Present Value of a Perpetuity

[@jaycalderon9989]

Im curious. How can we get the present value if the payments are infinite? Since we can’t quantify infinity. Thank you.

[@areebanwar9229]

because that present value will continue to grow so that u can still pay 500 forever. a dollar less and ude not have enough for a specific payment

[@zimbabwebassguy3441]

By also discounting perpetually

[@malakai0321]

I think it’s because after so many years into the future , the value of the future payments (which are always being discounted) are so close to zero that they do not add up to much. If you were to graph the cash flows that were discounted on this perpetuity they’d you’d see that it would be an asymptote. (Approaches zero but never actually touches)

[@snappysharonxx]

What if you need to work out the discount rate and the information given is perpetual extra net income and what the income stream is valued at?

[@OJEL]

What if a discount value isn’t given? I have come across a question with the cash flows alternating between two values year on year and was asked to calculate the PV without interest or discount rates

[@sagenoise]

Thank you Govna'! quick and straight to the point.

[@emiliaarimah9637]

I have a perpetuity of x and an initial cash outflow of y, the discount rate is unknown. How do I discern the discount rate so that I can solve for the IRR?

[@emiliaarimah9637]

Also, does this mean that the initial cash outflow of y is the PV of the perpetuity x?

[@snappysharonxx]

Did you ever find out how?

[@joannelim4205]

Hi sir, when you say 'discount rate', what does that mean? I would be so thankful if you could explain that for me. Cheers, Jo

[@Edspira]

+Joanne Lim Hi Jo! People take the discount rate to mean a lot of things depending on the context, but I would suggest you think of it as follows: it is the rate of return (or interest rate) you could have earned on an investment with similar risk. In that sense you could see the discount rate as representing the opportunity cost of capital. The basic principal of time value of money is that $1 received today is not equivalent to $1 received one year from now, because the $1 received today could have earned interest and grown to an amount larger than $1 by the end of the year. The rate by which we assume the $1 received today would have grown is the discount rate; thus, if we want to look at cash flows received in the future and discount them to their present value (their equivalent value in today's dollars) we use the discount rate to do the discounting.

[@daniel97144]

@@Edspira So basically it is the interest rate?

[@thesuperiorman8342]

@@daniel97144 Did you not read? He said it depends on the context

[@montrealshen]

do you have video talks about Growing Perpetuity?

[@achyutbhattarai6158]

Wow perpetuity investment sounds good!

[@syrinesoussi6612]

Thank you so much, very clear explanation and all your videos are really helpful

[@MikeS29]

So a lifetime pension, such as a social security payment of $1300 monthly, starting next month with a rate of 3.5% would have a PV of about $446,000; does that sound accurate? Now what if those payments did not begin for 10 years? Would you solve for PV of the $446K to see what that would be worth today, using the single cash flow method? I hope I made that clear enough. Thanks for these wonderful videos!

[@EOCmodernRS]

This should be AFTER a payment is made, according to a test I'm taking. So, if you were trying to find the value BEFORE a payment is made, it would be the number you came up with (8 333,33333) + 500 (one cash flow) = 8 888,3333. If this is correct, why is it so?

[@kythoaipham3083]

how about if receiving 500 starts from the second year??

[@xMiertjx]

Then you have to count backwards. You calculate like you're in year 1 instead of year 0. And you discount year 1 to year 0 with the normal PV formula.

[@kythoaipham3083]

hi thank you, i asked this question when i was sophomore but now i am studying master degree in Finance.

[@danielj5650]

@@kythoaipham3083 now what are you doing?

[@kythoaipham3083]

@@danielj5650 Hi, I am currenly a senior risk consulting at PwC

[@havoc170]

@@kythoaipham3083 damn, nice. how stressful is a job at PwC?

[@MosesTheExplorer]

what if I had 10 years of different CF and afterward it becomes a perpuity with a growth rate??

[@burhanmohammedahmedhassan3326]

hi if i have pvp 950 and c is 85 how i will acount R

[@dovakim2313]

「あなたのコンテンツはとても感動的です」、

[@Flowerz__]

what does this PV actually tell you tho is where i am confused.... so that 8.3k is the PV of the perpetuity but like what does that mean?

[@Edspira]

It is the value of the stream of cash flows in today's dollars (assuming that the investment continues to perform at the same rate). If you were offered 9,000 today or $500 every year in perpetuity, you should choose the $9,000 today since it is greater than 8.3k. You could hypothetically invest the 9,000 today and make more money in the long run than taking $500 each year in perpetuity.

[@Flowerz__]

Edspira Thank you for the reply!

[@gamaslazuardi330]

Edspira is this 500$ per year in perpetuity payed until its sum up to 9000$? Thanks Edit: wait is this stream of money which we receiving forever, the total money would never reach above 8.333 dollar or what?

[@Edspira]

Yes, perpetuity is forever. The logic is that you can make more money by investing the 9,000 now then getting 500 a year forever.

[@kalebplayz7228]

what if you've got the PV and the interest rate but not the cash flow

[@garrychumbila4670]

What if your parents deposited a fixed amount in a savings account for you starting with the first birthday and now you are 20 and want to withdraw. Can this be a perpetuity or an annuity

[@sandunikanirmanidezoysa9307]

What would be if we are receiving $500 monthly with a discounted annual rate of 6%? Do we have to multiply the monthly cash flow by 12?

