Transcript Money and Banking - Holy Family University

Chapter 4: Interest Rates
Objectives
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Define interest and explain its importance.
Write and explain the present value formula.
Write and explain the future value formula.
Calculate present and future value for multiple periods with annual and more
frequent compounding.
Define and price major types of debt instruments including discount bonds,
simple loans, fixed payment loans, coupon bonds, and perpetuities.
Define yield to maturity and identify the types of financial instruments it is
relatively easy to calculate.
Explain why bond prices move inversely to market interest rates.
Explain why some bond prices are more volatile than others.
Define rate of return and explain how it differs from yield to maturity.
Explain the difference between real and nominal interest rates.
1. The Interest of Interest
• Interest rates are crucial determinants of
– Prices of assets, especially financial instruments like
stocks and bonds, and general macroeconomic
conditions (economic growth). It is the price of
money.
• Ways of measuring interest rates
– Yield to maturity (YTM): The most economically
accurate way of measuring interest rates
– Present value (PV): The value of money today
– Future value (FV): The value of money at some point
in the future
2. Present and Future Value
• Money today is always worth more than
money tomorrow
• Nominal interest rates: the one we see
• Real interest rate: The rate adjusted for
inflation
• Compounding: Earning interest on interest
• Compounding period: The amount of time
that passes before interest begins to earn
interest
Future Value (FV)
• FV = PV(1 + i)n , where
– FV = the future value (the value of your
investment in the future)
– PV = the present value (the amount of your
investment today)
– (1 + i)n = the future value factor
– i = interest rate
– n = number of terms (years, quarters, months,
days)
Present Value (PV)
• PV = FV/(1 + i)n, where
– PV = the present value (the amount of your
investment today)
– FV = the future value (the value of your
investment in the future)
– (1 + i)n = the future value factor
– i = interest rate
– n = number of terms (years, quarters, months,
days)
3. Compounding Periods
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Interest is more valuable when received
sooner than end of the year
Interest may be compounded
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Annually
Quarterly
Monthly
Daily
Continuously
• i - interest paid per period
• n - number of periods (rather than the number of years)
4. Pricing Debt Instruments
A bond, IOU, or other contract (like a discount bond, simple loan, fixed payment loan, or coupon bond) promising the payment of money in
the future
Discount Bond
• Known as a zero coupon bond, it is a debt instrument that makes only one payment, its
face value on its maturity or redemption date
Simple Loan
• A debt instrument where the borrower repays the principal and interest at the end of the
loan
Fixed-payment Loan
• A debt instrument in which the borrower makes periodic repayments of principal and
interest
Coupon Bond
• A debt instrument that makes interest payments periodically until its maturity or
redemption date, when the final interest payment and the principal are to be paid
4. Pricing Debt Instruments
• The sum of the present values of each future
payment will give you the price
• When the bond pays a rate lower than the
going market, people are not willing to pay as
much for it, so its price sinks
– If the rate is pays is higher, the price of the bond
will be higher than the face value
5. What’s the Yield on That?
Calculating Yield to Maturity: Zero coupon bond
• i = (FV – PV)/PV
Calculating Yield to Maturity: Perpetuity
• i = FV/PV
• Current yield: A quick but flawed method for
calculating interest rates of nonperpetual debt
– i = FV/PV
6. Calculating Returns
• Return: A measure of the profitability of an investment
that takes into account changes in the value of the bond
or other asset
• R = (C + Pt1 – Pt0)/Pt0 where
• R: return from holding the asset for some time period, t0 to t1
• Pt0: the price at time t0 (this can also be thought of as the
purchase price)
• Pt1: the price at time t1 (this can also be thought of as the sale
or going market price)
• C: coupon (or other) payment
6. Calculating Returns
• Bond prices and interest rates are inversely
related
• Even if there is no default, wealth can be lost
by investing in bonds or other fixed-rate
financial instruments, e.g. Is Treasury Bond
risk free?
6. Calculating Returns
Interest Rate Risk
• The risk that the market price of a bond or other debt
instrument will decrease due to increases in the interest
rate
Default Risk
• The risk that a bond or other debt instrument will not
make the promised payments
7. Inflation and Interest Rates
• If nominal rates do not increase:
– lenders receive more nominal dollars than they
lent but actually get back less purchasing power
7. Inflation and Interest Rates
• The Fisher Equation (approximate!!!):
i = ir + π or, ir = i – π or, π = i - ir
• ir: the real interest rate
• i: the nominal interest rate
• π: inflation (or expected inflation)
7. Inflation and Interest Rates
• Ex post: After the fact, the nominal interest
rate is equal to the real interest rate plus
actual inflation
• Ex ante: Before the fact, the nominal interest
rate is equal to the real interest rate plus the
expectation of inflation