Again, take the mortgage case example. Initially, at month 0, you get a bunch of money from the bank (positive cash flow) to buy a house. Then, every month you pay bank a monthly payment (negative cash flow for you). The cash flow basically look like this :
Let (x0,x1,x2,...xn) be a cash flow stream. Then the Internal Rate of Return is a number r satisfying the following equation
In this case, the IRR is your mortgage rate (more specifically, APR/12, since your mortgage APR is quoted as annual rate and you pay mortgage on monthly basis).
Note that the internal rate of return is defined without reference to the market interest rate. It is determined entirely by the cash flow stream.
Now let's look at a case study :
In order to pay for a new iPad2, I want to grow Christmas trees in my backyard and later sell them. The project requires an initial investment of $100 to purchase and plant the trees. No other case flow occurs until the trees are sold. The interest rate is 10%.
I have two choices as to when to cut the tree
-- Choice 1 : cut after one year and sell for $200 USD. The cash flow is
(-$100, $200)
-- Choice 2 : cut after two year and sell for $300 USD. The cash flow is
(-$100, 0, $300)
Now, which is the better choice ? Let's look at next.
