2. Present and Future Values Flashcards
What is the definition of “Present Value”?
Value today of a future cash flow
What is the definition of “Future Value”?
Amount to which an investment will grow after earning interest
How would you write a formula to calculate the Future Value of $100?
where:
r = interest rate
t = time
What would be the power (variable t) if you are calculating on a 2 year timespan?
2
What is the interest that you earn called?
COMPOUND INTEREST
How do you calculate the present value if you have the discount factor?
Multiply the amount by the discount factor
What are the 3 rules of Time Travel
1) Only values at the same point in time can be compared or combined
2) To move a cash flow forward in time, you must compound it
3) To move a cash flow backward in time, you must discount it
What is the formula to calculate the discount factor?
Say a building costs 700k to build, and is sold after a year for 800k, at a cost of capital of 7%, what is the rate of return?
What happens if the discount rate increases?
The PV will decrease
What is the opportunity cost of capital (r)?
The opportunity cost of capital is the rate of return that the shareholders could get by investing on their own at the same level of risk
Whenever the return is greater than the opportunity cost of capital (r), the NPV must be greater than ___
0
What is important about small NPVs?
If the NPV is very small, if things change (Risk of project - discount rate), then you could be in the negative. So not EVERY positive NPV investment is necessarily great.
What is the “Internal Rate of Return”?
The internal rate of return (IRR) is the discount rate that makes the net present value (NPV) of a project zero.
What is a “perpetuity”?
“A perpetuity is a financial concept in which a cash flow is theoretically received forever”
How would you calculate the “return” - perpetuities?
How would you calculate the PV of a cash flow?
Add ALL cash flows together, and divide it by the discount rate
What is the PV of $1 billion every year, for all eternity, if you estimate the perpetual discount rate to be 10%?
What is the PV of $1 billion every year, for all eternity, if you estimate the perpetual discount rate to be 10%?
BUT: the investment does NOT start making money for 3 years…
What is an “annuity”?
An asset that pays a fixed sum each year for a specified number of years
How do you calculate the PV of an annuity?
where C is the CONSTANT cash flow
How do you calculate the FV of an annuity?
What is the present value of growing perpetuity?
Used if we need to value a stream of cash flows that grows at a constant rate
What is the present value of $1 billion paid at the end of every year in perpetuity, assuming a rate of return of 10% and a constant growth rate of 4%?
What is the “Annual Percentage Rate”?
Interest rate that is annualized using simple interest
–> IGNORES compounding, does NOT say how much interest an investor accumulates over the year
What is the “Effective Annual Interest Rate”?
Interest rate that is annualized using compound interest
How do you calculate the Annual Percentage Rate (AR)?
Annual Percentage Rate (APR):
APR = MR x 12
–> where MR is monthly interest rate
How do you calculate the Effective Annual Interest Rate (EAR)?
Effective Annual Interest Rate (EAR):
EAR = (1+MR)^12 - 1
–> where mr = monthly interest rate
How do you calculate the Effective Annual Interest Rate (EAR) that is compounded M times per year?
EAR = (1+((r/m))^m - 1
–> where mr = monthly interest rate, r is yearly rate, m is number of times per year compounding
