Chapter Two Determinants of Interest Rates Mc GrawHillIrwin

Chapter Two Determinants of Interest Rates Mc. Graw-Hill/Irwin 1 © 2007, The Mc. Graw-Hill Companies, All Rights Reserved

Interest Rate Fundamentals • Nominal interest rates - the interest rate actually observed in financial markets – directly affect the value (price) of most securities traded in the market – affect the relationship between spot and forward FX rates Mc. Graw-Hill/Irwin 2 © 2007, The Mc. Graw-Hill Companies, All Rights Reserved

Time Value of Money and Interest Rates • Assumes the basic notion that a dollar received today is worth more than a dollar received at some future date • Compound interest – interest earned on an investment is reinvested • Simple interest – interest earned on an investment is not reinvested Mc. Graw-Hill/Irwin 3 © 2007, The Mc. Graw-Hill Companies, All Rights Reserved

Calculation of Simple Interest Value = Principal + Interest (year 1) + Interest (year 2) Example: $1, 000 to invest for a period of two years at 12 percent Value = $1, 000 + $1, 000(. 12)(2) = $1, 240 Mc. Graw-Hill/Irwin 4 © 2007, The Mc. Graw-Hill Companies, All Rights Reserved

Value of Compound Interest Value = Principal + Interest + Compounded interest Value = $1, 000 + $1, 000(. 12) = $1, 000[1 + 2(. 12) + (. 12)2] = $1, 000(1. 12)2 = $1, 254. 40 Mc. Graw-Hill/Irwin 5 © 2007, The Mc. Graw-Hill Companies, All Rights Reserved

Present Value of a Lump Sum • PV function converts cash flows received over a future investment horizon into an equivalent (present) value by discounting future cash flows back to present using current market interest rate – lump sum payment – annuity • PVs decrease as interest rates increase Mc. Graw-Hill/Irwin 6 © 2007, The Mc. Graw-Hill Companies, All Rights Reserved

Calculating Present Value (PV) of a Lump Sum PV = FVn(1/(1 + i/m))nm = FVn(PVIFi/m, nm) where: PV = present value FV = future value (lump sum) received in n years i = simple annual interest rate earned n = number of years in investment horizon m = number of compounding periods in a year i/m = periodic rate earned on investments nm = total number of compounding periods PVIF = present value interest factor of a lump sum Mc. Graw-Hill/Irwin 7 © 2007, The Mc. Graw-Hill Companies, All Rights Reserved

Calculating Present Value of a Lump Sum • You are offered a security investment that pays $10, 000 at the end of 6 years in exchange for a fixed payment today. PV = FV(PVIFi/m, nm) • • at 8% interest - = $10, 000(0. 630170) = $6, 301. 70 • at 12% interest - = $10, 000(0. 506631) = $5, 066. 31 • at 16% interest - = $10, 000(0. 410442) = $4, 104. 42 Mc. Graw-Hill/Irwin 8 © 2007, The Mc. Graw-Hill Companies, All Rights Reserved

Calculation of Present Value (PV) of an Annuity nm PV = PMT (1/(1 + i/m))t = PMT(PVIFA i/m, nm) t=1 where: PV = present value PMT = periodic annuity payment received during investment horizon i/m = periodic rate earned on investments nm = total number of compounding periods PVIFA = present value interest factor of an annuity Mc. Graw-Hill/Irwin 9 © 2007, The Mc. Graw-Hill Companies, All Rights Reserved

Calculation of Present Value of an Annuity You are offered a security investment that pays $10, 000 on the last day of every year for the next 6 years in exchange for a fixed payment today. PV = PMT(PVIFAi/m, nm) at 8% interest - = $10, 000(4. 622880) = $46, 228. 80 If the investment pays on the last day of every quarter for the next six years at 8% interest - = $10, 000(18. 913926) = $189, 139. 26 Mc. Graw-Hill/Irwin 10 © 2007, The Mc. Graw-Hill Companies, All Rights Reserved

Future Values • Translate cash flows received during an investment period to a terminal (future) value at the end of an investment horizon • FV increases with both the time horizon and the interest rate Mc. Graw-Hill/Irwin 11 © 2007, The Mc. Graw-Hill Companies, All Rights Reserved

Future Values Equations FV of lump sum equation FVn = PV(1 + i/m)nm = PV(FVIF i/m, nm) FV of annuity payment equation (nm-1) FVn = PMT (1 + i/m)t = PMT(FVIFAi/m, mn) (t = 0) Mc. Graw-Hill/Irwin 12 © 2007, The Mc. Graw-Hill Companies, All Rights Reserved

Calculation of Future Value of a Lump Sum • You invest $10, 000 today in exchange for a fixed payment at the end of six years – – at 8% interest = $10, 000(1. 586874) = $15, 868. 74 at 12% interest = $10, 000(1. 973823) = $19, 738. 23 at 16% interest = $10, 000(2. 436396) = $24, 363. 96 at 16% interest compounded semiannually • = $10, 000(2. 518170) = $25, 181. 70 Mc. Graw-Hill/Irwin 13 © 2007, The Mc. Graw-Hill Companies, All Rights Reserved

