Discounted Payback Period Calculator
This tool calculates the Discounted Payback Period for an investment. It determines how many years it takes for the cumulative present value of future cash flows to equal the initial investment, considering the time value of money.
Enter Investment Details
Expected Annual Cash Flows
Enter the *net* cash flow expected for each year (inflows minus outflows). Use negative for any future outlays. Leave blank or enter 0 for no cash flow in a given year.
This tool provides inputs for 8 years. For projects with longer paybacks, manual calculation or a more advanced tool is needed.
Understanding the Discounted Payback Period
What is Discounted Payback Period?
The Discounted Payback Period is a capital budgeting technique used to estimate the length of time required to recover the initial investment in a project, taking into account the time value of money. Unlike the simple payback period, it discounts future cash flows back to their present value using a specified discount rate.
Why Use Discounted Payback?
- It considers the time value of money, which the simple payback period ignores.
- It provides a measure of liquidity and risk – projects with shorter discounted payback periods are generally considered less risky as the initial investment is recovered sooner.
- It is relatively easy to understand.
Limitations
- It ignores cash flows that occur *after* the discounted payback period is reached, potentially overlooking profitable long-term projects.
- It does not provide a measure of profitability or the total return of a project (like Net Present Value or Internal Rate of Return).
- Selecting the appropriate discount rate can be subjective.
How it's Calculated
The calculation involves these steps:
- Determine the initial investment (outflow at Year 0).
- Choose an appropriate discount rate (cost of capital or required rate of return).
- Calculate the present value (PV) of each future cash flow using the formula:
PV = CFt / (1 + r)t, where CFt is the cash flow in year t, r is the decimal discount rate, and t is the year number. - Calculate the cumulative discounted cash flow for each year by adding the current year's PV to the previous year's cumulative total (starting with the initial investment as a negative value).
- Identify the first year where the cumulative discounted cash flow becomes zero or positive.
- If the cumulative discounted cash flow changes from negative to positive during a year, the discounted payback period is calculated as:
Year Before Payback + |Cumulative Balance Before Payback Year| / Discounted Cash Flow in Payback Year.
Discounted Payback Period Examples
Click on an example to see the scenario and calculation details:
Example 1: Basic Scenario
Scenario: A project requires an initial investment of $10,000 and is expected to generate $3,000, $4,000, $5,000, and $3,500 in cash flows over the next four years. The required rate of return is 10%.
Inputs: Initial Investment = $10,000, Discount Rate = 10%
Cash Flows: Year 1 = $3,000, Year 2 = $4,000, Year 3 = $5,000, Year 4 = $3,500
Calculation:
- Initial Outlay: -$10,000 (Cumulative PV: -$10,000)
- Year 1: PV = $3,000 / (1.10)¹ ≈ $2,727.27. Cumulative PV = -$10,000 + $2,727.27 = -$7,272.73
- Year 2: PV = $4,000 / (1.10)² ≈ $3,305.79. Cumulative PV = -$7,272.73 + $3,305.79 = -$3,966.94
- Year 3: PV = $5,000 / (1.10)³ ≈ $3,756.57. Cumulative PV = -$3,966.94 + $3,756.57 = -$210.37
- Year 4: PV = $3,500 / (1.10)⁴ ≈ $2,391.61. Cumulative PV = -$210.37 + $2,391.61 = +$2,181.24
Payback occurs in Year 4. Balance before Year 4 PV was -$210.37. PV in Year 4 is $2,391.61.
Fraction = |-210.37| / $2,391.61 ≈ 0.088 years.
Result: Discounted Payback Period ≈ 3 + 0.088 = 3.09 years.
Example 2: Slower Payback
Scenario: Initial Investment: $100,000. Discount Rate: 8%. Cash Flows: Y1: $20k, Y2: $25k, Y3: $30k, Y4: $35k, Y5: $40k.
Inputs: Initial Investment = $100,000, Discount Rate = 8%
Cash Flows: Y1=$20k, Y2=$25k, Y3=$30k, Y4=$35k, Y5=$40k
Calculation: (Cumulative PV after discounting)
- Year 0: -$100,000
- Year 1: -$100,000 + $20,000/(1.08)¹ ≈ -$100k + $18,518.52 = -$81,481.48
- Year 2: -$81,481.48 + $25,000/(1.08)² ≈ -$81,481.48 + $21,433.47 = -$60,048.01
- Year 3: -$60,048.01 + $30,000/(1.08)³ ≈ -$60,048.01 + $23,815.16 = -$36,232.85
- Year 4: -$36,232.85 + $35,000/(1.08)⁴ ≈ -$36,232.85 + $25,724.06 = -$10,508.79
- Year 5: -$10,508.79 + $40,000/(1.08)⁵ ≈ -$10,508.79 + $27,223.68 = +$16,714.89
Payback in Year 5. Balance before Y5 PV: -$10,508.79. PV in Y5: $27,223.68.
