Money banking and the financial system 1e by hubbard and OBrien chapter 03

Interest Rates and Rates of ReturnC H A P T E R 3 3.1 3.2 3.3 Explain how the interest rate links present value with future value LEARNING OBJECTIVES After studying this chapter, you sho

Interest Rates and Rates of Return

C H A P T E R 3

3.1 3.2

3.3

Explain how the interest rate links present value with future value

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

Distinguish among different debt instruments and understand how their prices are determined

Explain the relationship between the yield to maturity on a bond and its price

3.4 3.5

Understand the inverse relationship between bond prices and bond yields Explain the difference between interest rates and rates of return

3.6 Explain the difference between nominal interest rates and real interest rates

BANKS IN TROUBLE

• During the financial crisis, the number of insolvent banks increased sharply

• With the collapse of the housing market, increasing numbers of homeowners had stopped making payments on their mortgage

loans Banks that held these loans saw their value drop

• Mortgage loans that were turned into mortgage-backed securities, similar to bonds, declined by 50% or more during 2008 and

2009

• Banks had badly misjudged both the default risk and the interest-rate risk on these bonds.

• An Inside Look at Policy on page 78 discusses the performance of the bond market through 2010

Interest Rates and Rates of Return

C H A P T E R 3

Key Issue and Question

Issue : During the financial crisis, soaring interest rates on assets such as mortgage-backed securities caused their prices

to plummet

Question : Why do interest rates and the prices of financial securities move in opposite directions?

3.1 Learning Objective

Explain how the interest rate links present value with future value

The Interest Rate, Present Value, and Future Value

Why Do Lenders Charge Interest on Loans?

The interest rate on a loan should cover the opportunity cost of supplying credit, particularly, the costs associated with three factors:

• Compensation for inflation: if prices rise, the payments received will buy fewer goods and services

• Compensation for default risk: the borrower might default on the loan.

• Compensation for the opportunity cost of waiting for the money to be paid back

The Interest Rate, Present Value, and Future Value

Most Financial Transactions Involve Payments in the Future

The importance of the interest rate comes from the fact that most financial transactions involve payments in the future; the interest rate provides a link between the financial present and the financial future.

Compounding and DiscountingFuture value The value at some future time of an investment made today.

Compounding The process of earning interest on interest as savings accumulate over time

If:

i = the interest rate

Principal = the amount of your investment (your original $1,000)

FV = the future value (what your $1,000 will have grown to in one year)

then we can rewrite the expression as:

Compounding for More Than One Period

If you invest $1,000 for n years, where n can be any number of years, at an interest rate of 5%, then at the end of n years, you will have:

The Interest Rate, Present Value, and Future Value

Solved Problem 3.1AComparing Investments

The Interest Rate, Present Value, and Future Value

Suppose you are considering investing $1,000 in one of the following bank CDs:

• First CD, which will pay an interest rate of 4% per year for three years

• Second CD, which will pay an interest rate of 10% the first year, 1% the second year, and 1% the third year

Which CD should you choose?

Solved Problem 3.1AComparing Investments

Solving the Problem

Step 1 Review the chapter material.

Step 2 Calculate the future value of your investment with the first CD.

Step 3 Calculate the future value of your investment with the second CD and decide which CD you should choose.

Principal = $1,000, i = 4%, n = 3 years

FV = $1,000 x (1 + 0.04)3 = $1,124.86

Principal = $1,000, i1 = 10%, i2 = 1%, i3 = 1%, n = 3 years

FV = $1,000 x (1 + 0.10) x (1 + 0.01) x (1 + 0.01) = $1,122.11 Decision: You should choose the investment with the highest future value, so you should choose the first CD.

The Interest Rate, Present Value, and Future Value

Present value The value today of funds that will be received in the future.

Time value of money The way that the value of a payment changes depending on when the payment is received

Discounting The process of finding the present value of funds that will be received in the future.

Some Important Points about Discounting

1 Present value is sometimes referred to as “present discounted value.”

2 The further in the future a payment is to be received, the smaller its present value (See Table 3.1).

3 The higher the interest rate used to discount future payments, the smaller the present value of the payments (See Table 3.1).

4 The present value of a series of future payment is simply the sum of the discounted value of each individual payment.

The Interest Rate, Present Value, and Future Value

Solved Problem 3.1BValuing a Contract

Jason Bay played the 2009 baseball season with the Boston Red Sox

When he became a free agent, the Red Sox offered him a contract for $15 million per year for four years The New York Mets offered him

a contract that would pay him a total of $66 million

According to sportswriter Buster Olney: “The Mets’ offer to Jason Bay is heavily backloaded, to the point that the true value of the

four-year [contract] falls to within the range of the offer he turned down from the Red Sox.”

