IRR and Pay Back

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Permalink Reply by Sanjib Sahu on January 18, 2010 at 10:27am

a broad rule of thumb is 1/IRR = payback period...u can use this for the back-of-the-envelope calculation.

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Permalink Reply by Ahmadeeb on January 18, 2010 at 10:47am

Rule of thumb? your saying that IRR should be treated or considered as ROE ?? that wont make sense since IRR captures the discounted value of cash flows , and ROE doesn't.

consider this example 2 projects generate the exact amount of cash flows , but one has a 1M capital and the the other is 10M capital , IRR would be the same , but payback wont.

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Permalink Reply by Hitanshu Agrawal on January 23, 2010 at 12:59am

At the point of full payback IRR = 0. You could do sequential IRR calculation to see in which investment option, IRR is approaching 0 or near 0 (from negative) the earliest. (However, that might not be the best investment option if your holding period is longer.)

Pls see attached file as an illustration.

Attachments:

• IRR_Payback.xls, 19 KB

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Permalink Reply by Dipu James on January 23, 2010 at 1:31am

Ahmadeeb in your example IRR will not be the same
IRR is the rate at which the present value of the investment is 0
so when the present value of the amount invested in the beginning changes(1mn and 10 mn in your example) the IRR will change

Higher IRR means a lower PBP when compared relatively to a lower IRR

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Permalink Reply by Ashwin on January 25, 2010 at 4:22am

Hi,

I agree with Dipu. Higher IRR means a lower PBP when compared relatively to a lower IRR

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Permalink Reply by Dipu James on January 23, 2010 at 1:37am

i totally agree with sanjib, well this is what my book says ;-)

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Permalink Reply by Hitanshu Agrawal on January 28, 2010 at 3:17am

If you look at the excel sheet I have attached in my earlier post, for an 11 period (much longer than PBP for either options) holding, the invt option with lower IRR gives a faster PBP. PBP depends on the nature (amount) of exact cashflows in each period, while IRR depends on the holding period.

Hence the statement that higher IRR means lower PBP is not correct. Exact relationship would depend on the cashflow stream to be analyzed. Further, PBP does not consider PV of cashflows (and hence is not a good capital budgeting tool for holding period longer than the longest PBP in all invt options).

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Permalink Reply by Dipu James on January 28, 2010 at 8:37am

you have misunderstood me ... you are comparing 2 different projects with different cashflows i am talking about a single project with 2 different cash flows.

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Permalink Reply by kipkorir maritim reuben on February 4, 2010 at 5:25am

Hi ahmedeeb.Payback period is the number of years it is expected to take to recover the original investment from the net cash flows resulting from a capital investment project.But the IRR of an investment project is the cost of capital or required rate of return which,when used to discount the cash flow project,produces a net present value.
The decision rule when using payback period to appraise investments is to accept a project if its payback period is equal to or less than a predetermined target value.The IRR decision rule is to accept all independent investment projects with an IRR greater than the company's cost of capital or target rate of return.It therefore implies that payback period and IRR are inversely related.

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Permalink Reply by Tore Olafsen on February 5, 2010 at 4:47am

Hi,
It is just two different ways of using the same cash flow series. IRR is the discount factor giving zero value to the sum while payback is the point in time when the accumulated sum (discounted or not) is zero. So increasing IRR reduces payback time. Have in mind that if you have multiple investments in non-consecutive periods the IRR will have more than one solution. Note also that the IRR assumes that the proceeds from the investment can be invested - elsewhere - with the same return as in the original investment.

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Permalink Reply by muhammad murtaza tipu on February 8, 2010 at 9:43am

these are techniques for calculation of cash flows for long term projects. if you are analyzing the techniques then you can say that a higher IRR will lower down your payback period. for example you IRR is 10 % and at the same time payback period is 1 year. but if your IRR is 12 % then it will take less time to payback.

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Permalink Reply by Sachidanand (Sacha) Singh on February 8, 2010 at 12:14pm

If cash flows are non-uniform then there is no relationship between IRR and PBP as can be seen from this table:

If cash flows are uniform i.e. CF1 = CF2 = CF3 = ... = CFn, then
CF0 = CF/(1+IRR) +CF/(1+IRR)^2 +CF/(1+IRR)^2 +CF/(1+IRR)^3+... +CF/(1+IRR)^n
Or, CF0/CF = 1/(1+IRR) +1/(1+IRR)^2 +1/(1+IRR)^2 +1/(1+IRR)^3+... +1/(1+IRR)^n
(It can be reduced further but that is not necessary for understanding the qualitative relationship between IRR and PBP.)
PBP will be short if the LHS (CF0/CF) is low and for that IRR will be high. Thus, for uniform cash flows higher the IRR, shorter the PBP.

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