Interest Rate Meaning: An interest rate can represent:
- Required Rate of Return
- Discount Rate
- Opportunity Cost
1.Interpretation of Interest Rates (LOS 1.a)
Definitions
Discount Rate:
Minimum rate needed to justify investment risk.
Discount Rate
Used to calculate the present value of future cash flows.
Opportunity Cost
Reflects the cost of consuming now versus investing for future gains.
2.Types of Risk-Free Rates (LOS 1.b)
Real Risk-Free Rate: Theoretical return on a riskless investment with no inflation expectation (often in short periods).
Nominal Risk-Free Rate: Incorporates the real risk-free rate plus expected inflation.
- Formula: Nominal Risk-Free Rate = Real Risk-Free Rate + Expected Inflation Rate.
3.Risk Premiums in Interest Rates
Securities carry additional risks that increase the required rate of return:
- Default Risk Premium: Compensates for the risk of non-payment.
- Liquidity Premium: Compensates for potential difficulties in selling the security quickly without a discount.
- Maturity Risk Premium: Reflects the risk associated with longer maturities (price volatility increases with time).
To remember :
Formula: Required Rate of Return = Real Risk-Free Rate + Expected Inflation + Default Risk Premium + Liquidity Premium + Maturity Risk Premium.
4.Time Value of Money (TVM) Concepts
Future Value (FV): The amount an investment will grow to over a period with compound interest.
- Formula: FV=PV×(1+I/Y)N
Present Value (PV): The value today of a future sum, discounted at a specified interest rate.
- Formula: PV=FV/(1+I/Y)N
Effective Annual Rate (EAR): Reflects the actual annual interest earned or paid, accounting for compounding.
To remember :
EAR or EAY
- Formula (for m compounding periods):EAR=(1+stated rate/m)m−1
- Observation: As compounding frequency increases, so does the EAR.
5.Time Lines in TVM Calculations
To remember :
Time Line Usage: A visual tool for illustrating cash flows over time to aid in solving TVM problems.
- Cash flows are marked at period ends.
- The end of one period aligns with the start of the next.
6.Annuities and Perpetuities
Annuity: Series of equal cash flows at regular intervals.
- Ordinary Annuity: Payments occur at the end of each period.
- Annuity Due: Payments occur at the beginning of each period.
Perpetuity: An annuity with an infinite life (no end date).
To remember :
Present Value of Perpetuity formula: PV=PMT/(I/Y)
7. Non-Annual Compounding Adjustments
Either:
- Use formula to find EAR with SAR
- Adjust Rate: Divide the stated annual rate by the number of periods per year (m) AND Adjust Periods: Multiply the number of years by the compounding periods per year.
Or:
To remember :
Interest rate conversion: Use calculator 2nd - ICONV AND Set NOM to SAR - Set C/Y to compounding frequency - CPT the EFF (EAR).
