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Payback period

S

shdh

Ton up Member
Hi,
I am having a bit of difficulty in understanding payback period concept (chapter 10, page 17). What does it actually signify and when is it considered?

Some briefing would be great!

Thanks and regards,
Shyam
 
Last edited:
First the basics -

  • There are two rates of interest assumed under DPP - Rate of interest (j1) paid on the borrowing made by the investor (an outflow) & the Rate of interest (j2) earned by him made on the investments made by him (an inflow)
  • All the outflows being made by the investor are borrowed & hence he has to pay an interest on any outstanding borrowed amount at rate (j1)
  • We have net cashflows in the equations given - ( C[t] ) - Net cashflow at time (t)
  • ( A[t] ) - the accumulated value at time (t) - the equation given has two components, just to take into consideration the discrete & continuous part (concept is same)
  • We assume we have both inflows and outflows. Also we know generally at the beginning of the project the initial investment is usually large and decreases with following years. Also our inflows are generally less in initial years and increases and become constant with years. Also it is assumed that the inflows are used to pay off the loan as and when the investor receives them & not invests it until all the loan has been paid out. So in initial years we have Net Outflow and an interest is being paid on the borrowed amount from which the outflow was done.
  • The DPP is that year until which we have a NPV of zero. It differs from DP as it takes into consideration the interest paid on outflows.
Now the 1st equation -

  1. It is assumed here that (t) is the DPP, which implies that at time (t) the accumulated value of cashflows is ( A[t] >= 0 ). Which we can also say that NPV >= 0.
  2. This means till time (t) we were having outflows >= inflows, such that the investor had to pay interest on his borrowed amount at rate (j1).
  3. So for the Net Outflow every year (time in equation), we are paying an interest at rate (j1).
  4. Now with every year we had our outflow amount decreasing so is our interest paid decreasing. This differs by situation - but the thing is that till time (t), we had some net outflow upon which some interest was being paid.

Now at time (t) all the outflows have been paid out with the inflows and the investor has no loan amount outstanding. Still the project is running and the investor is having inflows. Now since the loan has been paid off the inflows are surplus and are invested by the investor on which he earns a rate of interest (j2).


Now the 2nd equation -

  1. The first component means that obviously at time (t) he has atleast a zero NPV or a small minimal positive NPV. So he invests this amount at rate (j2).
  2. Second component is for the inflows after time (t), where he is still having inflows and hence invests them at rate (j2).
  3. Third component is same as second component, just taking into consideration continuous inflows.
Hope this suffices.
 
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