EME 460
Geo-Resources Evaluation and Investment Analysis

Payback Period Analysis

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Payback period is the time required for positive project cash flow to recover negative project cash flow from the acquisition and/or development years. Payback can be calculated either from the start of a project or from the start of production.

Payback period is commonly calculated based on undiscounted cash flow, but it also can be calculated for Discounted Cash Flow with a specified minimum rate of return. The intuition behind payback period measure is that the investor prefers to recover the invested money as quickly as possible.

One of the disadvantages of the payback period is that it doesn’t analyze the project in its lifetime; whatever happens after investment costs are recovered won’t affect the payback period. For example, if two investment alternatives have 10-year lifetimes, and investment alternatives A and B have 4 and 6 year payback periods, alternative A is more desirable from the payback period point of view, and it is not important how profitable alternative A would be after the 4th year and B after the 6th year.

Payback period can be useful when the investor has some time constraints and wants to know the fastest time that s/he can get her money back on the investment.

Example 9-1

Calculate the payback period for an investment with following cash flow.

C=\$200 C=\$250 I=\$150 I=\$180 I=\$220 I=\$200
0 1 2 3 4 5
Solution
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
ATCF -200 -250 150 180 220 200
Cummulative ATCF -200 -450 -300 -120 100 300

As you can see, in year 4, the cumulative cash flow sign changes from negative to positive, meaning that at some point between year 3 and 4, costs (the summation of 200 at time zero and 250 dollars investments in year 1) would be recovered by generated profit. So, the payback period is somewhere in third year. To calculate the fraction, we can simply divide the 120 (cumulative cash flow in year 3) by 220 (cash flow in year 4). Therefore the payback period equals: 3 + 120/220 = 3.55 years.

Note that payback period can be reported from the beginning of the production. In this case, the payback period for the above example is 3.55 - 2 = 1.55 years after production begins, because production starts from year 2.

As explained, payback period can be calculated for discounted cash flow as well. The following example includes these calculations.

Example 9-2

Calculate the discounted payback for the cash flow in example 9-1 considering a minimum rate of return of 15%.

Solution
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
ATCF -200 -250 150 180 220 200
DCF -200 -217.39 113.42 118.35 125.79 99.44
Cummulative DCF -200 -417.39 -303.97 -185.62 -59.83 39.60

Similar to the calculations in Example 9-1, the discounted payback period equals 4 + 59.83/99.44 = 4.6 years. And the discounted payback period from the beginning of production (year 2) equals 2.6 years.

Mutually exclusive investments and payback analysis

Example 9-3

Consider two mutually exclusive investments with the following cash flows. Which project is more economically satisfactory assuming a minimum rate of return of 15%?

Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
A -$200 $600
B -$200 $80 $80 $80 $80 $80
Solution for Project A
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
ATCF -200 0 0 0 0 600
CumulativeATCF -200 -200 -200 -200 -200 400

Payback period = 4+200/600=4.33

NPVA = 98.31 dollars at i*=15%

Solution for Project B
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
ATCF -200 80 80 80 80 80
Cumulative ATCF -200 -120 -40 40 120 200

Payback period = 2+40/80=2.5

NPVB = 68.17 dollars at i*=15%

Solution for Incremental Snalysis A-B:
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
0 -80 -80 -80 -80 520

For project A-B:

NPVA-B= 30.13 dollars at i*=15%

RORA-B= 20.40%

So, we can conclude that project A is more economically satisfactory than project B. Note that although project B has a lower payback period, project A is better for investment and has better return. It could be concluded by comparing the NPVs as well.


Italicized sections are from Stermole, F.J., Stermole, J.M. (2014) Economic Evaluation and Investment Decision Methods, 14 edition. Lakewood, Colorado: Investment Evaluations Co.

Payback Period Analysis
Click for the transcript for Payback Period Analysis Video

PRESENTER: In this video, I'm going to talk about the payback period. Payback period is the earliest time that an investor can recover his or her investment-- his capital cost. Payback period is the time that is required for the positive cash flow, the earnings, to recover the negative cash flow, which was the investments, which was the capital cost.

Payback period can be calculated for undiscounted cash flow and also for discounted cash flow. And it can be calculated from the beginning of the project or from the start of the production. And obviously, the earlier-- the shorter-- the payback period is better for the investor. It is reflecting the time that the investor can get his or her money back.

A disadvantage of a payback period is the payback period is not reflecting any information about the performance of the project after the capital cost is recovered. So let's work on this example and see how we can calculate the payback period for a cash flow.

So this cash flow is an after-tax cash flow for a project. We are going to have the investment at the present time, at year 1, and we are going to have earnings from year 2 to year 5. The first step in calculating the payback period, is calculating the cumulative cash flow.

So in this row, I have calculated the cumulative cash flow for year 0, or present time, the cumulative cash flow equals the capital cost at present time. For year 1, the cumulative cash flow is the cumulative cash flow of the previous year plus the cash flow at year 1, which the summation is going to be $450.