What does Olney mean by the payments in the Mets’ contract being “backloaded”? What does he mean by the “true value” of the

contract?

How would backloading the payments affect the true value of the contract?

The Interest Rate, Present Value, and Future Value

Valuing a Contract

Solving the Problem

Step 1 Review the chapter material.

Step 2 Explain what Olney means by “backloaded” and “true value.”

A “backloaded” contract means that the Mets offered Jason Bay lower salaries in the first years and higher salaries in the later years of the contract The

“true value” probably refers to the present value of the contract.

Step 3 Explain how backloading affects the value of the contract.

We know that the present value of payments is lower the further away in time those payments are made So, if the Mets’ contract pays Bay most of the $66 million in the third and fourth years of the contract, it could have a present value similar to the Red Sox contract that paid $60 million spread out as four

annual $15 million payments.

The Interest Rate, Present Value, and Future Value

A Brief Word on Notation This book will always enter interest rates in numerical calculations as decimals For instance, 5% will be 0.05,

not 5.

Discounting and the Prices of Financial Assets

Discounting gives us a way of determining the prices of financial assets By adding up the present values of all the payments, we have the dollar amount that a buyer will pay for the asset In other words, we have determined the asset’s price

The Interest Rate, Present Value, and Future Value

3.2 Learning Objective

Distinguish among different debt instruments and understand how their prices are determined

Debt instruments (also known as credit market instruments or fixed income assets) Methods of financing debt, including simple

loans, discount bonds, coupon bonds, and fixed payment loans

Equity A claim to part ownership of a firm; common stock issued by a corporation

The price of a financial asset is equal to the present value of the payments to be received from owning it.

Debt Instruments and Their Prices

Loans, Bonds, and the Timing of Payments

In this section, we discuss four basic categories of debt instruments:

Simple loan A debt instrument in which the borrower receives from the lender an amount called the principal and agrees to repay the

lender the principal plus interest on a specific date when the loan matures

Simple Loan

After one year, Nate’s would repay the principal plus interest: $10,000 + ($10,000 × 0.10), or $11,000

Debt Instruments and Their Prices

Discount Bond

The lender receives interest of $10,000 - $9,091 = $909 for the year Therefore, the interest rate is $909/$9,091 = 0.10, or 10%

Discount bond A debt instrument in which the borrower repays the amount of the loan in a single payment at maturity but receives less

than the face value of the bond initially

Debt Instruments and Their Prices

Coupon Bonds

Terminology of coupon bonds:

• Face value, or par value, is the amount to be repaid by the bond issuer (the borrower) at maturity.

• The coupon is the annual fixed dollar amount of interest paid by the issuer of the bond to the buyer.

• The coupon rate is the value of the coupon expressed as a percentage of the par value of the bond.

• The current yield is the value of the coupon expressed as a percentage of the current price.

Coupon bond A debt instrument that requires multiple payments of interest on a regular basis, such as semiannually or annually, and a payment of the face value at maturity

Debt Instruments and Their Prices

Coupon Bonds

• For example, if IBM issued a $1,000 30-year bond with a coupon rate of 10%, it would pay $100 per year for 30 years and a final

payment of $1,000 at the end of 30 years The timeline on the IBM coupon bond is:

• Maturity is the length of time before the bond expires and the issuer makes the face value payment to the buyer.

Debt Instruments and Their Prices

Fixed-Payment Loan

• For example, if you are repaying a $10,000 10-year student loan with a 9% interest rate, your monthly payment is approximately

$127 The time line of payments is:

Fixed-payment loan A debt instrument that requires the borrower to make regular periodic payments of principal and interest to the

lender

Debt Instruments and Their Prices

Making the Connection

Do You Want the Principal or Do You Want the Interest?

