Hong Life CalculatorsUnderstanding the payback and discounted payback period — concept and principle
The payback period is the time it takes for an investment's cash inflows to repay the money put in. The discounted payback period asks the same question after converting each future cash flow to today's value. Managers use both to screen projects such as a new machine or an energy upgrade, especially when cash is tight.
How it is calculated
Cash flows are CF0 = −initial investment and CF1 to CF5 for years 1 to 5.
- Payback: add cash flows year by year. In the first year t where the running total turns zero or positive, payback = (t − 1) + (amount still unrecovered at the start of year t) ÷ CFt.
- Discounted payback: first replace each cash flow with its present value, PVt = CFt ÷ (1 + r)^t, where r is the discount rate per year, then apply the same rule.
If the total never reaches zero within five years, there is no finite payback. Any currency works.
The principle
Payback measures how long your money is at risk. The fractional part assumes cash arrives evenly through the year, so the unrecovered balance is paid off proportionally. Simple payback treats $1 in year 4 like $1 today. Discounting fixes that: money received later is worth less because it could have earned the return r elsewhere, so discounted payback is always the same or longer than simple payback.
Worked example
- Inputs: investment $100,000; cash flows $30,000, $35,000, $40,000, $30,000, $20,000; discount rate 8%.
- Simple running total: −100,000 → −70,000 → −35,000 after year 2. Year 3 brings 40,000, so payback = 2 + 35,000 ÷ 40,000 = 2.875, shown as 2.88 years.
- Present values: 30,000 ÷ 1.08 = 27,777.78; 35,000 ÷ 1.08² = 30,006.86; 40,000 ÷ 1.08³ = 31,753.29; 30,000 ÷ 1.08⁴ = 22,050.90.
- Discounted running total after year 3: −100,000 + 27,777.78 + 30,006.86 + 31,753.29 = −10,462.07.
- Discounted payback = 3 + 10,462.07 ÷ 22,050.90 = 3.474, shown as 3.47 years.
How to read the result
Shorter is safer and frees cash sooner. Many firms set a maximum acceptable period and reject projects that exceed it. The gap between the two figures shows how much the time value of money matters; it widens with higher discount rates and later cash flows.
Common mistakes
- Using payback alone to choose projects: it ignores everything after the payback year, such as the $20,000 in year 5 here.
- Entering profit instead of cash flow, or forgetting maintenance and tax payments.
- Choosing a discount rate that does not match the project's risk.
Frequently asked questions
Is a shorter payback always better?
No. A longer-payback project can create far more value over its life.
What discount rate should I use?
Usually your cost of capital or the return you require for projects of similar risk.
What if a cash flow is negative in a later year?
The calculator stops at the first year the running total turns non-negative, so a later negative flow is not reflected. Check the full cash flow table in that case.
Sources: Richard A. Brealey, Stewart C. Myers and Franklin Allen, Principles of Corporate Finance, McGraw-Hill (payback and discounted payback)