Present Value

Present value (PV) is the value today of an amount of money that will be received or paid in the future. Because money available now can be invested to earn a return, a dollar received in the future is worth less than a dollar today. Present value converts future amounts into today's terms by discounting them at an appropriate interest rate, known as the discount rate. The idea is the foundation of the time value of money.

Present value is the reverse of compounding. Where compound interest shows how much a sum invested today will grow to, present value shows how much needs to be invested today to reach a given future amount. It is used to value bonds, loans, leases and pension obligations, to compare investment options, and to measure many assets and liabilities in financial statements.

For a single future amount, the formula is:

• $PV$ is the present value.
• $FV$ is the future amount to be received or paid.
• $r$ is the discount rate per period.
• $n$ is the number of periods until the payment.

The factor $1 \div (1 + r)^{n}$ is called the discount factor or present value factor. The higher the rate or the longer the wait, the smaller the present value.

A business is promised $10,000 in three years. If it could earn 5 percent a year elsewhere, the present value is $10,000 divided by 1.05 to the power of 3, or $10,000 times about 0.8638, which is $8,638.38. That means the business should be indifferent between receiving $8,638.38 today and $10,000 in three years.

For a series of future cash flows, the present value is the sum of the present values of each one. A project that will return $4,000 at the end of each of the next three years has a present value at 5 percent of $3,809.52 plus $3,628.12 plus $3,455.35, or $10,892.99. If the project costs $10,000 today, its net present value (NPV) is about $893, so it adds value at that rate. Equal regular payments like these form an annuity, for which shortcut formulas exist.

• Bonds and notes: debt is issued at the present value of its interest and principal payments, discounted at the market rate, which determines whether it sells at a premium or discount.
• Leases: lessees record lease liabilities at the present value of future lease payments under ASC 842 and IFRS 16.
• Pensions: defined benefit obligations are the present value of expected future benefit payments.
• Long-term provisions: obligations such as asset retirement and environmental cleanup are measured at present value where the effect is material.
• Impairment and fair value: value-in-use tests under IFRS and income-approach fair values rely on discounted cash flows, as in the discounted cash flow model.
• Long-term receivables and payables with no or below-market interest are recorded at present value, with the difference recognized as interest over time.

The result depends heavily on the discount rate. It should reflect the risk-free rate, expected inflation and the risk of the specific cash flows. Accounting standards specify the rate for some items: the market rate at issue for bonds, the rate implicit in the lease or the incremental borrowing rate for lessees, and high-quality corporate bond yields for pensions. Small changes in the rate can produce large changes in value, especially for long-dated cash flows: at 5 percent, $1,000,000 due in 30 years is worth about $231,000 today, but at 7 percent it is worth only about $131,000. Present value calculations are also only as reliable as the cash flow forecasts they discount. The rate that makes present value equal a given price is the internal rate of return (IRR).