Cumulative cash flow at year 2 is the summation of cash flow at year 2 and the cumulative cash flow at year 1, and so on. So as we can see here, the sign of cumulative cash flow changes between year 3 and year 4. So the payback period is going to be 3 plus something-- some fraction.

So the investor is going to recover the capital cost of $200 at present time and $250 at year 1. The investor is recovering this capital cost somewhere between year 3 and year 4. So the payback period is going to be 3-point-something. And, how do we calculate that fraction? The fraction is actually-- is 120 divided by this interval. The difference between these two numbers-- the cumulative cash flow at your 3 and the cumulative cash flow at year 4.

So 120 divided by this difference, which is going to be 220, is going to give us the fraction of the payback period. So the payback period for this investment is going to be 3 plus 120 divided by 220, which is going to be 3.55 years. And we can also calculate the payback period from the beginning of the production, as you can see here. The production, it starts from year 2.

So the payback period from the beginning of the project is going to be 3.55. And if you want to calculate the payback period from the beginning of the production, the production starts from year 2. So we have to deduct 2 years from the payback period that we calculated. So payback period from the beginning of the project minus 2, the production year, equals 1.55 for the payback period after the production.

Please note that the payback period is 3.55, and it is not going to consider any payments or project performance months after these-- year 4. So whatever happened in the project is not going to be reflected in the payback period.

So lets use an Excel spreadsheet to calculate the payback rate for this example. First step is calculating the cumulative cash flow. For the present time, the cumulative cash flow equals $200-- the capital cost at present time. Cumulative cash flow for the year 1 equals the cumulative cash flow of the previous year plus the cash flow at year 1. And we can apply these to the other cells, and we can calculate the cumulative cash flow for other years similarly.

So as you can see here, the sign of the cumulative cash flow changes from negative to positive between year 3 to year 4. So payback period is going to be 3 plus a fraction. And, how do we calculate the fraction? We have to calculate the 120 divided by the difference between these two numbers, which is 220. So it is 120 divided by 220, which is going to be 3.5.

I could also refer to the cells here, but be careful when you're referring to these cells-- this has a negative sign, so you need to add a negative sign to make sure the result is going to positive. This number divided by this one minus this one. And again, please double-check. You have to include a negative sign here because this number has a negative, and you want to make sure your payback period is 3 plus something.

We can also calculate the payback period for discounted cash flow. And let's work on this example. Considering the 15% minimum rate of return or discount rate, and calculate a discounted payback period. First, we need to calculate the discounted cash flow. So we discount every year's cash flow by 15% and number of years.

And then we calculate the cumulative discounted cash flow, which is the summation of cumulative-- for present time, it equals the cash flow at the present time. For year 1, it equals the cumulative cash flow at year 0 plus the cash flow of year 1, and so on. Same for the other years.

So again, as you can see here, the cumulative discounted cash flow-- the sign of cumulative discounted cash flow changes from negative to positive between year 4 and 5. So the payback period for the discounted cash flow-- discounted payback period-- is 4 plus a fraction. How do we calculate the fraction? The fraction equals the cumulative cash flow at year 4, cumulative discounted cash flow, at year 4 divided by this difference. Divided by the difference between cumulative cash flow-- cumulative discounted cash flow-- of year 5 and year 4, which equals the cash flow at year 5.

So it is going to be 4 plus 59.83 divided by 99.44, which is going to be 4.6 years, discounted payback period. And again, we can calculate this from the beginning of the production, which is year 2. So we deduct 2 years from this 4.6, and report 2.6 as for the discounted payback period from the beginning of production.

So let's calculate the discounted payback period using an Excel spreadsheet. So I need to calculate-- the first thing is, I have to calculate the discounted cash flow.

So the discount rate was 15%, so I discount the cash flow by 1 plus 0.15, power, the year-- present time, capital cost doesn't need to be discounted. And the power is 0, so it has to be the same. And we apply that to the other years. And then, we have to calculate the cumulative discounted cash flow, which for the present time, equals the discounted cash flow for year 1-- equals the cumulative discounted cash flow of the previous year plus the cash flow of the current year.

So this is the cumulative discounted cash flow for year 1. And I will apply this to the other years. And as you can see here, the cumulative discounted cash flow-- the sign of cumulative discounted cash flow changes from negative to positive, somewhere between year 4 and year 5. Now I have to calculate a discounted payback period.

So discounted payback period equals 4 plus a fraction. To calculate the fraction, we have to divide 59.83 by the difference between the cumulative discounted cash flow of year 4 and year 5. This difference equals this one, so I can either use this number or I can calculate the difference. Again, because this number has a negative sign, please make sure that you include a negative sign for this number.

So I will say minus this, divided by this number minus this number. And it should be 4-something. So again, as you can see here, this is the discounted payback period-- it is 4.6, [AUDIO OUT]

Credit: Farid Tayari