What Is Payback and Discounted Payback

22/07/2026, محدث 29/10/2026 •0•0

How to calculate Simple and Discounted Payback, with worked examples, the partial-period formula, differences, limitations and exercises.

كتب بواسطةLeon Diniz

تمت الترجمة بواسطةEditorial

تمت المراجعة بواسطةEditorial

Imagine you have R$ 200,000 to open a coffee shop.

After talking to a consultant, he estimates that the business will generate the following annual net cash flow:

Year	Cash flow (R$)
1	50,000
2	70,000
3	90,000
4	100,000

The first question we usually ask is: how long will it take to recover the money invested? That question is answered by the Payback. Throughout the article we will see how to calculate it and, at the end of the first part, we will come back to the coffee shop.

What is Payback?

The Payback (payback period) is the time needed to recover the initial investment through the cash flows generated by the project.

In other words, Payback is the time it takes for the money received to equal the money invested. In general, the shorter the Payback, the faster the capital returns, the greater the investment's liquidity and the lower the exposure to the risk of something going wrong along the way.

Intuitive example

You lend R$ 1,000 to a friend. He promises to pay you back:

Month	Amount (R$)
1	300
2	300
3	400

After three months you have received:

\[ 300+300+400=1,000 \]

Your Payback was 3 months.

How to calculate the Simple Payback

The calculation follows three steps.

Step 1: identify the initial investment

It is the amount spent at date 0.

Step 2: accumulate the cash flows

Add up the cash flows period by period, building a column of accumulated values.

Step 3: find the moment of recovery

Find the period in which the accumulated amount reaches the initial investment and, if necessary, calculate the fraction of that period.

Example 1

A company invests R$ 100,000.

Forecast cash flows:

Year	Cash Flow (R$)
0	-100,000
1	30,000
2	40,000
3	50,000

Accumulating the inflows:

Year	Accumulated (R$)
1	30,000
2	70,000
3	120,000

The investment is recovered during the third year.

Finding the fraction of the last period

After the second year, there was still:

\[ 100,000-70,000=30,000 \]

In the third year, the inflow is:

\[ 50,000 \]

So,

\[ \frac{30,000}{50,000}=0.6 \]

Therefore,

\[ \boxed{\text{Payback}=2.6\text{ years}} \]

Payback formula

When recovery happens in the middle of a period:

\[ \boxed{\text{Payback}=t+\frac{\text{Amount not yet recovered}}{\text{Cash flow of the following period}}} \]

where $t$ is the last full period before recovery. This fraction assumes the period's cash flow comes in evenly throughout it; if all the money arrives at the end of the year, in practice the Payback is the whole year.

Interpretation

A Payback of 2.6 years means the investment is recovered after approximately two years and seven months (0.6 × 12 = 7.2 months).

Back to the coffee shop

For the coffee shop at the beginning, the accumulated amount is R$ 50,000 in year 1, R$ 120,000 in year 2 and R$ 210,000 in year 3. At the end of year 2, R$ 80,000 is still missing, and year 3 brings R$ 90,000:

\[ \text{Payback}=2+\frac{80,000}{90,000}\approx 2.89\text{ years} \]

or about two years and eleven months.

An investment of R$ 60,000 generates R$ 15,000 in year 1, R$ 25,000 in year 2 and R$ 40,000 in year 3. What is the Simple Payback?

Answer: 2.5 years — at the end of year 2 the accumulated amount is R$ 40,000 and R$ 20,000 is still missing; year 3 brings R$ 40,000, so the fraction is 20,000 / 40,000 = 0.5. Answering 3.0 years means forgetting that recovery happens in the middle of the third year.

The problem with Simple Payback

Consider two projects, both with an initial investment of R$ 700.

Project A

Year	Cash Flow (R$)
1	100
2	100
3	800

Project B

Year	Cash Flow (R$)
1	350
2	350
3	300

Both return the same total, R$ 1,000. Project B pays back in exactly 2 years; Project A, in 2 + 500/800 ≈ 2.6 years. So far, Payback is right to prefer B. The problem lies in the calculation itself: to reach the R$ 700, Simple Payback adds up reais from different years as if they were worth the same. But money received in the third year is worth less than money received today: at 10% per year, Project A's R$ 800 in year 3 is worth about R$ 601 today. Simple Payback completely ignores this fact.

Enter the Discounted Payback

Receiving R$ 10,000 today is not the same as receiving R$ 10,000 five years from now. Why? Because today we can invest that money and earn interest. Money therefore has time value, one of the most important ideas in Financial Mathematics.

The Discounted Payback exists to correct this limitation: all cash flows are brought to present value before being accumulated. The rate normally used is the Minimum Attractive Rate of Return (MARR), the lowest return the company accepts on an investment (in Brazil it is called TMA).

