Present Value of a Delayed Perpetuity
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- Опубликовано: 28 авг 2024
- This video explain an EXTREMELY IMPORTANT calculation that many students find confusing. The present value of "ordinary" perpetuity formula (PV = C/r) can only be used when the FIRST cash flow is occurring one time-period into the future.
However, there can be instances where the perpetuity is "delayed", i.e. the first cash flow occurs MORE than one year into the future (You will see applications of this in more advance finance classes). In such cases, the PV = C/r "ordinary" perpetuity formula needs to be augmented. In this video, I explain how (using an example).
ABOUT ME:
My name is Atif Ikram. I am a member of the finance faculty at Arizona State University's W.P. Carey School of Business (wpcarey.asu.ed.... I love to teach! Over the past few years, I have taught a variety of economics and finance courses to undergraduate and graduate students at Rutgers University, Wayne State University, and Lahore University of Management Sciences (LUMS, Pakistan). Presently I teach advance corporate finance courses at ASU.
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is the calculation the same if the question changed to "you will get the first $500 that begins at the end of year 3" ?
Uff that's was so helpful
Gad to hear it Asif!
Considering that the normal perpetuity starts paying at year 1, shouldn’t we say that the delay is 2 years? I mean, the calculation comes up to the same. I just wanted to point out the confusion with the wordings
Hi K J. I understand your point. However, if I had done it the way you are suggesting and said "this perpetuity is delayed by 2 years", but then showed the first cash flow occurring after 3 years, that may have caused confusion of its own.
That said, you are absolutely right. I appreciate that comment and will keep that in mind for future videos.
What if the amount pays $11000 every 3 years starting 7 years form today, then how to solve?
I’ll make a video on this my friend. But first convert the APR into the three year “effective rate” by doing (1+r)^3-1. Now you have a three year rate, which maps the periodicity of your cash flows. So make a new time line in which each time period represents a three year period on the original time line.
In the example that you have given, this would mean that you would get $110,000 starting in “period” 2 (6 years on the original time line). You can determine the PV using delayed perpetuity formula (the subject of this video).
This will completely not solve your problem because the PV you will get from this will be at the end of Year 1 on your original time line. But that’s a simple discounting exercise - just discount that number back one year using your ORIGINAL APR.
lot of info here but hope you see the logic. Will make video on this too. Thanks for asking.
So does the present value of a perpetuity starting in one year have the same value as one starting today?
Hi Joe. No, that perpetuity would be worth more. In fact, we call such a perpetuity a perpetuity DUE. Here is a video that explains the PV of that perpetuity: ruclips.net/video/JK5-CB69FHk/видео.html
Feel free to reach out if you need additional clarification.
hello sir, i don't understand 1.04 came about? can you please explain it
Sure. Interest rate is 4% which is 0.04. So (1+0.04) gives you 1.04.
Very helpful thank you. Just wanted to know why we couldn't just start the perpetuity at year 3 using the PMT/r formula? then take your answer and discount it 3 years back. This is how i have it in my example. But in my case the perpetuity was paid 2 years from today. So basically they still used the perpetuity formula
Hello Ayesha - So the PMT/r formula to value a perpetuity ONLY works if the first payment that you are getting is ONE YEAR FROM TODAY (i.e. the present). Put differently, if you had started your hypothetical time line at Year 3 (instead of Year 2, as I did), then the first payment would be occurring at Year 3 as WELL, which means that you could NOT have applied PMT/r formula to value it [In fact, the correct formula would have been PMT [(1+r)/r] : For more details check out my Present Value of Perpetuity Due Video: ruclips.net/video/JK5-CB69FHk/видео.html].
ALWAYS REMEMBER: PMT/r can ONLY be used when the first cash flow of the perpetuity is starting one time period from today.
Thank you so much!!! Please keep making more videos, really appreciate it!@@professorikram
Aisha FYI I have recently confounded a platform, www.SimpliTaught.com. It contains a lot of useful videos mapped to specific business textbooks. Check it out, you may find it useful.
Thank you, sir!😁😁 @@professorikram
Thank you !
Thanks
how to calculate the NPV if not given the discount rate ?
You can’t calculate NPV without a discount rate. If not given, you need to estimate it.
what software is this ? ty
If in delayed years, i mean in year 1 and 2, i have a cash flows for example 200 for year 1 300 for year 2, what will i do?
Hi Eda. That wouldn’t be a perpetuity then, and you would t be able to use this formula. In a perpetuity, the cash flow has to be the SAME every time period. If cash flows are not the same then you would have to discount all cash flows individually. Advance mathematical techniques can be used too, but that’s beyond the scope.
@@professorikram Thank you! My lecturer asked us a question. In that question in year 1 2 and 3 cash flows are 850, in year 5, 6 and 7 cash flows are 500 in year 8 it is 850 and in year 9 it is 700. Starting in year 10 to infinity there are 500 cash flows. Can't i use perpuity like your example and then add previous cash flow to it ?
when do you deduct the initial investment?
HI Greg. Great question. You subtract the initial investment when, well, there IS an initial investment. The number that you would get in that case would be NET present value, i.e. present value that is NET of the initial investment.
In this example, if your uncle had additionally said, "You can purchase this perpetuity from me for $1,000", then the NET present value of this purchase (or investment) would have been $11,557 - $1,000 = $10,557. Is it a "good" investment? Yes, of course. Because it is literally like someone asking you "Would you give $1,000 today, if I gave you $11,557 back TODAY [Remember, $11,557 is PRESENT value]". Your answer to that would be .... HELLS YEAH, right?
Which is why, whenever NET present value > 0, the BENEFIT is > COST, and therefore all positive NPV > 0 investments are considered "good" investments.
Hope this helped! Feel free to ask more questions. Cheers!
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@@professorikramthank you for your generosity and time spent explaining this to us all
I dont understand how the 1.04 came about
cheeers!