Reading 6: Time Value of Money Flashcards
Required Rate of Return
Return (Interest Rate) that investors and savers require for them to willingly lend their funds I.e. “The Equilibrium Interest Rate”
Discount Rates
The interest rate used to discounts payments/cash flows to be made/received in the future to get to their equivalent value in current dollars
Opportunity Cost
The opportunity forgone when current consumption is chosen rather than saving.
Real Risk Free Rate
Theoretical rate of a single-period loan that has no expectation of inflation on it
Real Rate of Return
Investors increase in purchasing power (after adjusting for inflation)
Nominal Risk-Free Rates
Real risk-free rate + expected inflation rate (e.g. U.S Treasury Bills – T-Bills) (Note that this is an approximate relationship)
Default Risk
The risk that a borrower will not make the promised payments in a timely manner
Liquidity Risk
The risk of receiving less than fair value for an investment if it must be sold for cash
Maturity Risk:
Prices of long-term bonds are more volatile than shorter-term bonds. Longer-term bonds have more maturity risk and require a maturity risk premium
Required Interest Rate on a Security (Required Rate of Return)
Nominal risk-free rate +
Default risk premium +
Liquidity premium +
maturity risk premium
Effective Annual Rate (Definition)
Annual rate of return actually being earned after adjustments have been made for different compounding periods
Effective Annual Rate (Formula)
EAR = (1+Periodic Rate)m - 1
Periodic Rate = stated annual rate/m
M = number of compounding periods per year
What happens to EAR as compounding frequency increases?
EAR increases as the compounding frequency increases
Continuous Compounding (Definition)
The limit of shorter and shorter compounding periods i.e. the mathematical limit that compound interest can reach
Continuous Compounding (Formula)
Er - 1 = EAR
Future Value (Definition)
Amount to which a current deposit will grow when it is placed in an account paying compound interest
Future Value (Formula) (“Future Value Factor”)
FV = PV(1+I/Y)N
Present Value (Definition)
Today’s value of a cash flow that is to be received at some point in the future
Present Value (Formula) (“Present Value Factor”)
PV = FV/(1+1/Y)N
Discounting
The process of finding the present value of a cash flow i.e. future cash flows are discounted back to the present (also known as opportunity cost, discount rate, required rate of return, cost of capital)
Annuities
Stream of equal cash flows that occur at equal intervals over a given period
What are the two types of Annuities? Define.
- Ordinary Annuity: The most common type and characterized by cash flows that occur at the end of each compounding period (Typical cash flow pattern for many investment and business finance applications)
- Annuities Due: Payments/receipts that occur at the beginning of each period
Present Value of an Ordinary Annuity
The collective present value of a stream of cash flows that occur at the end of each compounding period over a stated number of periods
Future Value of an Annuity Due (FVAd)
FVAo x (1+I/Y) (Because FV is calculated at the end of a period whereas Annuities Due is made at the beginning of the period)
Present Value of an Annuity Due (PVAd)
PVAo x (1+I/Y)
Perpetuity (Definition)
A financial instrument that pays a fixed amount of money at set intervals over an infinite amount of time (Perpetual Annuity)
Perpetuity (Examples)
(1) British Consol Bonds
(2) Preferred Stock
As they promise fixed interest or dividend payments forever
PV of a Perpetuity (Formula)
PV = PMT/I/Y
I/Y of a Perpetuity (Formula)
I/Y = PMT/PV
PV of a Perpetuity (Definition)
PV of a Perpetuity is its value one period before the first payment i.e. if the first dividend payment occurs at Y4 then the PV will be as of Y3. The “N” variable will therefore be one less
Uneven Cash Flows
Stream of annual single sum cash flows (Sum of all the PVs/FVs of each individual cash flow)
Uneven Cash Flows (Calculator Methodology)
Use the CF Function
TVM Problems when compounding periods are other than annual
m = # of compounding periods per year I/Y = Annual Interest / m N = # of compounding periods
Loan Amortization
The process of paying off a loan with a series of periodic loan payments, whereby a portion of the loan is paid off, or amortized, with each payment
Loan Amortization (Characteristics of Payment)
Size of the payment remains fixed over the course of the loan (monthly, quarterly or annually). However, the portion of the principal/interest component of the loan does not remain fixed.
Funding a Future Obligation (Common Examples)
- Funding program for future college tuition
2. Funding a retirement program
Cash Flow Additivity Principle
Present value of any stream of cash flows equals the sum of the present values of the cash flows
Compound Annual Growth Rate (Methodology)
If given a dividend/payment at t=0 and a dividend at t=x, then you can use t=0 as the PV and t=x as the FV and solve for I/Y on the calculator
