Present Value Calculator
Present value of a lump sum, an annuity or a cash flow series, shown across four discount rates because the rate decides the answer.
Cash flows 6
period 0 -$120,000.00 → -$120,000.00 today
period 1 $32,000.00 → $28,571.43 today
period 2 $38,000.00 → $30,293.37 today
period 3 $44,000.00 → $31,318.33 today
period 4 $51,000.00 → $32,411.42 today
period 5 $58,000.00 → $32,910.76 today
Net present value $35,505.31
at 12%
decision worth doing at this discount rate
Internal rate of return 22.17%
sign changes 1
NPV at other rates
4% $76,284.99
8% $54,097.47
12% $35,505.31 ← yours
20% $6,422.33
The discount rate is the calculation. At 12% the answer is what it is
above; the table shows what happens at other rates, and the spread is
usually wider than any disagreement about the cash flows.
Use your own cost of capital rather than a number that feels prudent.
For a company it is what the money costs, or what it would earn in the
next best use; for a private business, 15 to 30 percent is the usual
range and it reflects how risky and illiquid the thing is.
The internal rate of return assumes every interim cash flow is
reinvested at the same rate, which is rarely true, and a series whose
sign changes more than once can have several rates that give a zero net
present value. When NPV and IRR disagree, NPV is the one to follow.
A perpetuity is payment divided by rate, and the arithmetic is worth
knowing because it shows how little the distant future contributes. At
10 percent, everything beyond year 30 is under 6 percent of the total
value, which is why a terminal value in a valuation is a smaller claim
than it looks and a discount rate is a larger one.
Inflation belongs in one place, not two. Either discount nominal cash
flows at a nominal rate, or real cash flows at a real rate. Mixing them,
which usually means real cash flows at a nominal rate, understates the
answer by roughly the inflation rate compounded.
Present value says nothing about risk beyond what the rate carries. Two
projects with the same NPV and different variance are not the same
decision, and raising the discount rate is a crude way to express that:
it penalises distant cash flows rather than uncertain ones.
The period does not have to be a year. Use monthly flows with a monthly
rate, which is the annual rate compounded down rather than divided by
twelve, and keep the two consistent.
Output is valid and updates as you type.
Fix the highlighted fields to update the output.
A pound in five years is worth 68 pence today at 8 percent, and 57 pence at 12. The cash flows did not change; the discount rate did, and that single assumption moves a decision further than any disagreement about the forecast.
So the answer here is always shown at four rates. Present value is arithmetic once the rate is chosen, and choosing the rate is the analysis.
How to use
- Pick a lump sum, a level stream of payments, or an explicit list of cash flows.
- Set the discount rate: your own cost of capital, not a number that feels prudent.
- Read the table of rates before quoting any single figure.
Example
An investment of 120,000 returning five years of growing cash, discounted at 12 percent:
period 0 -$120,000.00 → -$120,000.00 today
period 1 $32,000.00 → $28,571.43 today
period 5 $58,000.00 → $32,910.76 today
Net present value $35,505.31
decision worth doing at this discount rate
Internal rate of return 22.17%
sign changes 1
NPV at other rates
4% $76,284.99
8% $54,097.47
12% $35,505.31 ← yours
20% $6,422.33At 20 percent this is nearly a coin flip. That range is the honest presentation, and a single NPV quoted without its rate is a number without a claim attached.
Pitfalls
The discount rate is an assumption, not a fact. For a company, it is the cost of capital: what the money costs or what it would earn in the next best use. For a private business, 15 to 30 percent is the usual range, reflecting risk and illiquidity.
IRR assumes reinvestment at the same rate. Every interim cash flow is treated as reinvested at the internal rate, which is rarely available. That is why a 40 percent IRR on a small project is not comparable with a 20 percent one on a large.
A series can have several IRRs. Each time the sign of the cash flow changes, another root becomes possible. The output counts the sign changes for that reason, and where NPV and IRR disagree, NPV is the one to follow.
Keep inflation in one place. Either nominal cash flows at a nominal rate, or real cash flows at a real rate. The common mistake is real cash flows at a nominal rate, which understates the answer by roughly the inflation rate compounded over the term.
A perpetuity shows how little the far future matters. Payment over rate is the whole value; at 10 percent, everything beyond year thirty is under 6 percent of it. That is worth knowing both for terminal values in a valuation and for arguments about the distant future.
Present value is not a risk measure. Two projects with the same NPV and different variance are not the same decision. Raising the discount rate to express risk penalises distant cash flows rather than uncertain ones, which is a crude proxy and the usual one.
Match the period to the rate. Monthly cash flows need a monthly rate, and a monthly rate is the annual one compounded down rather than divided by twelve.
Compatibility
Arithmetic in the browser: nothing is uploaded and nothing is stored.
Payments in the annuity mode arrive at the end of each period, which is the ordinary convention; payments at the start are worth one more period, a factor of (1 + rate). The series mode places the first entry at time zero, undiscounted, which is where an initial investment belongs.
The internal rate of return is found by bisection rather than Newton’s method, because bisection cannot diverge, and the test suite checks it against cases with known answers: −100, 60, 60 gives 13.066 percent. Where the bracket contains no crossing the output says there is no single rate rather than printing one.
Cash flows are read from commas, spaces or newlines, and commas that are thousands separators are removed
first, so -120,000, 32,000 reads as two numbers rather than four.