The discounted payback period is the number of years it takes for the present value of a project's future cash flows to recover the initial investment, using a chosen discount rate. On a BA II Plus, you compute it by entering each year's cash flow into the cash flow worksheet, applying the discount rate stored in I/Y, and then watching the cumulative discounted cash flow switch from negative to positive. That point — or the fractional year that contains it — is the discounted payback period. The classical shortcut is payback period = years before full recovery + (unrecovered amount at start of that year ÷ discounted cash flow during that year). This is fundamentally different from the simple payback period, which ignores the time value of money by adding up undiscounted cash flows. The discounted version is stricter and more realistic, because a dollar five years from now is worth less than a dollar today, and the discount rate in the calculator's I/Y field translates that fact into a smaller number for every future period.
What the Discounted Payback Period Measures
The discounted payback period is a capital budgeting metric that answers one specific question: how long until the project pays for itself, once you account for the fact that future dollars are worth less than present dollars? Two companies with the same five-year horizon can have very different discounted payback periods if their cost of capital differs, because a higher discount rate shrinks the present value of distant cash flows dramatically.
Unlike the simple payback period, which treats a dollar in year five the same as a dollar today, the discounted version applies a discount rate — the firm's cost of capital, a hurdle rate, or a project-specific required return — to each year's cash inflow before summing. This is the same discount rate used in net present value calculations, and the same concept as the discount rate in dividend discount models. The result is a number, expressed in years (or fractions of a year), that you can compare against a target payback horizon.
In practice, the discounted payback period is most useful when a company has a self-imposed cap on how long strategic investments should take to recover. A firm that demands payback within four years will reject a project whose discounted payback period is 4.2 years, even if net present value is positive. The metric forces a focus on near-term cash recovery rather than long-term value creation.
The Formula Behind the Discounted Payback Period
The formula for a single discounted cash flow in year t is:
DCF_t = CF_t / (1 + r)^t
where r is the discount rate (as a decimal) and t is the number of years from the initial outlay. The discounted payback period is the lowest t for which the running sum of DCF_1 through DCF_t is greater than or equal to the absolute value of the initial investment.
A common way to express the fractional payback period, once you know the integer year of crossover, is:
Discounted payback period = A + (B / C)
where A is the last year with a negative cumulative discounted cash flow, B is the absolute value of that cumulative total at the end of year A, and C is the discounted cash flow in year A+1.
The table below shows the differences between the simple payback period and the discounted payback period.
| Feature | Simple Payback Period | Discounted Payback Period |
|---|---|---|
| Discount rate applied | No | Yes — uses cost of capital or hurdle rate |
| Time value of money | Ignored | Reflected in every cash flow |
| Result for positive discount rate | Shorter or equal to discounted version | Always longer or equal to simple version |
| Common use | Quick screen for early cash recovery | Strategic cap on how long capital is tied up |
| Main weakness | Ignores cash flows after payback | Still ignores cash flows after payback |
For a deeper walkthrough of the formula and a worked variance example, the guide on how to calculate a discounted payback period covers the same algebra with more variance.
How to Calculate Discounted Payback Period on the BA II Plus
The BA II Plus is well suited to this calculation because it stores a list of cash flows and applies the I/Y rate to each one for you. The key is to use the cash flow worksheet (the CF button), not the time-value-of-money worksheet (the TVM button), and to remember that the standard BA II Plus does not directly compute a payback period — it computes a net present value, which you then have to track cumulatively by hand or on paper.
Follow these steps to compute the discounted payback period on a BA II Plus:
- Press 2nd → CF to open the cash flow worksheet. The display should show CF0 =, the initial outlay at time zero.
- Enter the initial investment as a negative number (because it is an outflow) and press Enter. Then press the down arrow to move to C01.
- Enter the cash flow for year 1 and press Enter. Press the down arrow to move to F01 (the frequency of that cash flow).
- If year 1's cash flow is a one-time event, type 1 and press Enter. If the same cash flow repeats for several years, enter the number of consecutive years it repeats and press Enter. Press the down arrow to continue.
- Repeat the previous two steps for C02, F02, C03, F03, and so on until you have entered every year of the project's life.
- Press the NPV button. The calculator will prompt you for I, the discount rate per period. Enter the cost of capital as a percentage (for example, 10 for 10%) and press Enter. Then press the down arrow to load the variable NPV.
- Press CPT to compute the net present value. The display shows the present value of all cash flows from year 1 onward, discounted at the I/Y rate you entered. This is not yet the discounted payback period — it is the discounted sum of inflows.
