Why You NEED to know the Time Value of Money Formula (Excel NPV function)

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  • Опубліковано 27 жов 2024

КОМЕНТАРІ • 170

  • @LeilaGharani
    @LeilaGharani  4 роки тому +16

    Grab the file I used in the video from here 👉 pages.xelplus.com/time-value-file
    Get access to the full "Fundamentals of Financial Analysis" course here: www.xelplus.com/course/learn-financial-analysis/

  • @uxo2255
    @uxo2255 4 роки тому +21

    Leila is the best instructor that I have ever had to pleasure of learning from. I just love her.

  • @jamesperry1602
    @jamesperry1602 4 роки тому +24

    _Love the clarity and simplicity and variety of this NPV video._ TᕼᗩᑎK YOᑌ!

    • @LeilaGharani
      @LeilaGharani  4 роки тому +4

      My pleasure. I'm glad you like the tutorial.

    • @Sands2022
      @Sands2022 4 роки тому

      @@LeilaGharani thank you Leila you're amazing

  • @Betterifitsfree
    @Betterifitsfree 4 роки тому +15

    So well explained. I used this formula (with a financial calculator) to beat up on my car finance guy and got super low rates. Glad you are explaining this Leila, excellent job once again. ⏳💰

    • @LeilaGharani
      @LeilaGharani  4 роки тому +7

      That's what I'm talking about! It pays off to have some basic understanding of finance :)

    • @MrSupernova111
      @MrSupernova111 4 роки тому +2

      That's awesome! I have a degree in finance and I work in asset management. I'm dying for the day I need to buy a car so I can take my calculator with me and haggle the salespeople. haha

  • @sachinrv1
    @sachinrv1 4 роки тому +1

    NPV reminds me, "A bird in the hand (right now) is worth more than two in the bush".
    Wonderfully explained. Even the non finance guys can easily follow this.

  • @excelisfun
    @excelisfun 4 роки тому +15

    One of the greatest functions ever : )

    • @LeilaGharani
      @LeilaGharani  4 роки тому +3

      Agree! Thank you Mike :)

    • @johugra1
      @johugra1 4 роки тому

      Yes but... Doing lease or buy analysis on IT equipment the lease looked best in NPV terms. But we did not know when we would be ready to replace the equipment and the lease expiry date was fixed. So we bought saving loads of money in the end as the replacement was delayed. NPV is a useful tool that looks impressive but the answer can easily be overwhelmed in the real world.

  • @EricaSeeling
    @EricaSeeling 4 роки тому +4

    Leila, you are amazing in explaining Excel in such a clear and easy manner!

  • @keltonbolokonya5442
    @keltonbolokonya5442 10 місяців тому

    I appreciate the clarity, the voice renders it to comfort in listening

  • @shahidulhasansarker
    @shahidulhasansarker 8 місяців тому

    I have seen 10+ tutorial about npv but dont understand fully but now i understand. Thanks my Lady Excel Lord Leila Gharani. I always ..............You

  • @PaulTrz
    @PaulTrz 4 роки тому +1

    Fantastic video, Leila. Thanks to it's simplicity I have finally grasped the concept of NPV!!!!

  • @ReiszRiann
    @ReiszRiann 4 роки тому +2

    Good thing there are like you here in YT discussing these things in a very knowledgeable and clear way! :)
    Maybe you can add to your next video about WACC, NPV, IRR, FV and Ratio analysis. This will be good for MBA and accounting students like me!
    Thank you very much! Much support!

  • @denconstutube
    @denconstutube 4 роки тому

    Another excellent video. I am embarrassed to keep on saying how good your videos are. People will think I'm just a fan without a real background in business to be a real judge of the quality of the presentation. Just so you know, I have over 40 years as a senior executive in billion-dollar companies, and I have personally done thousands of presentations in Excel, Powerpoint, pertaining to various subjects including finance. When I say I think your presentations are excellent, I do mean excellent. I wish I had your training when I was in business. Thank you for all of your videos.

  • @Nico-vr1kx
    @Nico-vr1kx 3 роки тому +1

    Its incredible how easy it is to understand and how difficult some teachers make it look

  • @S_M_0009
    @S_M_0009 4 роки тому +1

    I just love the way you explain. You make excel so easy. Thanks

  • @peterasteberg9926
    @peterasteberg9926 2 роки тому

    This is the best explanation I've ever heard, never understood this before... Thanks!

