Present value of a lump sum calculator

Two inputs drive present value: how far away the money is and how high the discount rate is. Here is what $10,000 is worth today across both, with annual compounding.

Read it in both directions. At 6%, $10,000 due in 20 years is worth $3,118 today, less than a third of its face value. At 12%, the same payment is worth $1,037. Both the wait and the rate matter, and they multiply each other.

A quick check is the rule of 72. Divide 72 by the rate to estimate how many years it takes for the present value to fall by half: at 6%, about 12 years. The table agrees. At 10 years the value is 56% of face, and it crosses 50% between years 11 and 12.

The formula treats the discount rate as given, and the rate is where most of the judgment sits. It should reflect what you could earn on an alternative with the same risk as the payment you are valuing. It should not reflect what you wish the money would earn.

Moving from the lowest rate to the highest here changes the answer from $8,219 to $6,209, a swing of 24%. The arithmetic is the same in every row, and the rate choice alone produces the gap. Riskier payments deserve higher rates, because there is a larger chance you will not collect in full.

For a business, build the rate from its funding costs with the WACC calculator. For a personal decision, ask what the money would earn elsewhere after tax, and use that.

The more often you compound, the lower the present value. For $10,000 in 5 years at 6%, annual compounding gives $7,472.58, monthly compounding gives $7,413.72, and the limit of continuous compounding gives $7,408.18.

The gap between annual and continuous discounting is $64.40 on $10,000. Compare that with the effect of a one-point change in the rate: moving from 6% to 7% takes the annual answer from $7,472.58 to $7,129.86, a difference of $342.72. Pick the compounding convention that matches your contract or model, and spend your effort on the rate.

A nominal rate includes expected inflation. A real rate removes it. The rule is to match the rate to the cash flows: nominal cash flows use a nominal rate, and inflation-adjusted cash flows use a real rate.

Take a 6% nominal rate and 2.5% expected inflation. The real rate is (1.06 ÷ 1.025) − 1 = 3.41%. A fixed $10,000 payment in 5 years has a present value of $7,472.58 at the nominal rate. If the payment is indexed to inflation instead, so it delivers $10,000 of today's purchasing power, it will be $10,000 × 1.025⁵ = $11,314.08 in nominal dollars. Discounted at 6%, that is worth $8,454.54 today, the same answer as discounting $10,000 at the 3.41% real rate.

The common mistake is to mix them: discounting inflation-indexed payments at a nominal rate understates their value, and discounting fixed payments at a real rate overstates it.

Settlement now or more later

You are offered $85,000 today or $100,000 in three years. At a 6% discount rate, the $100,000 is worth $100,000 ÷ 1.06³ = $83,962 today, so the $85,000 in cash is worth $1,038 more. At 4%, the later payment is worth $88,900 and waiting wins. At 8%, it is worth $79,383 and the cash wins by a wider margin.

The break-even rate is (100,000 ÷ 85,000)^(1/3) − 1 = 5.57%. If your best alternative use of the money earns more than that, take the cash. Before you decide, consider the risk that the later payment isn't made, and any tax difference between the two.

A deferred payment from a buyer

A buyer offers a $200,000 note due in 4 years. At 8%, roughly the rate a lender would charge for that buyer's risk, its present value is $200,000 ÷ 1.08⁴ = $147,006, or 73.5% of face value. If you want the equivalent of $200,000 in cash terms today, the note is worth about $53,000 less. That gap is a fair starting point when you negotiate the price or ask for a security interest.

Real decisions often involve many payments. The present value of a level annuity, a fixed payment at the end of each period, is the sum of each payment discounted separately.

Five annual payments of $10,000 at 6% have a present value of $42,124 against $50,000 of total payments. If the payments arrive at the start of each year instead (an annuity due), each one is discounted one year less, and the value rises to $44,651. For uneven cash flows, add the present values year by year and subtract the initial outlay to get net present value. The IRR calculator does this with NPV and payback together, the DCF calculator applies it to a business, and the payback period calculator covers the time to recover an outlay.

Investors value an asset as the present value of the cash it will produce. Suppose a small rental property earns $40,000 of net operating income each year for 5 years and is then sold for $500,000. At an 8% required return, the five income payments are worth $159,708 and the sale is worth $340,292 today, so the property is worth $500,000.

Raise the required return to 10% and the same cash flows are worth $151,631 plus $310,461, or $462,092. An investor who wants 10% should pay no more than that. This is the logic behind a discounted cash flow valuation, and it shows why a two-point change in the rate moves the price by about 8%. To apply it to a business, use the DCF calculator and the business valuation calculator.

• Using a rate that is too low. It makes distant payments look more valuable than they are. Choose the rate from the risk of the payment, not from a savings account.
• Mixing periods. An annual rate with monthly periods needs r ÷ 12 and 12 × years. Entering 6% with 60 periods gives a very different answer from 6% with 5 years.
• Mixing real and nominal. Match the rate to the cash flows, as shown above.
• Treating a stream like a lump sum. Discounting the total of five payments as if it arrived at the end overstates the discount. Discount each payment for its own timing.
• Ignoring taxes and fees. A lump sum and a series of payments can be taxed differently, and the after-tax figures are what you compare.
• Treating the result as certain. Present value depends on the assumed rate and on the payment actually arriving. Test a range of rates before deciding.