Interest Rates I Money amp Banking ECO 473 Dr D Foster The Basics What is interest Payment made to savers to compensate them for foregoing consumption The most powerful force in the universe is compound interest ID: 761417
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Interest Rates I: Money & Banking - ECO 473 - Dr. D. Foster The Basics
What is interest? Payment made to savers to compensate them for foregoing consumption.“The most powerful force in the universe is compound interest.” Interest rates embody our expectations of the future.
What affects interest? Who cares? Time value of moneyLiquidity Risk Savers Borrowers Policymakers Forecasters
Interest Rates & Bonds Face value (FV) $$$ mm/yyyy $ $ $ $ $ $ Bond Maturity date (in n years) Coupons & value (C) We will only consider annual coupons
Calculating Interest Nominal yield: i N = C/FCurrent yield: iC = C/P Yield to maturity (YTM) . . . interest return if bond held to maturity i = nominal interest rate aka, coupon yield
$1 today is worth more than $1 tomorrowPV shows the “discounted” value of future $ $X in “n” years = $X/[(1+i) n] todayFV show the “compounded” value of present $ $X today = $X·(1+i) n in n years Present & Future Values
You have $1000 now; i=5%, n=18. What is FV?You get $1000 in 9 years; i=7%. What is PV? You get $2000 in 4 years and $500 in 2 years; i=8%. What is the PV? Problems 1000*(1.05 18 ) = $2406 1000/(1.07 9 ) = $544 2000/(1.08 4 ) + 500/(1.08 2 ) = $1470 + $429 = $1899
If the bond price is $950, the coupon is $60 and it matures in 3 years, what is its YTM? Problems $950 = + + + Solve for i: On calculator: FV=1000 PMT=60 PV=-950 n=3 (annual) Compute i i = 7.94%
If the bond price is $950, the coupon is $60 and it matures in 3 years, what is its YTM? Problems $950 = $55.58 + $51.50 + $47.71 + $795.16 Confirm by using i = 7.94% $949.95 $950 = + + +
If the bond price is $950, the coupon is $60 and it matures in 3 years, what is its YTM? Problems $950 = + + + No financial calculator? Trial & error We know that i > 6% because … At i =7%, PV=$973.76 … too high, so iAt i=8%, PV=$948.46 … too low, but close, so i At i =7.9, PV=$950.94 … too high, closer, so …At i=7.92%, PV=$950.45 … almost there!
Interest Rates & Bond Pricing Face value (FV) $$$ mm/yyyy $ $ $ $ $ $ Bond Maturity date (in n years) Coupons & value (C) Market price of the bond = present value of income stream discounted at the relevant market interest rate : Special case: Perpetuity Price = C/ i
Monetary policy Bond Price will interest rate Fed buys bonds - price rises - interest rates fall - spending rises - GDPFed sells bonds - price falls - interest rates rise - spending falls - Inflation
Interest Rates, Bonds & the Fed Face value (FV) $$$ mm/yyyy $ $ $ $ $ $ Bond Maturity date (in n years) Coupons & value (C) When the Fed buys bonds, their prices will ___ and interest rates will ___. When the Fed sells bonds, their prices will ___ and interest rates will ___.
Quick Hits A wide spectrum of interest rates: Federal Funds ratePrime rate30 year bond rateReal interest rate (r)= i - ( = inflation)Note, this can only be calculated for past.Note, i = r e + e (e = expected values for r & ) Irving Fisher
Real and Nominal Interest Rates, 1980-2015 Nominal interest rate on 3 month Treasuries and real interest; derived as (3 month rate - CPI).
Bond Pricing Worksheet I A bond has a face value (FV) of $1000, will mature in 2024 and has an annual coupon of $74 and the market rate of interest is 8.1%. What is the current market price of this bond? Suppose that interest rates change such that the current yield on this bond is 7.067%. What will be the market price for this bond? From this find the current market interest rate. Suppose that when the bond was first sold, it’s market price was $1000. What must have been the market rate of interest then? Consider a bond with FV=$1000, maturity = 2026, C=$81 and i =7.25% What is the current price of this bond? If the Fed jumps into the bond market, even though it just buys U.S. Treasuries, it will affect all interest rates to some extent. If they buy lots of bonds and interest rates fall to 6.88%, what will happen to the price of your bond? The bond in #2 was given to you by your kindly aunt. She told you it matures in 2026, but her eyesight isn’t so good. You take a close look at the bond and see that it matures in 2022. Market i=7.25%. What is the price of this bond? Why is it different than what you calculated in #2a?
Bond Pricing Worksheet II Four years ago today, Koala, Inc. issued a 10 year bond w/coupon=$55. Initially, the bond sold for $1025. Today it is at $955. The riskless rate of interest four years ago was 4.5%; today it is 4% (including expected inflation). 1. What was the nominal and current yield on this bond at both times? 2. What was the YTM on this bond at both times? 3. What was the risk premium on this bond at both times? 4. Speculate about why the risk premium would have changed. 5. Suppose that suddenly today the riskless rate falls (from 4%) to 2.5%. a. What will be the new selling price of this bond today? b. Identify the income stream and its present value for this bond for the next 6 years. What do you notice about the sum of these PVs ? 2020 2021 2022 20232024 2025 income: PV:
Interest Rates I: Money & Banking - ECO 473 - Dr. D. Foster The Basics