  • @dennisd5776
    @dennisd5776 4 роки тому +1

    Nice introduction to Present Value. When I teach The Time Value of Money I always start with Future Value as the idea that if I invest a dollar and earn interest I will have a dollar plus. Students tend to understand this better. Then I can explain Present Value by show that I am indifferent to a dollar now or the dollar plus in the future (for the given discount rate).

  • @Sons_of_Eden
    @Sons_of_Eden 4 роки тому

    This took my back to my Series 7 and 66. Usually I get simple Excel tips, but wow this a great refresher.

  • @revikoreparambil8702
    @revikoreparambil8702 Рік тому

    Hi Leila, You have explained the concept of npv with the actual calculation part and then proceeded on to the excel fuction. So it is easy to understand the concept intuitively, otherwise the excel fuction would have remained a blackbox. Thank you.

  • @katerina6495
    @katerina6495 4 роки тому +1

    Danke Liebe Leila, die schönste Erklärung des Kapitalwerts, Viele Liebe Grüsse 🤗

  • @farzanmoha8935
    @farzanmoha8935 4 роки тому +2

    I appreciate you Leila, you are an amazing teacher. The way that you explain along with visual features, make learning sweet and easy.

    • @LeilaGharani
      @LeilaGharani  4 роки тому

      Thank you for the kind words. I'm glad you like the video.

  • @mikehoffman1475
    @mikehoffman1475 4 роки тому +1

    Excellent video and explanations. The authors of Accounting text books should watch this video and learn to present in a clear manner.

  • @amirierfan
    @amirierfan 4 роки тому +1

    Hey Leila! This series is truly useful! Please keep going...

  • @47Yeoman
    @47Yeoman 4 роки тому +1

    Ms. G, nice job as always. Your knowledge of Excel is the cake; your clear, concise presentation is the icing on that cake. Thank you.

  • @garydbowen
    @garydbowen 4 роки тому

    Leila is an excellent teacher.

  • @ICallItFutile
    @ICallItFutile 3 роки тому

    You explain this better than my accounting books and teachers.

  • @ilaitiatoroki7311
    @ilaitiatoroki7311 2 роки тому +1

    WELL PRESENTED. THANKS.

    • @Potencyfunction
      @Potencyfunction 9 місяців тому

      Well that not a biggie shit. Its just the value of money in time .

  • @adrianvivas4953
    @adrianvivas4953 4 місяці тому

    Hi from Argentina! what a straight to the point, cristral clear explanation! subscribed!

  • @juniordelgiorno5260
    @juniordelgiorno5260 4 роки тому +3

    Another fantastic learning opportunity, great Video!

  • @ashkanahmadi
    @ashkanahmadi 4 роки тому

    In 10 minutes you just explained this much better than my corporate finance classes during my MBA 🤦‍♂️🤦‍♂️

  • @tarekalsherif57
    @tarekalsherif57 3 роки тому

    Simple and clear as usual, thanks Leila!

  • @MrSupernova111
    @MrSupernova111 4 роки тому

    I love this video! I watch almost every video from you and this is my bread and butter. I have a degree in finance and I work in asset management. TVM of money should be taught in every high school as a mandatory part of a personal finance course. The world would be a lot better if people knew how to manage personal finances.

  • @theowemer5782
    @theowemer5782 4 роки тому +1

    brilliant explanation

  • @dennisBZC
    @dennisBZC Рік тому

    Absolutely brilliant suite of videos! Since I discovered Leila’s videos, I’ve been trying to learn the tips and tricks in Excel. Your explanations of some basics accounting and investment analysis are so clear and easy to understand.
    Also CONGRATULATIONS on getting 2m followers too! I remember you were on about 1.2m when I came across your videos. That was only a few months ago!

  •  4 роки тому

    I have started following Leila just for pleasure and I think I will finish up as a finance professional at the end :D Thank you again..

  • @leilatavakoli2242
    @leilatavakoli2242 4 роки тому +1

    This video is very informative. It is too important in Financial Management.

    • @LeilaGharani
      @LeilaGharani  4 роки тому +1

      Glad you like it. Nice name 😉

  • @MarcosReisPT
    @MarcosReisPT 4 роки тому +1

    Hello Leila! Thank you for your great content. Your videos and clarity on explaining the concepts is great.
    Keep on the good work!

