Cash flows, NPV and IRR
Cash flow series
3 min
Real investments rarely involve a single payment. They are series of cash flows — money going out and coming in across many periods. Learning to lay these out cleanly is the foundation of NPV and IRR.
The timeline
A cash flow series is a list of amounts, one per period, with a sign:
- Negative = money you pay out (an investment, a cost).
- Positive = money you receive (a return, income).
Suppose a project costs 10,000 units today and returns 4,000, 4,000 and 5,000 over the next three years. The timeline is:
Period 0: -10,000
Period 1: +4,000
Period 2: +4,000
Period 3: +5,000
You cannot just add them up
A naive total is +3,000 (the flows sum to 13,000 in, 10,000 out). But that ignores when each amount arrives. The 5,000 in year 3 is worth far less than 5,000 today, as the discounting lesson showed.
To value the series correctly, you discount each flow to today and then add the present values:
PV of series = CF0 + CF1/(1+i) + CF2/(1+i)^2 + CF3/(1+i)^3
That sum is the heart of NPV, which we compute fully in two lessons. First, a special, very common shape of series: the annuity.
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