering 5% coupon bond
If YTM is 5% then price is
$5
$ 100
+
= $100
(1 + .05) (1 + .05)
If YTM is 4% then price is
$5
$ 100 = $100.96
+
(1 + .04) (1 +.04)
If YTM is 6% then price is
$5
$ 100
+
= $99.06
(1 + .06) (1 +.06)
Generally
If the yield to maturity equals the coupon rate, the price of the bond is the same as its face value.
If the yield is greater than the coupon rate, the price is lower;
If the yield is below the coupon rate, the price is greater
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Table of Contents:
  1. TEXT AND REFERENCE MATERIAL & FIVE PARTS OF THE FINANCIAL SYSTEM
  2. FIVE CORE PRINCIPLES OF MONEY AND BANKING:Time has Value
  3. MONEY & THE PAYMENT SYSTEM:Distinctions among Money, Wealth, and Income
  4. OTHER FORMS OF PAYMENTS:Electronic Funds Transfer, E-money
  5. FINANCIAL INTERMEDIARIES:Indirect Finance, Financial and Economic Development
  6. FINANCIAL INSTRUMENTS & FINANCIAL MARKETS:Primarily Stores of Value
  7. FINANCIAL INSTITUTIONS:The structure of the financial industry
  8. TIME VALUE OF MONEY:Future Value, Present Value
  9. APPLICATION OF PRESENT VALUE CONCEPTS:Compound Annual Rates
  10. BOND PRICING & RISK:Valuing the Principal Payment, Risk
  11. MEASURING RISK:Variance, Standard Deviation, Value at Risk, Risk Aversion
  12. EVALUATING RISK:Deciding if a risk is worth taking, Sources of Risk
  13. BONDS & BONDS PRICING:Zero-Coupon Bonds, Fixed Payment Loans
  14. YIELD TO MATURIRY:Current Yield, Holding Period Returns
  15. SHIFTS IN EQUILIBRIUM IN THE BOND MARKET & RISK
  16. BONDS & SOURCES OF BOND RISK:Inflation Risk, Bond Ratings
  17. TAX EFFECT & TERM STRUCTURE OF INTEREST RATE:Expectations Hypothesis
  18. THE LIQUIDITY PREMIUM THEORY:Essential Characteristics of Common Stock
  19. VALUING STOCKS:Fundamental Value and the Dividend-Discount Model
  20. RISK AND VALUE OF STOCKS:The Theory of Efficient Markets
  21. ROLE OF FINANCIAL INTERMEDIARIES:Pooling Savings
  22. ROLE OF FINANCIAL INTERMEDIARIES (CONTINUED):Providing Liquidity
  23. BANKING:The Balance Sheet of Commercial Banks, Assets: Uses of Funds
  24. BALANCE SHEET OF COMMERCIAL BANKS:Bank Capital and Profitability
  25. BANK RISK:Liquidity Risk, Credit Risk, Interest-Rate Risk
  26. INTEREST RATE RISK:Trading Risk, Other Risks, The Globalization of Banking
  27. NON- DEPOSITORY INSTITUTIONS:Insurance Companies, Securities Firms
  28. SECURITIES FIRMS (Continued):Finance Companies, Banking Crisis
  29. THE GOVERNMENT SAFETY NET:Supervision and Examination
  30. THE GOVERNMENT'S BANK:The Bankers' Bank, Low, Stable Inflation
  31. LOW, STABLE INFLATION:High, Stable Real Growth
  32. MEETING THE CHALLENGE: CREATING A SUCCESSFUL CENTRAL BANK
  33. THE MONETARY BASE:Changing the Size and Composition of the Balance Sheet
  34. DEPOSIT CREATION IN A SINGLE BANK:Types of Reserves
  35. MONEY MULTIPLIER:The Quantity of Money (M) Depends on
  36. TARGET FEDERAL FUNDS RATE AND OPEN MARKET OPERATION
  37. WHY DO WE CARE ABOUT MONETARY AGGREGATES?The Facts about Velocity
  38. THE FACTS ABOUT VELOCITY:Money Growth + Velocity Growth = Inflation + Real Growth
  39. THE PORTFOLIO DEMAND FOR MONEY:Output and Inflation in the Long Run
  40. MONEY GROWTH, INFLATION, AND AGGREGATE DEMAND
  41. DERIVING THE MONETARY POLICY REACTION CURVE
  42. THE AGGREGATE DEMAND CURVE:Shifting the Aggregate Demand Curve
  43. THE AGGREGATE SUPPLY CURVE:Inflation Shocks
  44. EQUILIBRIUM AND THE DETERMINATION OF OUTPUT AND INFLATION
  45. SHIFTS IN POTENTIAL OUTPUT AND REAL BUSINESS CYCLE THEORY