Fraction = |-10,508.79| / $27,223.68 ≈ 0.386 years.
Result: Discounted Payback Period ≈ 4 + 0.386 = 4.39 years.
Example 3: Project Never Pays Back
Scenario: Initial Investment: $50,000. Discount Rate: 12%. Cash Flows: Y1: $10k, Y2: $12k, Y3: $15k, Y4: $8k, Y5: $5k.
Inputs: Initial Investment = $50,000, Discount Rate = 12%
Cash Flows: Y1=$10k, Y2=$12k, Y3=$15k, Y4=$8k, Y5=$5k
Calculation: (Cumulative PV after discounting)
- Year 0: -$50,000
- Year 1: -$50k + $10k/(1.12)¹ ≈ -$50k + $8,928.57 = -$41,071.43
- Year 2: -$41,071.43 + $12k/(1.12)² ≈ -$41,071.43 + $9,566.33 = -$31,505.10
- Year 3: -$31,505.10 + $15k/(1.12)³ ≈ -$31,505.10 + $10,676.70 = -$20,828.40
- Year 4: -$20,828.40 + $8k/(1.12)⁴ ≈ -$20,828.40 + $5,084.13 = -$15,744.27
- Year 5: -$15,744.27 + $5k/(1.12)⁵ ≈ -$15,744.27 + $2,837.14 = -$12,907.13
After 5 years, the cumulative discounted cash flow is still negative. Based on these cash flows, the project never pays back within this period.
Result: Payback does not occur within the period analyzed (5 years).
Example 4: Impact of Higher Discount Rate
Scenario: Same as Example 1, but with a Discount Rate of 15% instead of 10%.
Inputs: Initial Investment = $10,000, Discount Rate = 15%
Cash Flows: Year 1 = $3,000, Year 2 = $4,000, Year 3 = $5,000, Year 4 = $3,500
Calculation: (Cumulative PV after discounting at 15%)
- Year 0: -$10,000
- Year 1: -$10,000 + $3,000/(1.15)¹ ≈ -$10,000 + $2,608.70 = -$7,391.30
- Year 2: -$7,391.30 + $4,000/(1.15)² ≈ -$7,391.30 + $3,024.56 = -$4,366.74
- Year 3: -$4,366.74 + $5,000/(1.15)³ ≈ -$4,366.74 + $3,281.04 = -$1,085.70
- Year 4: -$1,085.70 + $3,500/(1.15)⁴ ≈ -$1,085.70 + $1,999.03 = +$913.33
Payback occurs in Year 4. Balance before Year 4 PV: -$1,085.70. PV in Year 4: $1,999.03.
Fraction = |-1,085.70| / $1,999.03 ≈ 0.543 years.
Result: Discounted Payback Period ≈ 3 + 0.543 = 3.54 years. (Higher rate leads to longer payback).
Example 5: Annuity-like Cash Flows
Scenario: Initial Investment: $25,000. Discount Rate: 7%. Cash Flows: $6,000 per year for 8 years.
Inputs: Initial Investment = $25,000, Discount Rate = 7%
Cash Flows: Y1-Y8 = $6,000 each
Calculation: (Cumulative PV after discounting)
- Year 0: -$25,000
- Year 1: -$25k + $6k/(1.07)¹ ≈ -$25k + $5,607.48 = -$19,392.52
- Year 2: -$19,392.52 + $6k/(1.07)² ≈ -$19,392.52 + $5,240.64 = -$14,151.88
- Year 3: -$14,151.88 + $6k/(1.07)³ ≈ -$14,151.88 + $4,897.80 = -$9,254.08
- Year 4: -$9,254.08 + $6k/(1.07)⁴ ≈ -$9,254.08 + $4,577.38 = -$4,676.70
- Year 5: -$4,676.70 + $6k/(1.07)⁵ ≈ -$4,676.70 + $4,277.92 = -$398.78
- Year 6: -$398.78 + $6k/(1.07)⁶ ≈ -$398.78 + $3,998.06 = +$3,599.28
Payback in Year 6. Balance before Y6 PV: -$398.78. PV in Y6: $3,998.06.
Fraction = |-398.78| / $3,998.06 ≈ 0.0997 years.
