Blog · Finance metrics and formulas · Finance and FP&A teams
A constant perpetual cash flow is an equal business cash payment expected to continue indefinitely. Calculate its present value, test the payment timing and compare supplied cash and discount-rate assumptions before a capital decision.
Perpetual cash flow is a recurring business cash stream assumed to continue indefinitely; the constant case has no growth. Its present value is the cash received each period divided by the matching positive discount rate, with the first receipt one period away. The useful work is proving the cash amount and timing before dividing.
Present value today = Cash flow next period / Discount rate per period
PV₀ = C₁ / r, with constant cash flows, r > 0 and the first payment at the end of the next period.
An annual cash stream needs an annual rate. State whether amounts and rates are nominal or inflation-adjusted. Keep the currency, tax basis and financing perspective consistent throughout the workbook.
Aswath Damodaran's present-value teaching notes derive the perpetuity formula as the limiting case of a constant annuity. The formula summarizes the discounted future payments, rather than adding their undiscounted dollar amounts.
For a business capital decision, the numerator should be sustainable cash after the costs needed to keep generating it. Revenue, EBITDA and accounting earnings are not interchangeable with that cash. The free cash flow glossary explains why reinvestment belongs in the calculation.
Bring a business forecast or operating schedule with separately identified receipts, operating payments, cash taxes and sustaining capital expenditures. If the workbook starts from earnings instead of cash receipts, it also needs the appropriate noncash and working-capital adjustments. Use one starting convention throughout.
The assumption sheet should identify the valuation date, first payment date, recurring cash amount, payment frequency, discount rate and owner of each assumption. The rate must be supplied and justified for the cash stream; it is not inferred from a bank balance or chosen to make a project appear attractive.
For this example, a hypothetical US industrial service operation is evaluated at the end of its setup period. Management supplies an annual recurring cash budget. Collections and operating payments already incorporate working-capital timing, so no separate working-capital deduction is made.
| Annual cash-budget row | Amount (USD) | Treatment |
|---|---|---|
| Recurring customer receipts | 1,600,000 | Cash collected, not invoiced sales |
| Operating payments | 1,050,000 | Labor, suppliers and other operating payments |
| Cash taxes | 100,000 | Supplied recurring cash-tax estimate |
| Sustaining capital expenditures | 210,000 | Replacement spending required to maintain the activity |
The annual after-tax business discount rate supplied for the illustration is 8%. It is an assumption for this example, not a recommended hurdle rate. The first annual net cash receipt is one year after the valuation date. There is no borrowing, interest, owner distribution or separate disposal payment in this cash stream.
Compute the numerator from the budget before applying the perpetuity formula. A positive operating surplus is not the final cash available if assets still need replacement.
| Step | Calculation | Result (USD) |
|---|---|---|
| Operating cash surplus before taxes | 1,600,000 − 1,050,000 | 550,000 |
| Cash after taxes | 550,000 − 100,000 | 450,000 |
| Recurring annual cash after sustaining investment | 450,000 − 210,000 | 240,000 |
| Present value | 240,000 / 0.08 | 3,000,000 |
The assumed perpetual stream is worth $3,000,000 at the stated date and rate. That is the value of the future cash stream before subtracting any separate cash paid at the valuation date to acquire or establish it. A complete investment case also tests those initial costs and any cash flows outside the continuing stream.
For a known project life, use net present value with the actual dated payments and any terminal proceeds. The project cash flow guide covers the separate task of establishing those project inputs.
The perpetuity must equal the present value of the first receipt plus the present value of all later receipts. After the first payment, the remaining identical stream still has a value of $3,000,000 at that later date.
| Check component | Calculation | Present value today (USD) |
|---|---|---|
| First annual receipt | 240,000 / 1.08 | 222,222 |
| All payments after that first receipt | 3,000,000 / 1.08 | 2,777,778 |
| Combined present value | (240,000 + 3,000,000) / 1.08 | 3,000,000 |
Displayed present values are rounded to the nearest dollar. Calculations use unrounded amounts. This identity is a useful timing check: the continuing value belongs after the first receipt, so both components are discounted once in this split.
If the first payment instead arrives at the end of year six, the continuing value is $3,000,000 at the end of year five. Its present value today is $3,000,000 / 1.08⁵ = $2,041,750. Do not put a year-five value into a current budget without that discounting step.
Hold annual cash at $240,000 and compare the supplied rates below. The exercise shows sensitivity; it does not establish which rate is appropriate.
| Annual cash (USD) | Annual discount rate | Calculation | Present value (USD) |
|---|---|---|---|
| 240,000 | 6% | 240,000 / 0.06 | 4,000,000 |
| 240,000 | 8% | 240,000 / 0.08 | 3,000,000 |
| 240,000 | 10% | 240,000 / 0.10 | 2,400,000 |
Now keep the rate at 8% and change only annual sustaining capital expenditures from $210,000 to $250,000. Recurring cash becomes $450,000 − $250,000 = $200,000, and present value becomes $200,000 / 0.08 = $2,500,000. The additional $40,000 annual investment requirement reduces value by $500,000.
Operations owns whether replacement spending supports the assumed activity. Finance owns the approved rate and cash definition. The controller checks the historical starting amounts. Recording those responsibilities makes the comparison reviewable when someone challenges a continuing-cash assumption.
A growing perpetuity uses next-period cash divided by the discount rate minus growth, subject to the required assumptions and a discount rate above growth. Setting growth to zero returns the constant formula. Do not introduce growth just because the constant result falls below an investment request.
Damodaran's terminal-value discussion stresses consistency between the cash-flow definition and discount rate, as well as the reinvestment needed to support a continuing business. A terminal calculation should follow the explicit forecast rather than replace analysis of the early years. The cash flow forecast guide addresses that dated operating schedule.
Upload a sample of your own cash budget and supplied discount-rate scenarios; Covirage maps the columns, and its tools compute and check the figures from those inputs. The external AI model explains the comparison with every figure traced to its rows. Create a free Covirage account, then set up your business and bring your workbook.
See FP&A reporting with Covirage for the supporting workflow.
It is an assumption used to summarize a continuing business cash stream, not evidence that the business has an unlimited life. Test whether customer demand, operating rights, asset replacement and other recurring costs support that assumption. Use a finite schedule when the activity has a known ending.
A perpetuity can be used to calculate terminal value at the end of an explicit forecast. That terminal value sits at the forecast end date. Discount it back to the decision date before combining it with the present value of earlier cash flows.
The constant-perpetuity formula requires a positive discount rate for a positive cash stream. At a zero rate, an infinite series of positive payments has no finite present value. Entering a very small rate also creates a result that is highly sensitive to the assumption.