    • @LeilaGharani
      @LeilaGharani  4 роки тому

      Thank you for the kind feedback Marcos. I'm glad you like the videos.

  • @TheTraffic247
    @TheTraffic247 4 роки тому +1

    Excellent video! 👍

  • @vanshsethi2276
    @vanshsethi2276 4 роки тому

    Hey Leila! I absolutely love your work. I have improved my excel skills significantly through your tutorials. I would love to see your videos on some more financial excel functions like PPMT, IPMT and other advanced finance functions. Really need it. Thank you so much for all the lectures delivered till now. Cheers! :)

    • @LeilaGharani
      @LeilaGharani  4 роки тому +1

      Glad you like the videos. Many thanks for your suggestions. I'll add them to my list.

  • @sjn7220
    @sjn7220 4 роки тому +1

    Very nice! Including IRR would have rounded this out nicely.

  • @zeno2712
    @zeno2712 4 роки тому +1

    One pitfall to be wary of is to calculate the rate you need to make the investment worthwhile (in terms of npv) then to let yourself be convinced (with ad hoc reasoning) that rate is perfectly reasonable and achievable. You really need to understand what rate you need before you work out what the npv is for a particular investment!

  • @tnkwok9682
    @tnkwok9682 4 роки тому +1

    Great video as always!👍

  • @nirmaluae
    @nirmaluae 4 роки тому

    Explanation is Cristal clear. Thank you 😊

  • @kranthimadanu2886
    @kranthimadanu2886 4 роки тому

    Got clarity on the concept and excel functionality.....Thanks

  • @darkshinigami9438
    @darkshinigami9438 4 роки тому +2

    Great video, time value of money is a key concept in finance. Could you make a video about how to calculate the discount rate in case we don't deal with a company? Keep up the great work :D

  • @GirGirGirGir160
    @GirGirGirGir160 11 місяців тому

    Thank you so much Leila you are a gem

  • @cfaprashant45
    @cfaprashant45 2 роки тому

    Very well done Madam.

  • @keno9964
    @keno9964 4 роки тому

    Excellent, thanks Leila.

  • @cdyard1
    @cdyard1 4 роки тому +1

    Another great video. Thanks!

    • @LeilaGharani
      @LeilaGharani  4 роки тому +2

      Thanks Claire. Glad you like it.

  • @sachinkishore4115
    @sachinkishore4115 3 роки тому

    thanks a lot for excellent explanation. great

  • @abdulwakeel8127
    @abdulwakeel8127 4 роки тому

    Great job Leila Gharani...

  • @wayneedmondson1065
    @wayneedmondson1065 3 роки тому

    Thanks Leila! Thumbs up!!

  • @Amine-xl5ut
    @Amine-xl5ut 4 роки тому

    Thank you Laila for the efforts ..

  • @alexanderwassie9672
    @alexanderwassie9672 3 роки тому

    concise & clear

  • @sachinpesalangan3839
    @sachinpesalangan3839 4 роки тому

    You are good in explanation!

  • @kazminhenkin
    @kazminhenkin 3 роки тому

    Good Work! Great content

  • @RahulJauhari
    @RahulJauhari 4 роки тому

    Very useful for personal finance thanks

  • @md.niazomartorabee5439
    @md.niazomartorabee5439 4 роки тому

    NPV, PBP, IRR, BCR all are essential for time value of money.
    It's our request that you'll make some tutorial for those

  • @watchknight201
    @watchknight201 4 роки тому +1

    Just when you need the information 🤩

  • @barttitulaerexcelbart9400
    @barttitulaerexcelbart9400 4 роки тому

    As always: very good explained. One critical point: in the first "manual" solution, this is only valid if all the amounts are the same (in this case 2.700), but the second formula also is valid if the numbers are different, so that's why I always would recommend the CF/(1+%)^n formula. Another issue is that the NPV is confusing: the economic NPV is the "Excel NPV" - initial investment. To make your next video: NPV requires constant time intervals (like one year), but did you try XNPV ? You can enter any dates !!