[@Edspira]

That's covered in my video on the present value of an ordinary annuity

[@ivornworrell]

*Hello, assuming ,hypothetically speaking, that the inflation rate (cost of living) is perpetually constant and so too is the discount rate applied to the perpetuity:Wouldn't the value of the perpetuity EXCEED its present value after a certain period of time has passed and once funds are not drawn from the perpetuity? Therefore it would be foolish for one to accept the present value of such an investment as opposed to its future cash streams (assuming it is a risk-free perpetuity). Am I right?*

[@Edspira]

Ivor, Since a perpetuity is paying out a cash flow of $500 per period, this is a "withdraw" from the pool of funds every period that could have otherwise been earning interest. Thus, I don't agree with your statement that "funds are not drawn from the perpetuity". The perpetuity is paying-out $500 every period. This equation is calculating the present value of the perpetuity. Thus, if given the option of receiving $500 a period for the rest of your life or $8,333.33 now these two amounts would be equivalent.

[@ivornworrell]

Thank you for the reply.I was thinking of an annuity (investment fund) which is why I said funds were not withdrawn, but thank you for the clarification.But I am still puzzled because if I am receiving $500.00 annually for the rest of my life, $8333.33/$500=17 approx. So after 17 years the total accumulated $500 annual amts will EXCEED the present value of $8333.33, so how can it be equivalent to accept either $8333.33 now or $500 for life?

[@norro4816]

@@ivornworrell The present value of the 17 payments of $500 will accumulate into $5552.95 by the 17th year with an interest rate if 6%.

[@ivornworrell]

@@norro4816 May I ask how did you compute it?

[@acoessimples8453]

what software is this ? ty

[@samuelcastillo5026]

This is not working for me?... This is the question.. Harold brother owes him 1000 but instead of pating him the entire 1000 his brother promises to pay him 5$ at the beginning of each month for the rest of hislife. The prevailing market nomina rate is 5.5% is the present value of the perpertual more than 1000? That harold is owed.. In the book it says the value is 1,095.91? this calculation does not give me that amount?

[@samuelcastillo5026]

+Samuel Castillo I get - 1090.90

[@iandms1160]

since it is the beginning of each month its a perpetuity due so rather then doing payment/I you have to divide payment by the discount rate instead, alternatively you could just add the payment to the value you got which gives you 5+1090.909 which with rounding gets 1095.91

[@simpleministry9155]

But why is it worth 8k? I don't understand how it works, could you give me a more qualitative answer? Thanks.

[@iandms1160]

as time goes on under whatever your constant interest rate is the value of those future cash flows becomes smaller and smaller, think of a graph with a curve and asymptotes. The curve approaches it but never gets past it, think of the present value of a perpetuity as this asymptote.

[@thomascao-t8s]

@@iandms1160 well explained, the PV of cash flow far into the future wont affect much

[@You7aRe7My7LivE]

Thank you bud. Greetings from Frankfurt

[@MrShinobiguy]

Does anyone know how to calculate the discount rate in this problem using the other two?

[@thefuckingpearl]

Usually the inflation rate + risk free rate is considered as the discount rate

[@IamPaste]

What if the initial investment cost in that case what $3,000?

[@miguelconfesor4701]

Great explanation 👍

[@dw61w]

Shouldn't it be 500*1.06/0.06, the sum of a geometric series?

[@olivierst-hilaire9439]

No, because the 500 you will receive dont have interest

[@Jhanvi-sr3pz]

Thank you sir🙏

[@Edspira]

Most welcome!

[@DeepakSharma-xx8hu]

Thank You for explaining

[@Raphi]

So the lower the interest rate, the higher the present value. The higher the interest rate the lower the present value. How does that make sense? Wouldn't a lower interest make it less valuable?

[@ronyap28]

A high interest rate means that you could have invested those streams of cash for a higher gain. But you are receiving in instalments every year so you are losing out. Which means a lower NPV

[@todayu]

ronyap28 Bravo! I was really struggling with this, then you came along and cleared everything up. It totally makes sense now. Thank you!

[@icecold1805]

No no, you are missing the point. Say you got this awesome opportunity to earn a 100% interest in an awesome investment, but you don't have the money. Your mom offers you to give you money, but next month. Yeah well that money is not worth sh*t for you, cause by the time your mom gives you that money you just wasted an entire month you could have used in earning those awesome interests. See? the higher the interest, the less the present value.

[@fasihz]

@@icecold1805 Thanks for this man.

[@michaellai6619]

Thanks

[@jahanzebmemon]

Thank you. Love from Pakistan.

[@Edspira]

My pleasure. Best wishes and good tidings to you!

[@bhargavvenn]

Why is it called discount rate?

[@zeekyboi123]

Thank you Sir!!

[@gulhayoraxmonova3460]

Amazing ☺️

[@Edspira]

Thanks 😄

[@calmwins]

can any investment pay me 6% forever? I don't think so.

[@EnriqueSordo5]

What would happen if instead of receiving 500 every year, it´s every two years?

[@paultristan2094]

Same question, did you know the answer now?

[@EnriqueSordo5]

Paul Tristan I adjust the interest to calculate the value of it every 2 years

[@shivakumarchandrapattana8506]

@@EnriqueSordo5 ok in that case you should consider annuity amount = two year payment that's it

[@brainlife]

where did u get your numbers. makes zero sense

[@vivianesibusisiwe3991]

ooops i thot 6% conveted to a decimal is 0,06 buh this dude is sayn its 0,6

[@jacobg9690]

0.06 is Forsure 6%.