Chapter 4: Interest Rates Objectives 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.

Interest rates are crucial determinants of 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 Interest is more valuable when received sooner than end of the year Interest may be compounded 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

i = ir + π or, ir = i – π or, π = i - ir 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