    • @LeilaGharani
      @LeilaGharani  4 роки тому

      Very true. Thank you for the suggestion for the next video :)

  • @unitedpens
    @unitedpens 3 роки тому +1

    Thank you a million :)

    • @LeilaGharani
      @LeilaGharani  3 роки тому +1

      Our pleasure :)

    • @Potencyfunction
      @Potencyfunction 9 місяців тому

      What a million cost the value ? The value is 0 is not worth it for the future with that returns, rate and value.

  • @labonnasaha9675
    @labonnasaha9675 4 роки тому

    Thanks. You are doing a great job. Could you please make a video showing how to make coupon schedule of bond investment quickly?

  • @mohamedelkhateeb6224
    @mohamedelkhateeb6224 4 роки тому

    you are amazing !!!! Thank you for all this info.

  • @aboelmagd100
    @aboelmagd100 4 роки тому +2

    Beautiful as usual

  • @Deependra1991
    @Deependra1991 4 роки тому

    This is part of project management and management accounts part of mba finance and bbm (economics honors)

  • @alirezalashgari1311
    @alirezalashgari1311 Рік тому

    سلام.ممنون بابت مطالب کاربدی که مطرح می کنید

  • @angelomagtira1998
    @angelomagtira1998 4 роки тому

    This helped me in my management advisory service subject =)

  • @valueStocks
    @valueStocks 4 роки тому +7

    The most basic concept that should be taught to every child. Still dont know why excel hasn't fixed the issue of giving negative values with PV and FV though.

    • @dennisd5776
      @dennisd5776 4 роки тому +1

      All calculators (Excel, HP, Google Sheets, BI, etc) use the negative/positive switch in computing cash flows. The reason for this that the first period is general considered a payout (you buy the investment), which is a negative cash flow. There are examples where the first payment is received and the subsequent are payouts, but it is still a combination of paying and receiving. Advance business analysis can include both positive and negative cash flows; way to advance for this introduction.

    • @MrSupernova111
      @MrSupernova111 4 роки тому

      I highly agree with the first part. However, the negative thing is not an Excel issue. Its a cash flow issue. Money coming in and going out. They can't both have the same sign for that reason. I have a degree in finance.

    • @MrSupernova111
      @MrSupernova111 4 роки тому

      @@dennisd5776 . Well stated. I saw your comment after I posted my comment.

    • @valueStocks
      @valueStocks 4 роки тому +1

      @@dennisd5776 Not quite sure what you mean. When I did my degree in finance I was told my my profs that this was just an excel issue. For example: Future Value function. Giving the arguments of PV: 100,000, I: 10%, PMT, 10,000, NPR: 10. You get -418,748, which is obviousness incorrect. I was always just told to multiple FV results by -1.

    • @dennisd5776
      @dennisd5776 4 роки тому

      @@valueStocks The rational is: I buy (Payout) an investment of 100,000 and I add payments (Payout of 10,000). So, in the formula the enter payments with a negative sign (payout) I will get a positive 418,748. In the FV formula enter the 100,000 PV as -100,000 and the payments of 10,000 as -10,000 you will get the correct answer of 418,748. Yea, sometimes it is just simpler to take the easy short cut.

  • @stressboy4326
    @stressboy4326 3 роки тому

    Hi, loved your video! Do you have any teaching videos that do not start from Year 0 or Year 1 but rather problems based on years (for example 3 to 8 or 5 to 10 etc etc)?

  • @bradroberts8047
    @bradroberts8047 10 місяців тому

    Thanks for your many helpful videos. Wondering if you can help me understand the MIRR function (MIRR(values,finance_rate, reinvest_rate). When I change the finance_rate, the result of the function does not change? Not sure why? Can you explain this function please. Thanks.

  • @taizoondean689
    @taizoondean689 4 роки тому

    Thanks Ma'am

  • @gFowmy
    @gFowmy 4 роки тому

    Could you break down the XNPV function as you did here?

  • @steventate9276
    @steventate9276 Рік тому

    I got another question. So I am doing the =pmt and =nper functions and in the function arguments box you are always supposed to put 0 in the FV future value. ( that's what my cheat sheets says) I am wondering if there is ever a situation where the FV is not 0. I would like to see an example of where we would type something other than 0 for the FV. when doing a pmt or nper function. I ask this question because you don't know if a video tutorial will cover a specific question until you watch the whole video. for so many questions you can't tell by the title of the video if will cover the specific thing you are wanting to know.

