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Hello sir,
Sir, in this question there were 4 years and production units in 4th year were
450 units and after tax flows were
$ 2017.The question asked “after 4th year of operation degnis co continue to produce and sell 450 p.a for foreseeable future..
Calculate the NPV.?Sir,
I calculated the perpetuity of 2017/11%
and inorder to bring it to present value terms I discounted using 5 year since cash beyond 4th year would be receivable at 5th year.
However in answer a 4 year discounting factor was used.Also, tax savings were there for 6 yrs
So I took annuity factor 6 years and then discounted back to P.V using 5 year annuity factor .Herein too 4 year d.cf were usedThe discount factor for a perpetuity starting in 1 years time is 1/r and gives a PV at time 0.
Here the perpetuity starts at time 5 which is four years later than at time 1 and therefore discounting using 1/r gives a PV four years later which is at time 4 instead of at time 0.
Therefore we need to then discount for 4 years to arrive at a PV ‘now’.
It is the same reasoning for the tax saving. The annuity factor is for flows starting in 1 years time and gives a PV at time 0. Here, the flows start in 5 years time and therefore using the annuity factor gives a PV in 4 years time.
Sir if
1/r = PV 0
Then ,Flows starting in 5 years
1/r^4=PV 0.Is it correct?
No it isn’t.
1/r gives the PV of a perpetuity.
If the perpetuity starts 4 years late then the result needs discounting for 4 years as I explained before.
If you are still unsure then do watch the Paper MA (as F2) lectures on investment appraisal where I explain all the discounting.
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