Example

Same R$ 100,000 investment and same cash flows as in Example 1:

Year	Cash Flow (R$)
0	-100,000
1	30,000
2	40,000
3	50,000

MARR: 10% per year.

Calculating the present values

Year 1

\[ PV=\frac{30,000}{1.10}=27,273 \]

Year 2

\[ PV=\frac{40,000}{1.10^2}=33,058 \]

Year 3

\[ PV=\frac{50,000}{1.10^3}=37,566 \]

Accumulating

Year	Accumulated PV of inflows (R$)	Still to recover (R$)
1	27,273	72,727
2	60,331	39,669
3	97,896	2,104

Note that, even at the end of the three years, the accumulated present value (R$ 97,896) does not reach R$ 100,000. Since the project ends in year 3, the investment is not recovered in discounted terms: about R$ 2,104 is still missing, which is exactly the project's negative NPV at 10% per year. A project that pays back in 2.6 years under Simple Payback may therefore never pay back once the time value of money is taken into account.

A project has a Simple Payback of 3 years. What can be said about its Discounted Payback, calculated with a positive MARR?

Answer: It will be longer than 3 years, or the project may not pay back at all — discounting reduces the value of each inflow, so the accumulated amount takes longer to reach the investment. If the discounted inflows do not add up to the investment by the end of the project, it does not pay back, as in the example above.

Overall comparison

Method	Result in the example
Simple Payback	2.6 years
Discounted Payback (10% MARR)	not recovered within the project's 3 years

This happens because part of the value of the cash flows was "consumed" by discounting.

Simple Payback	Discounted Payback
Does not consider interest.	Considers interest.
Easier to calculate.	More realistic.
Underestimates the real payback period.	Reflects the time value of money.
Widely used in quick analyses.	Widely used in companies.

Limitations of Payback

Both methods share an important problem: they ignore everything that happens after the investment is recovered.

Example: Project A recovers the investment in 2 years and generates a total profit of R$ 300 thousand; Project B also recovers in 2 years, but generates a total profit of R$ 3 million. Both have the same Payback, and Project B is clearly much better.

Project X pays back in 2 years and stops generating cash in year 3. Project Y pays back in 4 years and generates cash for 15 years. Under the Payback criterion, which one is chosen, and why might this be a mistake?

Answer: X, although Payback ignores the 11 years of cash Y generates after paying back — Payback only measures the recovery period. To know which project creates more wealth, you need to look at NPV, which considers all the cash flows.

When to use it?

Payback is appropriate when the goal is to answer questions such as: how long will it take to recover the investment? Which project returns the money fastest and therefore leaves me exposed for less time? Many companies also use it as a filter, setting a maximum acceptable period.

To assess a project's profitability, however, other indicators are more suitable, such as Net Present Value (NPV), Internal Rate of Return (IRR) and Modified Internal Rate of Return (MIRR).

Exercises

1) Mariana wants to open a food truck specializing in artisanal burgers. To do so, she will need to invest R$ 180,000. Calculate the Simple Payback of the investment, given that she expects the following annual net cash flows:

Year	Cash Flow (R$)
1	40,000
2	50,000
3	60,000
4	70,000

2) A gym invested R$ 350,000 in new equipment. Calculate the Simple Payback considering the following cash flows:

Year	Cash Flow (R$)
1	90,000
2	100,000
3	120,000
4	130,000

3) A businesswoman plans to open a gourmet coffee shop and will invest R$ 250,000. Consider a MARR of 10% per year. Calculate the present value of each cash flow and the Discounted Payback. The expected net cash flows are:

Year	Cash Flow (R$)
1	70,000
2	80,000
3	90,000
4	100,000

4) An amusement park will invest R$ 900,000 in a new attraction. MARR = 8% per year. Calculate the Discounted Payback. Cash flows:

Year	Cash Flow (R$)
1	220,000
2	250,000
3	280,000
4	320,000
5	350,000

5) A manufacturer will buy a machine for R$ 600,000. MARR = 15% per year. Calculate the Discounted Payback. Cash flows:

Year	Cash Flow (R$)
1	180,000
2	190,000
3	200,000
4	220,000

Answer key

1) 3.43 years (at the end of year 3, R$ 30,000 is still missing; 30,000 / 70,000 ≈ 0.43).

2) 3.31 years (at the end of year 3, R$ 40,000 is still missing; 40,000 / 130,000 ≈ 0.31).

3) Present values: R$ 63,636, R$ 66,116, R$ 67,618 and R$ 68,301. Discounted Payback ≈ 3.77 years.

4) Present values: R$ 203,704, R$ 214,335, R$ 222,273, R$ 235,210 and R$ 238,204. Discounted Payback ≈ 4.10 years.

5) Present values: R$ 156,522, R$ 143,667, R$ 131,503 and R$ 125,786, totaling ≈ R$ 557,478. The investment is not recovered within the project's 4 years (≈ R$ 42,522 is still missing).

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