Calculation of the Future Value of an Annuity • You invest $10, 000 on the last day of every year for the next six years, – at 8% interest = $10, 000(7. 335929) = $73, 359. 29 • If the investment pays you $10, 000 on the last day of every quarter for the next six years, – FV = $10, 000(30. 421862) = $304, 218. 62 • If the annuity is paid on the first day of each quarter, – FV = $10, 000(31. 030300) = $310, 303. 00 Mc. Graw-Hill/Irwin 14 © 2007, The Mc. Graw-Hill Companies, All Rights Reserved

Relation between Interest Rates and Present and Future Values Present Value (PV) Future Value (FV) Interest Rate Mc. Graw-Hill/Irwin 15 © 2007, The Mc. Graw-Hill Companies, All Rights Reserved

Effective or Equivalent Annual Return (EAR) Rate earned over a 12 – month period taking the compounding of interest into account. EAR = (1 + r) c – 1 Where c = number of compounding periods per year Mc. Graw-Hill/Irwin 16 © 2007, The Mc. Graw-Hill Companies, All Rights Reserved

Loanable Funds Theory • A theory of interest rate determination that views equilibrium interest rates in financial markets as a result of the supply and demand for loanable funds Mc. Graw-Hill/Irwin 17 © 2007, The Mc. Graw-Hill Companies, All Rights Reserved

Supply of Loanable Funds Interest Rate Demand Supply Quantity of Loanable Funds Supplied and Demanded Mc. Graw-Hill/Irwin 18 © 2007, The Mc. Graw-Hill Companies, All Rights Reserved

Funds Supplied and Demanded by Various Groups (in billions of dollars) Funds Supplied Funds Demanded Households Business - nonfinancial Business - financial Government units Foreign participants Mc. Graw-Hill/Irwin $34, 860. 7 12, 679. 2 31, 547. 9 12, 574. 5 8, 426. 7 19 $15, 197. 4 30, 779. 2 45061. 3 6, 695. 2 2, 355. 9 Net $19, 663. 3 -12, 100. 0 -13, 513. 4 5, 879. 3 6, 070. 8 © 2007, The Mc. Graw-Hill Companies, All Rights Reserved

Determination of Equilibrium Interest Rates D S Interest Rate IH i E IL Q Mc. Graw-Hill/Irwin 20 Quantity of Loanable Funds Supplied and Demanded © 2007, The Mc. Graw-Hill Companies, All Rights Reserved

Effect on Interest rates from a Shift in the Demand Curve for or Supply curve of Loanable Funds Increased supply of loanable funds Increased demand for loanable funds Interest Rate SS DD DD SS* i* E E* i** Q* Q** Mc. Graw-Hill/Irwin i* Quantity of Funds Supplied 21 DD* E Q* Q** SS E* Quantity of Funds Demanded © 2007, The Mc. Graw-Hill Companies, All Rights Reserved

Factors Affecting Nominal Interest Rates • • • Inflation Real Interest Rate Default Risk Liquidity Risk Special Provisions Term to Maturity Mc. Graw-Hill/Irwin 22 © 2007, The Mc. Graw-Hill Companies, All Rights Reserved

Inflation and Interest Rates: The Fisher Effect The interest rate should compensate an investor for both expected inflation and the opportunity cost of foregone consumption (the real rate component) i = RIR + Expected(IP) RIR = i – Expected(IP) or Example: 3. 49% - 1. 60% = 1. 89% Mc. Graw-Hill/Irwin 23 © 2007, The Mc. Graw-Hill Companies, All Rights Reserved

Default Risk and Interest Rates The risk that a security’s issuer will default on that security by being late on or missing an interest or principal payment DRPj = ijt - i. Tt Example for December 2003: DRPAaa = 5. 66% - 4. 01% = 1. 65% DRPBaa = 6. 76% - 4. 01% = 2. 75% Mc. Graw-Hill/Irwin 24 © 2007, The Mc. Graw-Hill Companies, All Rights Reserved

Term to Maturity and Interest Rates: Yield Curve (a) Upward sloping (b) Inverted or downward sloping (c) Flat Yield to Maturity (a) (c) (b) Time to Maturity Mc. Graw-Hill/Irwin 25 © 2007, The Mc. Graw-Hill Companies, All Rights Reserved

Term Structure of Interest Rates • Unbiased Expectations Theory • Liquidity Premium Theory • Market Segmentation Theory Mc. Graw-Hill/Irwin 26 © 2007, The Mc. Graw-Hill Companies, All Rights Reserved

Forecasting Interest Rates Forward rate is an expected or “implied” rate on a security that is to be originated at some point in the future using the unbiased expectations theory _ _ 1/2 - 1 R = [(1 + R )(1 + ( f ))] 1 2 1 where 2 f 1 Mc. Graw-Hill/Irwin = expected one-year rate for year 2, or the implied forward one-year rate for next year 27 © 2007, The Mc. Graw-Hill Companies, All Rights Reserved