Present Value Relations I 现值关系I
- Cashflows and Assets
What is an asset?
Business entity; property, plant, and equipment, patents, R&D; Stocks, bonds, options; Knowledge, reputation, opportunities, etc.
Patent [monopoly] - a legal agreement, grant ability of the sole user of the product for a finite period of time, sharing ideas
secret trading - keep it yourself
An asset is a sequence of current and future cashflows
- relatively to a pattern of time
- ordered in time, can be positive/negative, real numbers
Valuing an Asset Requires Valuing A Sequence of Cashflows
Value of Asset =
*Always draw a timeline to visualize the timing of cashflows
The Present Value Operator
- cashflows at different dates are different currencies
- given exchange rates [get from the market], either currency can be used as "numeraire"
steps to get the present value:
1. a numeraire date should be picked, typically t = 0 or "today"
2. cashflows can be converted to PV
Net Present Value: "net" of initial cost or investment,
- if there is an initial investment, then <0
- any future cashflow can be negative (costs)
- discount factor(due to impatience): a dollar today is not the dollar in the future, pay me 97 cents today and give you back $1 tomorrow
The Time Value of Money
Implicit assumptions/requirements for NPV Calculations:
- exchange rates are known (focus on this, where do they come from, how are they determined?)
- assume there is no frictions in current conversions
What determines the growth of $1 over T years? What determines the value today of $1 in Year T?
opportunity cost of capital r