- To find the payback period, exit the cash flow worksheet by pressing 2nd → Quit. Then, on paper, subtract the initial investment from the running total of discounted cash flows year by year until the cumulative sum turns positive. The fractional year where it crosses zero is the discounted payback period, using the shortcut formula shown in the previous section.
This procedure works on both the standard BA II Plus and the BA II Plus Professional. The professional version adds a "Discounted Payback Period" worksheet inside the cash flow analysis menu, but it works best with regular cash flow patterns. For projects with uneven inflows, the cumulative discounted cash flow method shown above is the safer approach.
Reading the BA II Plus Output and Verifying by Hand
A concise example makes the steps concrete. Consider a project with an initial outlay of $10,000 and the following cash inflows: year 1 = $4,000, year 2 = $4,000, year 3 = $4,000, year 4 = $2,000. Assume the discount rate is 10%.
Enter the cash flow worksheet:
- CF0 = -10,000
- C01 = 4,000, F01 = 1
- C02 = 4,000, F02 = 1
- C03 = 4,000, F03 = 1
- C04 = 2,000, F04 = 1
Press NPV, enter I = 10, then CPT. The display returns the present value of years 1 through 4, which equals $11,313.44. Subtract the initial $10,000 outlay and the net present value is $11,313.44 - $10,000 = $1,313.44, meaning the project as a whole is value-creative at a 10% discount rate.
But the net present value is not the discounted payback period. To find that, track the cumulative discounted cash flow year by year:
- Year 1: 4,000 / 1.10 = 3,636.36. Cumulative: -10,000 + 3,636.36 = -6,363.64.
- Year 2: 4,000 / 1.21 = 3,305.79. Cumulative: -6,363.64 + 3,305.79 = -3,057.85.
- Year 3: 4,000 / 1.331 = 3,005.26. Cumulative: -3,057.85 + 3,005.26 = -52.59.
- Year 4: 2,000 / 1.4641 = 1,366.03. Cumulative: -52.59 + 1,366.03 = 1,313.44.
The cumulative discounted cash flow turns positive during year 4. Using the shortcut formula:
Discounted payback period = 3 + (52.59 / 1,366.03) = 3.04 years
The BA II Plus's NPV result tells you the project is worth pursuing in present-value terms, but the cumulative tracking tells you the answer to the payback question. Both are useful, and reading them side by side is the core skill.
Common Mistakes When Using the BA II Plus for DPP
The first mistake is treating the NPV output as the answer. The BA II Plus's NPV function gives you the present value of every entered cash flow net of the initial outlay — it is a single number, not a year-by-year cumulative figure. You have to do the cumulative work yourself, or you have to use a separate cash flow analysis tool that tracks running totals.
The second mistake is forgetting to reset the worksheet between projects. The BA II Plus stores only one CF list at a time, so the previous project's C01, C02, and so on will still be there if you press 2nd → CF on a new project. Press 2nd → CLR WORK to clear all worksheets before entering a fresh cash flow stream, or manually overwrite each entry.
The third mistake is mixing the I/Y setting with the payments-per-year (P/Y) setting. If you are discounting annual cash flows, the P/Y setting should be 1 and the I/Y should be the annual discount rate. If the calculator is set to P/Y = 12 (monthly compounding) but you are discounting annual cash flows, the I/Y will be interpreted as a monthly rate and the NPV will be wildly wrong. Press 2nd → P/Y to confirm.
The fourth mistake is forgetting the sign convention. CF0 must be entered as a negative number if it represents an outflow. If you enter CF0 as positive, the NPV will still compute but the sign of the result will be flipped, and the cumulative tracking will never cross zero the way you expect.
The Word "Discount" Appears in Two Very Different Places
There is a clear risk of confusion between the discount rate used in this article and the discount percentage on a sale tag. The discount rate in capital budgeting is the firm's cost of capital, applied to future cash flows to express them in present-value terms. The discount percentage on a sale tag is a fraction of the original price, applied to the sticker price to express the sale price in dollars. The math is different, the inputs are different, and the outputs are different.
A free Discount Calculator handles the second meaning cleanly: type an original price and a percent off, and it instantly shows the sale price and the amount saved. It also handles stacked coupons correctly, so 20% off followed by another 10% off resolves to 28% off — not 30%, because the second percentage applies to the already-reduced price, not the original. That stacked-coupon logic is unrelated to the discounted payback period, but it is the same kind of "multiplication, not addition" pattern that drives present-value math.
For capital budgeting specifically, the BA II Plus procedure above is the standard approach. For shopping math, the discount calculator is the right tool. Mixing the two is easy to do, but the inputs (a price vs. a cash flow stream) and the outputs (a sale price vs. a payback year) make the right choice obvious once you stop and look at the labels.