  • @EricaSeeling
    @EricaSeeling 4 роки тому

    Would be useful to elaborating XNPV too, it is more accurate and useful

  • @jasonipfatsiong2062
    @jasonipfatsiong2062 4 роки тому

    You should considering lecturing...combining content with tools great value

  • @MrCharlieUK
    @MrCharlieUK Рік тому

    Is it possible do something like this over the period of a year rather than 4 years? so payments would be on a monthly basis rather than yearly?

  • @sulaimansait864
    @sulaimansait864 4 роки тому

    Thanks mam
    Tell about employee daily attandence for the excel sheet vlookup formula

  • @mkrlnstitute4520
    @mkrlnstitute4520 4 роки тому +1

    U r right mam

  • @anuragvermasblog
    @anuragvermasblog 3 роки тому

    Hi Leila
    I have question- could you help me in creating a worksheet, which will copy a cell value from sheet 1 to sheet 2 automatically and when I add sheet 3 it will automatically copy the cell value from sheet 2.
    For example I have cell value of 300 in cell C5. Now when I add a sheet c5 gets copied to a1 from sheet1. Next when I add Sheet 3 the cell value of c5 which can be 500 in sheet 2 should get copied to sheet 3 in cell a1 automatically as 500

  • @zander9486
    @zander9486 4 роки тому

    Hi
    I was wondering what would you like to see ms team add to Excel?
    Or do you think Excel has reached its limit
    Thanks

  • @yulinliu850
    @yulinliu850 4 роки тому +5

    In transport economics we have "money value of time" 😊

    • @LeilaGharani
      @LeilaGharani  4 роки тому +4

      Haha, there is value in many things :)

    • @Potencyfunction
      @Potencyfunction 9 місяців тому

      You mean logistics? That is totally another value as the transport implies other accounting type. But the value could be defined. People in hunger need transporations , if they can not be proviede from own organisational entreprises. Some companies are just distroing their own value, I dont even know why they exist.

  • @Joda-es5xd
    @Joda-es5xd Рік тому

    If there a way you cab create a video that uses goal seek to derive at the rate using the npv function?

  • @hosseinhosseinpoor4845
    @hosseinhosseinpoor4845 3 роки тому

    thanks.....

  • @MarkoVrbos
    @MarkoVrbos 4 роки тому

    I'm confused with the last example... Shouldn't minimum return be the profit that will be made by machines in 4 years?
    If yes, 6% is not discount rate... Discount rate is missing.
    Also, 6% of 50 000$ is 3000$, which means that the goal is still not reached...
    I think that to fulfill the "minimum return" requirement, there is a formula missing comparing NPV and expected return. And an actual discount rate is missing...
    Please correct me if I'm wrong, I'm not in accounting, I'm an engineer... Just interested in variety of topics, so trying to understand :-)

  • @rasoulkhoshravan5912
    @rasoulkhoshravan5912 4 роки тому

    I enjoyed it

  • @lucyene5060
    @lucyene5060 4 роки тому

    Amazing!!!!!!!!!!!!!!!

  • @SholaDsdg
    @SholaDsdg 4 роки тому

    This is a boom!!!

  • @ahmedalmubarak6612
    @ahmedalmubarak6612 4 роки тому +1

    When I make a chart, i can insert a the power trend function on that chart.
    Is there a way to find the expected value for the max r^2 by using Excel formulas...

  • @marstoilov
    @marstoilov 4 роки тому

    Great video, the only thing I didn't get is how we ended up with 10800 and why is not considered as changing variable. Why changing only the percentage not the 10800

    • @LeilaGharani
      @LeilaGharani  4 роки тому

      I'm not sure I understand. The 10800 was the alternative to getting 10000 right away. But because the 10800 consist of payments in the future we need to discount them.

    • @marstoilov
      @marstoilov 4 роки тому

      @@LeilaGharani yes, what I meant was is it 10800 picked randomly, because setting this amount is changing the picture as well?

    • @LeilaGharani
      @LeilaGharani  4 роки тому

      Yes, it was just a random number that somewhat makes sense for such a situation.

