Intro to Valuation: The Time Value of Money
What do we mean by the future value of an investment?
The cash value of an investment at some time in the future
What is the rule of 72
A shortcut that allows you to estimate the time it would take for an investment to double by dividing 72 by the annual interest rate.
What do we mean by discounted cash flow, or DCF, valuation?
Discounted cash flow (DCF) - Calculating the present value of a future cash flow to determine its worth today. Discount rate - the rate used to calculate the present value of future cash flow *Ex: suppose you need $1,000 in three years. You can earn 15% on your money. How much do you have to invest today? To find out, we determine the present value of $1,000 in three years at 15%. We do this by discounting $1,000 back three periods at 15%.* *As the length of time until payment grows, present values decline.
In general, what is the future value of $1 invested at r per period for t periods
Future value formula = $1 x (1 + r) ^t
Compound Interest
Interest earned on both the initial principal (money invested) and the interest reinvested from prior periods.
Simple Interest
Interest earned only on the original principal amount invested.
What does it mean to compound interest? How does compound interest differ from simple interest?
- Compounding interest means to leave your money and any accumulated interest in an investment for more than one person (reinvesting the interest). - Compound interest differs from simple interest because with simple interest, the interest is not reinvested.
What do we mean by the present value of an investment?
- The reverse of future value —> instead of compounding money forward into the future, we discount it back to the present. Ex: What amount, if invested today, will grow to x amount of money in one year if the interest rate is 10 percent? —> The amount invested today is the present value.
The process of discounting a future amount back to the present is the opposite of doing what?
Compounding or calculating the future value
What is the basic present value equation?
PV = present value FV = future value t = the life of the investment r = the discount rate PV = FVt / (1+r) ^t
Future Value
The amount an investment is worth after one or more periods.
Present Value
The current value of future cash flows discounted at the appropriate discount rate.
Interest on Interest
interest earned on the reinvestment of previous interest payments (what you earn with compound interest)