Normal Curve
SECTION 2: TIME VALUE OF MONEY
Decision problems in business usually involve a decision over whether to accept one alternative over another, or whether to implement a plan or not. In most cases, the effects of these decisions are felt in the future.
Examples:
Expand into a new market (geographical, consumer segment, etc.) or not? Now or later? Outsource production or keep it in-house? Grow organically or acquire a competitor? Or don't grow at all? Purchase shares in Microsoft, S&P index options, or a B-rated corporate bonds?
How could we make such decisions?
Lifeblood of a corporation:
Typical features:
How do we incorporate these two issues in our decision-making process?
Use “discounting” to “adjust” the value of future and/or risky payments!
Convert all future and/or uncertain cash flows into a “present value”!
The CAPM (we will cover its basics in this course) gives us a method to quantify our aversion to waiting (impatience) and our risk-aversion, by incorporating both into the discount rate. Notation and Terminology
Time Line: displays sizes and timing of cash flows
“Now” (“today”) is always time “zero”, i.e., the end of period “zero”.
So the first “future” cash flow accrues at time .....
We use the letter “t” to refer to a “generic” period.
“now” “in one year” “in two years” 0 1 2
CF0 CF1 CF2
APR: Annual Percentage Rate. EAR: Expected A Rate.
For simplicity, we will assume that all cash flows accrue at the very end of a “period”. That is unrealistic, but it simplifies things a bit.
Easy to adapt calculations where needed (using spreadsheets) Some asset pricing tools are based on “continuous time”: Time units are infinitesimally small (important for option pricing, dynamic hedging, high-speed trading, etc.)
Time can be measured in years (most common), or in other time
Decision problems in business usually involve a decision over whether to accept one alternative over another, or whether to implement a plan or not. In most cases, the effects of these decisions are felt in the future.
Examples:
Expand into a new market (geographical, consumer segment, etc.) or not? Now or later? Outsource production or keep it in-house? Grow organically or acquire a competitor? Or don't grow at all? Purchase shares in Microsoft, S&P index options, or a B-rated corporate bonds?
How could we make such decisions?
Lifeblood of a corporation:
Typical features:
How do we incorporate these two issues in our decision-making process?
Use “discounting” to “adjust” the value of future and/or risky payments!
Convert all future and/or uncertain cash flows into a “present value”!
The CAPM (we will cover its basics in this course) gives us a method to quantify our aversion to waiting (impatience) and our risk-aversion, by incorporating both into the discount rate. Notation and Terminology
Time Line: displays sizes and timing of cash flows
“Now” (“today”) is always time “zero”, i.e., the end of period “zero”.
So the first “future” cash flow accrues at time .....
We use the letter “t” to refer to a “generic” period.
“now” “in one year” “in two years” 0 1 2
CF0 CF1 CF2
APR: Annual Percentage Rate. EAR: Expected A Rate.
For simplicity, we will assume that all cash flows accrue at the very end of a “period”. That is unrealistic, but it simplifies things a bit.
Easy to adapt calculations where needed (using spreadsheets) Some asset pricing tools are based on “continuous time”: Time units are infinitesimally small (important for option pricing, dynamic hedging, high-speed trading, etc.)
Time can be measured in years (most common), or in other time