How to Calculate the Present Value of Cash Flows
Learn to assess the value of future cash flows by translating them into today's dollars, a core skill for financial analysis and decision-making.
The concept of present value is based on the time value of money, the principle that a specific amount of money is worth more now than the same amount in the future. Money on hand today can be invested to earn a return, and its purchasing power is higher before being eroded by inflation. Evaluating future amounts in today’s dollars allows for a fair comparison between cash received at different points, creating a baseline for financial decisions.
Key Inputs for the Calculation
To determine the present value of a future sum, three inputs are required. The first is the future cash flow, which is the amount of money you expect to receive at a future date. This could be a single payment, like the proceeds from selling an asset, or a series of payments over time.
The second input is the discount rate, which is the interest rate used to bring future cash flows back to their present-day value. It represents the return you could have earned on an investment of similar risk, also known as opportunity cost. For example, if you could have invested your money for a 7% annual return, that 7% is the opportunity you forgo by waiting for the future payment.
The discount rate must also account for the risk associated with receiving the cash flow, as higher risk demands a higher discount rate. For corporations, this rate is often their Weighted Average Cost of Capital (WACC). Individuals might base the rate on the expected return of a market index or a risk-free rate, such as the yield on a U.S. Treasury bond, plus an added percentage for risk.
The final input is the number of periods, representing the time between now and when the cash flow will be received. This is measured in units like years, quarters, or months. The time period must correspond to the discount rate, so an annual discount rate requires the number of periods to be in years.
The Calculation Process
The formula for calculating present value (PV) is PV = CF / (1 + r)^n. In this formula, “CF” is the future cash flow, “r” is the periodic discount rate expressed as a decimal, and “n” is the number of periods. The denominator, (1 + r)^n, is the compounding factor that reverses the effect of compound interest to determine the current worth.
For example, imagine you are promised $1,000 in five years and use a discount rate of 8%. The future cash flow (CF) is $1,000, the discount rate (r) is 0.08, and the number of periods (n) is 5. Plugging these into the formula gives you: PV = $1,000 / (1 + 0.08)^5. The calculation simplifies to PV = $1,000 / 1.4693, resulting in a present value of approximately $680.58.
Many financial situations involve multiple cash flows over different time periods. To find the total present value, you must calculate the present value of each individual cash flow separately and then sum the results. For instance, if you expect $500 in one year and $800 in two years with a 6% discount rate, you would perform two separate calculations. The first would be $500 / (1.06)^1 = $471.70, and the second would be $800 / (1.06)^2 = $712.00, for a total present value of $1,183.70.
A series of identical payments at regular intervals is known as an annuity. While you can calculate the present value of each payment, specialized annuity formulas exist to simplify the process. These formulas provide a shortcut for finding the total present value of the entire stream in a single step.
Applying Present Value with Net Present Value
A primary application of present value is determining the Net Present Value (NPV) of an investment. NPV is a method used in capital budgeting to assess the profitability of a project. It provides a metric for deciding whether an investment is likely to create value.
The calculation for NPV is the sum of the present values of all expected future cash flows minus the initial investment cost. The initial investment is treated as a negative cash flow at period zero, so its present value is its actual cost. The formula is: NPV = (PV of all future cash inflows) – (Initial Investment).
The decision rule for NPV is based on the result. A positive NPV suggests the investment will be profitable, as the present value of earnings exceeds the costs. Conversely, a negative NPV suggests a net loss, and the project should be rejected. An NPV of zero means the project is expected to earn exactly its required rate of return.
Consider a business owner deciding whether to purchase a new machine for $20,000. The machine is expected to generate cash flows of $6,000 per year for four years, and the company’s discount rate is 10%. The owner would calculate the present value of each $6,000 cash flow and sum them. After finding the total present value of the inflows, they subtract the $20,000 initial cost, and if the resulting NPV is positive, the purchase is justified.