Chapter 5

© 2003 South-Western/Thomson Learning

Interest Rates and Interest Rates and Bond PricesBond Prices

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Learning Objectives Why the interest rate represents the time

value of money What are compounding and discounting Why interest rates and bond prices are

inversely related

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Learning Objectives The major determinants of interest rates The relationship between nominal and real

interest rates How interest rates fluctuate over the

business cycle

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The Time Value of MoneyMoney represents purchasing

power … Short of funds for goods or

services?1. Borrow now and purchase now2. Save now and purchase laterThe higher the interest rates

the less appealing is #1 the more appealing is #2

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The Time Value of Money

Lending in present ENABLES Spending in the

future the sum of what is lent plus the interest earned

Borrowing in future ENABLES Spending in the

present, but requires paying back in the future what is borrowed plus interest

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Compounding and Discounting Compounding Future Values

What is the future value of money lent (or borrowed) today

AMOUNT REPAID = PRINCIPAL + INTEREST

INTEREST = PRINCIPAL x INTEREST RATE

amount of interest

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Compounding and Discountingsubstituting equation into yields

AMOUNT REPAID = PRINCIPAL + ( PRINCIPAL x INTEREST RATE )AMOUNT REPAID = PRINCIPAL + ( PRINCIPAL x INTEREST RATE )

AMOUNT REPAID = PRINCIPAL x ( 1 + i )

V1 = V0 ( 1 + i )

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Compounding and Discounting

V1 = the funds to be received by the lender at the end of one year

V0 = the funds lent now

This is present value

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Compounding and DiscountingIn the second year

V2 = V0 (1 + i )2

Vn = V0 (1 + i )n

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Discounting: Present Values

Discounting is backward-looking

What is the PRESENT VALUE of money to be received (or paid) in the future?

expressed

V0 = Vn / (1 + i )n

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Discounting: Present ValuesRECAP Compounding: finding the value of a

future sum. Discounting: finding the present value of a

future sum Future value: Vn of a sum, V0 invested

today for n years is V0 ( 1 + i )n Present value: V0, of the sum Vn, to be

received in n years is Vn / ( 1 + i )n

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Interest Rates, Bond Prices, and Present ValueTo compute the present value of each coupon payment and the present value of the final repayment of the face value on the maturity date.

P = the price (present value) of the bondC = the coupon payment on the bond (C1 in year 1, C2 in year 2

etc.F = the face or par value of the bondi = the interest raten = the number of years to maturity (on a five-year bond, n=5)

P = C1 / ( 1 + i )1 + C2 / ( 1 + i )2 + … + Cn / ( 1 + i )n + F / ( 1 + i )n

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Interest Rates, Bond Prices, and Present Value Discount from par - raises the yield on the

bond, called the yield to maturity Premium above par – a price above par value

There is an inverse relationship between the price of outstanding bonds trading in the secondary market and the prevailing level of market interest rates.

If bond prices are rising, then interest rates are falling, and vice versa.

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Interest Rates, Bond Prices, and Present Value

The price of the bond is the discounted value of the future stream of income over the life of the bond.

When the interest rate increases, the price of the bond decreases.

When the interest rate decreases, the price of the bond increases.

RECAP

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Determinants of Interest Rates Demand for loanable funds –

downward-sloping demand curve indicates that DSU’s are willing to borrow more at lower interest rates

Supply of loanable funds – originates The household, business, government and

foreign SSUs who are prepared to lend The Fed, which, in its ongoing attempts to

manage the economy’s performance, supplies reserves

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Exhibit 5–3The Supply of and Demand for Funds

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Determinants of Interest Rates Changes in the demand for loanable funds

Movements in gross domestic product (GMP) When GMP rises Firms & households become more willing and

able to borrow Firms expand inventory & engage in investment

spending Households willing to borrow, increased incomes,

and/or improved employment outlook

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Exhibit 5–4A Shift in the Demand for Funds

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Determinants of Interest Rates Changes in the demand for loanable funds

Increase their purchases of goods and services, particularly Auto Durable goods Houses

Items that require financing

Easier to make the interest and principal payments on new debt Increase in anticipated productivity of capital investment

• Lead to a greater demand for capital investment & hence increase the demand for loanable funds

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Determinants of Interest Rates

Changes in the supply of funds Monetary policy Disequilibrium – the quantity supplied of funds

exceeds the quantity demanded As interest rates fall, DSUs & SSUs revise their

borrowing and lending plans Increase in the money supply will lower the

interest rates Decrease in the money supply will raise the

interest rates

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A Shift in the Supply of Funds

The interest rate is a positive function of income or GDP, Y and negative function of the money supply, M

i = f ( Y+,M¯ )

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Exhibit 5–5A Shift in the Supply of Funds

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Determinants of Interest Rates

The demand for loanable funds originates from DSUs

The quantity demanded is inversely related to the interest rate

The supply of loanable funds originates from SSUs and from Fed

The quantity supplied is directly related to the interest rate

If the money supply increases, the supply of loanable funds increases and the interest rate falls: i = f ( Y+,M¯ )

RECAP

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Inflation and Interest Rates Lenders are concerned about

Nominal interest Inflation

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Inflation and Interest Rates

Nominal interest rate is not an adequate measure of the real return on an interest-bearing financial asset unless there is assurance of price stability.

Appropriate measure is the real interest rate, which is the return on the asset corrected for changes in the purchasing power of money.

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Inflation and Interest RatesMoney illusion is said to occur when investors react to nominal changes even though no changes in real interest rates or other real variables have occurred. i = r + pe

The equation says that nominal interest rate has parts: a real interest rate, r, and an inflation premium

i = r - pe

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Inflation and Interest Rates Major price indexes

Consumer Price Index (CPI) CPI is designed to measure changes in the cost of

goods and services purchased by a typical urban consumer Producer Price Index (PPI)

PPI measures the changes in the cost of goods and services purchased by a typical producer

Inflation rate is generally measured by the percentage change in one of these price indexes.

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Inflation and Interest RatesExpectations of inflation affect portfolio choices that help determine the demand and supply of loanable funds

i = f ( Y+,M¯, p+ e )

Nominal interest rate is positively related to the expected inflation rate

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Inflation and Interest Rates

The nominal interest rate is the real interest rate plus the expected inflation rate

Money illusion occurs when investors react to nominal changes when no real changes occurred

If expected inflation increases, the nominal interest rate will rise

Nominal interest rates are correlated with expected inflation i = f ( Y+,M¯, p+ e )

RECAP

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The Cyclical Movement of Interest Rates Stages of the business cycle are the recession trough, expansion, and peak Interest rates tend to fluctuate pro-cyclically-that is, they move with the

business cycle, rising during expansions and falling during recessions