Result: Discounted Payback Period ≈ 5 + 0.0997 = 5.10 years.
Example 6: Negative Cash Flow in a Future Year
Scenario: Initial Investment: $50,000. Discount Rate: 9%. Cash Flows: Y1: $15k, Y2: $20k, Y3: $25k, Y4: -$5k (maintenance), Y5: $30k.
Inputs: Initial Investment = $50,000, Discount Rate = 9%
Cash Flows: Y1=$15k, Y2=$20k, Y3=$25k, Y4=-$5k, Y5=$30k
Calculation: (Cumulative PV after discounting)
- Year 0: -$50,000
- Year 1: -$50k + $15k/(1.09)¹ ≈ -$50k + $13,761.47 = -$36,238.53
- Year 2: -$36,238.53 + $20k/(1.09)² ≈ -$36,238.53 + $16,833.60 = -$19,404.93
- Year 3: -$19,404.93 + $25k/(1.09)³ ≈ -$19,404.93 + $19,300.70 = -$104.23
- Year 4: -$104.23 + -$5k/(1.09)⁴ ≈ -$104.23 - $3,541.51 = -$3,645.74 (Cumulative balance gets worse!)
- Year 5: -$3,645.74 + $30k/(1.09)⁵ ≈ -$3,645.74 + $19,497.28 = +$15,851.54
Payback occurs in Year 5. Balance before Y5 PV: -$3,645.74. PV in Y5: $19,497.28.
Fraction = |-3,645.74| / $19,497.28 ≈ 0.187 years.
Result: Discounted Payback Period ≈ 4 + 0.187 = 4.19 years.
Example 7: Impact of Lower Discount Rate
Scenario: Same as Example 1, but with a Discount Rate of 5% instead of 10%.
Inputs: Initial Investment = $10,000, Discount Rate = 5%
Cash Flows: Year 1 = $3,000, Year 2 = $4,000, Year 3 = $5,000, Year 4 = $3,500
Calculation: (Cumulative PV after discounting at 5%)
- Year 0: -$10,000
- Year 1: -$10,000 + $3,000/(1.05)¹ ≈ -$10,000 + $2,857.14 = -$7,142.86
- Year 2: -$7,142.86 + $4,000/(1.05)² ≈ -$7,142.86 + $3,628.12 = -$3,514.74
- Year 3: -$3,514.74 + $5,000/(1.05)³ ≈ -$3,514.74 + $4,319.19 = +$804.45
Payback occurs in Year 3. Balance before Year 3 PV: -$3,514.74. PV in Year 3: $4,319.19.
Fraction = |-3,514.74| / $4,319.19 ≈ 0.814 years.
Result: Discounted Payback Period ≈ 2 + 0.814 = 2.81 years. (Lower rate leads to shorter payback).
Example 8: Uneven Cash Flows
Scenario: Initial Investment: $75,000. Discount Rate: 10%. Cash Flows: Y1: $10k, Y2: $15k, Y3: $5k, Y4: $30k, Y5: $20k, Y6: $40k.
Inputs: Initial Investment = $75,000, Discount Rate = 10%
Cash Flows: Y1=$10k, Y2=$15k, Y3=$5k, Y4=$30k, Y5=$20k, Y6=$40k
Calculation: (Cumulative PV after discounting)
- Year 0: -$75,000
- Year 1: -$75k + $10k/(1.10)¹ ≈ -$75k + $9,090.91 = -$65,909.09
- Year 2: -$65,909.09 + $15k/(1.10)² ≈ -$65,909.09 + $12,396.69 = -$53,512.40
- Year 3: -$53,512.40 + $5k/(1.10)³ ≈ -$53,512.40 + $3,756.57 = -$49,755.83
- Year 4: -$49,755.83 + $30k/(1.10)⁴ ≈ -$49,755.83 + $20,490.40 = -$29,265.43
- Year 5: -$29,265.43 + $20k/(1.10)⁵ ≈ -$29,265.43 + $12,418.43 = -$16,847.00
- Year 6: -$16,847.00 + $40k/(1.10)⁶ ≈ -$16,847.00 + $22,549.94 = +$5,702.94
Payback in Year 6. Balance before Y6 PV: -$16,847.00. PV in Y6: $22,549.94.
Fraction = |-16,847.00| / $22,549.94 ≈ 0.747 years.
Result: Discounted Payback Period ≈ 5 + 0.747 = 5.75 years.
Example 9: Cash Flows Recover Just Over Investment
Scenario: Initial Investment: $5,000. Discount Rate: 6%. Cash Flows: Y1: $1,000, Y2: $1,500, Y3: $2,000, Y4: $1,000.