  • @RobertLongM
    @RobertLongM 4 роки тому

    Someone help me understand why would money have less value in the future? Is inflation always a case? Does this apply to Companies or could this work for a friend-to-friend loan? Where do Discount Rates come from?
    This is really cool

    • @RobertLongM
      @RobertLongM 4 роки тому

      Bill Faulkner gotcha
      I was curious where that % Discount Rate even comes from

    • @roman75236
      @roman75236 4 роки тому

      From my understanding, inflation will exist most of the time, even in a friend-to-friend transaction. "A dollar today will not buy the same tomorrow." Everything is getting more expensive everyday, it is easier to notice when buying basic need products, whether they increase their price or decrease their size.

    • @RobertLongM
      @RobertLongM 4 роки тому

      Luis Roman ooooh I get it ! So the person borrowing makes out if the interest is low, since his $1 is worth more.

    • @AP2922
      @AP2922 4 роки тому +1

      @@RobertLongM inflation is always a consideration. Inflation is part of what makes our modern financial system work, and each country's Central Bank (government body) targets an inflation rate for the economy. For the US that is 1.7-2%
      Any transaction that involves borrowing or lending involves some kind of interest rate/discount rate/return rate. In the corporate example Leila mentioned that was the WACC which is the average cost to get money, averaging costs to borrow or sell shares.
      For an individual this is typically an interest rate. Interest rates can be decided on based on a number of factors. Such as the minimum amount you want to earn from loaning money, or you could figure out what the opportunity cost is to you to lend money. If you can put money in the bank and earn 2% with no risk that is your minimum opportunity cost. If you have somewhere else where you could put money and get 5% then you would use that as a minimum.
      Banks base their interest rates for loans and mortgages on the interest rate set by the country's Central Bank and then add a profit margin.
      That's long but I hope it helps.

    • @RobertLongM
      @RobertLongM 4 роки тому

      Adam Excellent explanation! - its a doozy when all my years had no financial experience in corporate settings. But I’m interested to know it Thank You

  • @amitsgvlog
    @amitsgvlog 4 роки тому

    Beautiful

  • @SahilKhan-pl6lq
    @SahilKhan-pl6lq 4 роки тому

    How can I show on charts ❓ is it possible..

  • @aliahamedchowdhury1697
    @aliahamedchowdhury1697 4 роки тому

    Dear Mam, Please Help me to set entry time.
    When a data input/entry in any sell in excel is made,
    its date and time will be automatically entered in a sell. plz help me the solution.

  • @radelpcpa_ph4155
    @radelpcpa_ph4155 4 роки тому

    May I request permission to use some of your visuals. I am a CPA from the Philippines. I will just indicate (Courtesy of: Leila Gharani). Thank you.

  • @enriquesanchez7442
    @enriquesanchez7442 4 роки тому

    You present D4 as a cell but change it to $D$4 without explanation. Can you elaborate?
    Thanks

    • @LeilaGharani
      @LeilaGharani  4 роки тому

      I fixed the cell reference because I dragged the formula to the right. You may want to have a look at that: ua-cam.com/video/FRu48zy-Djk/v-deo.html

    • @enriquesanchez7442
      @enriquesanchez7442 4 роки тому

      @@LeilaGharani Thanks, the video helped with explanation. Would you recommend a course of yours that I can take for excel fundamentals to advanced. ie on Udemy?

    • @LeilaGharani
      @LeilaGharani  4 роки тому

      The course Excel Essentials for the Real World will give you a good foundation in Excel. Hope you'll like it.

  • @AceHardy
    @AceHardy 4 роки тому

    💲

  • @graphguy
    @graphguy 4 роки тому

    The caveat to what seems to be a clear business decision is that $9,574 right now is better than getting zero right now.

  • @alias_peanut
    @alias_peanut 3 роки тому

    我们学到 present value = future cash flow / (1 plus disvount rate) Number period
    哇塞,太牛🐮

  • @PropertyX.Portugal
    @PropertyX.Portugal 4 роки тому

    Last 2 videos you left reproduction list initial topic, basic accountant

  • @IanTanLK
    @IanTanLK 4 роки тому

    Important stuff they don’t teach in school...

    • @LeilaGharani
      @LeilaGharani  4 роки тому

      So true. Definitely not in the school I was :)

    • @karhukivi
      @karhukivi 4 роки тому

      Actually they do but they call it "geometric series" and never mention money! Also used for valuing bonds and calculating mortgages.

  • @shreeganeshaaynamah353
    @shreeganeshaaynamah353 4 роки тому

    ❤❤