Creating New Financial Instruments

• Back when the U.S Treasury offered only short-term discount bonds, investors were seeking to benefit from longer terms knowing the exact return if they held the bonds to maturity

• In 1982, Merrill Lynch created the TIGR (Treasure Investment Growth Receipt), which is a discount bond that works like a Treasury Bill

• Two years later, the Treasury introduced its own version called STRIPS (Separate Trading of Registered Interest and Principal

Securities) These bonds allowed investors to buy each interest payment and the face value of the bond

• Individuals can obtain long-term discount bonds as well as the regular Treasury coupon bonds, thereby increasing their options for investment

Debt Instruments and Their Prices

3.3 Learning Objective

Explain the relationship between the yield to maturity on a bond and its price

Bond Prices

• Consider a coupon bond with i = 6%, FV = $1,000, n = 5 years The expression for the price, P, of the bond is the sum of the

present values of the six payments:

• Below is a general expression for a bond that makes coupon payments, C, has a face value, FV, and matures in n years:

Bond Prices and Yield to Maturity

Yield to MaturityYield to maturity The interest rate that makes the present value of the payments from an asset equal to the asset’s price today.

Whenever participants in financial markets refer to the interest rate on a financial asset, the interest rate is the yield to maturity.

Yields to Maturity on Other Debt Instruments

Simple Loans

• Consider a $10,000 loan required to pay $11,000 in one year

Value today = Present value of future payments

Discount Bonds

• Consider a $10,000 one-year discount bond with a value today of $9,200

Value today = Present value of future payments

Solving for i:

• A general equation for a one-year discount bond that sells for price, P, with face value, FV The yield to maturity is:

Bond Prices and Yield to Maturity

Fixed-Payment Loans

• Consider a $100,000 loan with annual payments of $12,731

Value today = Present value of future payments

• A perpetuity does not mature The price of a coupon

bond that pays an infinite number of coupons equals:

• So, a perpetuity with a coupon of $25 and a price of $500 has a yield to maturity of i = $25/$500 = 0.05, or 5%.

Bond Prices and Yield to Maturity

Solved Problem 3.3

Yield to Maturity for Different Types of Debt Instruments

For each of the following situations, write the equation that you would use to calculate the yield to maturity You do not have to solve the

equations for i; just write the appropriate equation.

a) A simple loan for $500,000 that requires a payment of $700,000 in four

years

b) A discount bond with a price of $9,000, which has a face value of $10,000

and matures in one year

c) A corporate bond with a face value of $1,000, a price of $975, a coupon rate

of 10%, and a maturity of five years

d) A student loan of $2,500, which requires payments of $315 per year for 25

years The payments start in two years

Bond Prices and Yield to Maturity

Solved Problem 3.3

Yield to Maturity for Different Types of Debt Instruments

Solving the Problem

Step 1 Review the chapter material.

Step 2 Write an equation for the yield to maturity for each of the following debt instruments.

a) A simple loan for $500,000 that requires a payment of $700,000 in four years

b) A discount bond with a price of $9,000, which has a face value of $10,000 and matures in one year

Bond Prices and Yield to Maturity

Solved Problem 3.3

Yield to Maturity for Different Types of Debt Instruments

Solving the Problem

Step 1 Review the chapter material.

Step 2 Write an equation for the yield to maturity for each of the following debt instruments.

c) A corporate bond with a face value of $1,000, a price of $975, a coupon rate of 10%, and a maturity of five years

d) A student loan of $2,500, which requires payments of $315 per year for 25 years The payments start in two years

Bond Prices and Yield to Maturity

(continued)

3.4 Learning Objective

Understand the inverse relationship between bond prices and bond yields

The Inverse Relationship between Bond Prices and Bond Yields

What Happens to Bond Prices When Interest Rates Change?

If the price of an asset increases, it is called a capital gain If the price of the asset declines, it is called a capital loss

• Coupon bonds may be sold many times in a secondary market.

• The issuer of the bond is no longer involved in these transactions

• If new bonds are issued at a higher interest rate, holders of bonds that pay lower rates would have to adjust the price at which they are willing to sell their bonds

• To calculate the new price, we need to use the same yield to maturity of the newly issued bonds

• Because the yield to maturity is higher, the bond’s market price will fall below its face value

• As interest rates rise, bond prices fall

Making the Connection

Banks Take a Bath on Mortgage-Backed Bonds

• Many mortgage-backed securities are similar to long-term bonds in that they pay regular interest based on the payments borrowers make on the underlying mortgages

• In the secondary market for mortgage-backed securities, as borrowers began to default on their payments, buyers required much

higher yields to compensate for the higher levels of default risk

• Higher yields on these securities meant lower prices By 2008, the prices of many mortgage-backed securities had declined by

50% or more

• By early 2009, U.S commercial banks had suffered losses on their investments of about $1 trillion

• Banks had relearned the lesson that soaring interest rates can have a devastating effect on investors holding existing debt

instruments

The Inverse Relationship between Bond Prices and Bond Yields