Inputs: Initial Investment = $5,000, Discount Rate = 6%
Cash Flows: Y1=$1k, Y2=$1.5k, Y3=$2k, Y4=$1k
Calculation: (Cumulative PV after discounting)
- Year 0: -$5,000
- Year 1: -$5,000 + $1,000/(1.06)¹ ≈ -$5,000 + $943.40 = -$4,056.60
- Year 2: -$4,056.60 + $1,500/(1.06)² ≈ -$4,056.60 + $1,334.99 = -$2,721.61
- Year 3: -$2,721.61 + $2,000/(1.06)³ ≈ -$2,721.61 + $1,679.24 = -$1,042.37
- Year 4: -$1,042.37 + $1,000/(1.06)⁴ ≈ -$1,042.37 + $792.09 = -$250.28
After 4 years, the cumulative discounted cash flow is still negative. Based on these cash flows, the project does not pay back within 4 years.
Result: Payback does not occur within the period analyzed (4 years).
Example 10: Zero Discount Rate (Simple Payback)
Scenario: Initial Investment: $10,000. Discount Rate: 0%. Cash Flows: Y1: $3,000, Y2: $4,000, Y3: $5,000.
Inputs: Initial Investment = $10,000, Discount Rate = 0%
Cash Flows: Y1=$3k, Y2=$4k, Y3=$5k
Calculation: (Cumulative CF - no discounting)
- Year 0: -$10,000
- Year 1: -$10,000 + $3,000 = -$7,000
- Year 2: -$7,000 + $4,000 = -$3,000
- Year 3: -$3,000 + $5,000 = +$2,000
Payback occurs in Year 3. Balance before Y3: -$3,000. Cash flow in Y3: $5,000.
Fraction = |-3,000| / $5,000 = 0.6 years.
Result: Discounted Payback Period ≈ 2 + 0.6 = 2.60 years. (This is the same as the Simple Payback Period when the rate is 0%).
Frequently Asked Questions about Discounted Payback Period
1. What is the main difference between Simple Payback Period and Discounted Payback Period?
The main difference is that the Simple Payback Period ignores the time value of money, treating all cash flows equally regardless of when they are received. The Discounted Payback Period, however, discounts future cash flows to their present value using a discount rate, providing a more accurate picture of the time to recover the investment in today's dollars.
2. Why is the Discounted Payback Period considered a better measure than Simple Payback?
Because it accounts for the time value of money, reflecting that money received sooner is worth more than money received later due to its earning potential. This makes it a more financially sound metric for comparing projects.
3. What does a shorter Discounted Payback Period indicate?
A shorter period suggests that the initial investment is recovered more quickly in present value terms. This is often seen as indicating lower risk and greater liquidity for the project, as the capital is tied up for a shorter time.
4. What does it mean if a project's cumulative discounted cash flow never turns positive within the analysis period?
It means the project's initial investment, when considering the required rate of return (discount rate), is not expected to be fully recovered by the future cash flows within the timeframe analyzed. Based on this metric alone, the project would be deemed unacceptable if the payback period is a decision criterion.
5. How does the discount rate affect the Discounted Payback Period?
A higher discount rate places less value on future cash flows, making the payback period longer. A lower discount rate places more value on future cash flows, resulting in a shorter payback period.
6. What cash flows should be included in the calculation?
All relevant incremental cash flows generated by the project should be included. This means the *net* cash flow (inflows minus outflows) directly attributable to the project in each period, excluding sunk costs or allocated overheads not tied to the project.
7. Can the Discounted Payback Period rule be used as the sole criterion for investment decisions?
It is generally not recommended as the sole criterion. While it's useful for liquidity and risk assessment, it ignores cash flows after the payback point and doesn't measure overall profitability. It's best used in conjunction with other methods like Net Present Value (NPV) or Internal Rate of Return (IRR).
8. What is a typical acceptable Discounted Payback Period?
This is subjective and depends on the company's policy, industry norms, and risk tolerance. Companies often set a maximum acceptable payback period; projects exceeding this limit are rejected.
9. What happens if cash flows are negative in some future years?
Negative cash flows in future years are simply treated as additional outlays in that year. Their present value will be calculated and added (as a negative value) to the cumulative discounted cash flow, potentially lengthening the payback period or causing it to never occur.
10. What units should I use for the inputs?
The currency or unit for the Initial Investment and Annual Cash Flows should be consistent (e.g., all in dollars, all in euros). The Discount Rate is entered as a percentage (e.g., 10 for 10%). The resulting Discounted Payback Period is in years.
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