Time Value of Money Flashcards
What is the formula for FV (without PV)
PMT.[[(1+r)^n]-1]/r
What is the formula for PV
PV=FV/(1+r)^n
What change is required when calculating Annuity Due and Ordinary Annuity
Change the calculator setting to compound at the beginning/end of the period.
[To switch between the BGN and END modes on the TI, press [2nd] [BGN] [2nd] [SET]) or(Calculate Ordinary annuity then multiply by the interest rate for one period: FVAd=FVAo.(1+i/y) and PVAd=PVAo.(1+i/y)]
What is a Discount Factor
1/(1+r)^n, also known as Present Value Interest Factor and Present Value Factor
PV(perpetuity)=
PMT/r
What is a nominal risk-free rate
Real Risk-Free Rate + Expected Inflation Rate
What is Maturity Risk
Refers to the uncertainty and opportunity cost of holding a security over a LONG period of time
What are the 3 ways of interpreting Interest Rates
Equilibrium Interest Rate or discount rate for calculating the PV of future cash flows or opportunity cost
How do you calculate FV or PV for uneven cash flows?
Treat each cash flow like a single sum, then sumup the answers.
Remember, for FV, N=period cash is held.
Suppose you must make five annual $1000 payments, the first one starting at the beginning of Year 4 (end of year 3). To accumulate the money to make these payments, you want to make 3 equal payments into and investment account, the first to be made one year from today. Assuming a 10% rate of return, what is the amount of these 3 payments?
Page 29, kaplan book.
Key Idea: To find the present value of the annuity due, the day the first payment must be made. There is more to the question however.
In this case the PV is the amount needed to meet the goal.
PV of a series of cash flows can be seen as the amount required to deposit today in order to make these future withdrawals and EXHAUST THE ACCOUNT with the final withdrawal.
For example $100 in Year 1, $200 in Year 2, $300
in Year 3, and an assumed interest rate of 10%.
100/1.1+200/1.1^2+300/1.1^3=$481.59.
To be sure of this it will help you to shift everything to the right side of the equation bit by bit: (multiply by 1.1, then minus 100 and so on)
What is used to refer to the answer of the following question; “How much would be in an account when the last of a series of deposits is
made?”
Future Value.
Remember there can be additional yearly payments plus the interest, a calculator tip for this would be as follows (using 100 yr 1, 22 yr 2 etc… as an example) : [(100 × 1.1) + 200] × 1.1 + 300 = 641 ……. Furthermore, for annuity due there is an extra compounding period.
What is the ADDITIVITY PRINCIPLE of present value
The PV of any stream of cash flows is the sum of the Present Values of the cash flows.
eg The additivity principle tells us that to get the present value of the original series, we can just
add the present values of series #1 (a 4-period annuity) and series #2 (a single payment three
periods from now).
For the annuity: N = 4; PMT = 100; FV = 0; I/Y = 10; CPT → PV = −$316.99
For the single payment: N = 3; PMT = 0; FV = 300; I/Y = 10; CPT → PV = −$225.39
The sum of these two values is 316.99 + 225.39 = $542.38.
There are two ways to use your financial calculator to compute PVs and FVs under different compounding periods:
- Adjust the number of periods per year (P/Y) mode on your calculator to correspond to the
compounding frequency (e.g., for quarterly, P/Y = 4). WE DO NOT RECOMMEND THIS
APPROACH! - Keep the calculator in the annual compounding mode (P/Y = 1) and enter I/Y as the interest
rate per compounding period, and N as the number of compounding periods in the
investment horizon. Letting m equal the number of compounding periods per year, the basic
formulas for the calculator input data are determined as follows:
I/Y = the annual interest rate/m
N = the number of years × m
The rate of interest that investors actually
realize as a result of compounding is known as:
the effective annual rate (EAR) or effective annual yield (EAY). EAR represents the annual rate of return actually being earned after
adjustments have been made for different compounding periods.
