Concept The of Net Present Value
Lecture 2 12 September 2009
Functions of money
Medium of exchange Means of payment Unit of account Store of value
Value of a good or service price Value of money = purchasing power
Time value of money
$1 now is not the same as $1 in a weeks time, because money changes its value over time
Inflation Growth of wealth ?
The time value of money is how much one unit of money is worthier today than it is tomorrow or at any other date in the future
Definition of interest rate - 1
An interest rate is the price a borrower pays for the use of money that he doesnt own, and the return a lender receives for deferring his consumption by lending to the borrower. Interest rates are normally expressed as a percentage over the period of one year. It is usually denoted as r or i.
Definition of interest rate - 2
An interest rate is the return you get on some investment One-year interest rate can be expressed by the following formula:
profit = ... investment investment _ valuet +1 investment _ valuet CFt +1 CFt CFt +1 ... = = = 1 investment _ valuet CFt CFt r=
Definition of interest rate - 3
Opportunity cost of holding money
Return foregone = loss Loss of value = loss of purchasing power When interest rate increases, the opportunity cost of holding money also increases => composition of wealth changes Low interest rates (what are the current rates in developed countries?) => liquidity trap (people are indifferent between investing and holding cash)
W=M+I
Comparing alternatives with interest rates (example)
Lets assume that you face two mutually exclusive opportunities:
To lend me $10 today for $12 in one year OR To lend me $9 today in exchange for $11 in one year
When deciding which one to choose you would find that opportunity 1 offers you a 20% return while opportunity 2 more than 22%. So, opportunity 2 is more profitable and you would choose it. What if we deal with a more complicated case?
More periods investment Different horizons Different risks
The concept of present value
The present value of a cash flow is the amount of money one would agree to receive right now in exchange of getting this cash flow in the future.
The concept of present value: Advantages
One could easily add PVs o various cash flows while you could NOT sum up the flows themselves (because of the time value of money)
Value additivity principle: PV (CF1 and CF2) = PV (CF1) + PV (CF2)
Investments with different horizons can now be compared Investments with different initial outlays can be compared
The concept of Net Present Value
The Net Present Value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows
NPV =
t =1
T
CFt (1 + r )
t
CF0
Decision rule
If the present value of cash inflows exceeds the present value of outflows, the project is worth investing in it: If NPV > 0 => accept the project If the present value of cash inflows is less than that of cash outflows, the project decreases your welfare and should be rejected If NPV < 0 => reject the project If NPV = 0 => youre indifferent
The concept of NPV: calculation example
Assume the discount rate is 10% p.a.
Time period 0 1 2 3 4 Cash Flow -500,0 100 120 160 210 Discount factor DCF
The concept of NPV: calculation example
Assume the discount rate is 10% p.a.
Time period 0 1 2 3 4 Cash flow -500,0 100,0 120,0 160,0 210,0 Discount factor 1 0,9091 0,8264 0,7513 0,6830 Net Present Value DCF -500,00 90,91 99,17 120,21 143,43 -46,27
Intertemporal consumption choice and NPV
Time value of money can differ among individuals => for some it is low, for others high (measured by the subjective rate of time preferences which describe the utility function)
Individuals can trade current consumption for future consumption Individuals try to maximize wealth
Non-satiation axiom
Wealth maximization = NPV maximization
Intertemporal consumption choice