The reason (at minute 7:03) for the small variance between initial FCF/discount rate and the value generated from the excel NPV function is that when using the NPV function in excel when selecting the range of values that are to be discounted in the second argument of the formula, excel treats the values in the range as occurring at the end of period values and applies a discount factor to each value selected in the range. As the initial value in range is in the current period it does not require discounting. To correct the issue when using the NPV function select a range that excludes the initial value and then add the initial value to the value calculated by the NPV.
Gajen Dhayanathan Yes, that is true, thanks for adding that. The issue is that the NPV function in Excel does not actually calculate the NPV but rather the PV, so it's better to do it the way you suggested. I didn't want to get into this as it was already quite a long tutorial, but it's worth pointing out.
@@JiHoonPark-n2k There isn't really much to say because... you take the forward multiple from the public comps and then cross-check it to make sure the implied growth rate is reasonable. But there is no real intuition, as it's just taking the multiple from another data set.
the tutorial is just exceptional. but i cant find the excel sheet or practice sheet in the description please practice sheet as well so we could practice along with the tutorial.
If you click "More" or "Show More" below the video, you can scroll down and find links to the files and resources where applicable (we don't have them for every video in this channel).
Hi, Thanks for the video! But I have one question: In the excel file, what you actually do is 100/0,07=1429, I get that. But in the formula it says final year times 1+growth rate divided by 7% = 1471. Can you please explain to me what I miss?
In the Excel file, we assume that the "Initial Free Cash Flow" of $100 *IS* the Final Year FCF * (1 + Growth Rate), in other words it is the first Free Cash Flow received IN the terminal period. So that entire portion from Year 1 onward is actually the Terminal Period of a DCF, which extends out from the first year beyond the end of the projection period. If you use $100 * (1 + 7%) instead, now you're 2 years after the Final Year in the DCF projection period rather than 1 year after the Final Year in the DCF projection period.
Hi, Really thank you for the video. Im confused in part of "Discount rate - fcf growth rate" If, discount rate : 10%, FCF growth rate : 5% FCF*(1+growth rate)*(1-discount rate) FCF*0.945 comes that we have finally discount rate of 5.5% If we just subtract fcf growth rate from discount rate we have 5% Is there any part i confused? thank you.!!!
Sorry, but I don't understand your question. You use (Discount Rate - FCF Growth Rate) in the denominator because you're willing to pay more for a company that is growing more quickly, and you're willing to pay less if you have higher-returning alternatives elsewhere (i.e., a higher Discount Rate).
is their a rule of thumb for the time frame before you calculate terminal value? for high growth startups 10 years? stable businesses 5 years? would like your insight. thanks
It depends greatly on the company and its current growth rate. If it's a super-high-growth startup, maybe as long as 20 years. If it's an average company growing at a moderate pace, maybe 10 years. If the business is already very stable and barely changing from year to year, maybe 5 years. We almost always use 10 years, and more like 20 for younger/higher-growth firms.
Hi Brian, First of all thank you for all your videos, it's amazing! For this video, I had a question: I understand the logic behind the Gordon Growth Rate method, however I was wondering why we get a different amount by simply using the formula: FCF*(1+Growth Rate)/(Discount-Growth) - that is 100*(1+3%)/(10%-3%) which equals 1471.43EUR? Thanks !
Discount Rate : 5% , Growth Rate : 3% Initial : $100 NPV : $5000 Excel NPV:$4269. It is quite different.Which should i use? Why does the yield i intend to get is decreasing, the price is upping in the formula?(The longer time i would get back my invest $, the higher the npv) Is the rate is using the long-term Treasury Bond for each country? What is the formula when the Growth Rate is beyond discount rate? Is the terminal value is intrinsic value?
$5,000 is correct because that is what the NPV is if you go out into "infinity." The Excel version here only goes out 100 years. I'm not sure I understand your second question, but when the discount rate is lower, the NPV goes up because you can afford to pay more and still get the same amount of cash flows because you're targeting a lower yield. The discount rate is typically based on WACC or Cost of Equity, depending on the analysis. You can't make the growth rate higher than the discount rate or the formula doesn't make sense. Terminal Value is one component of the company's implied value, but there's more to it than that.
Thanks a lot. In the right formula for the Gordon growth model, the numerator is actually the final year cash flow in the forecast period multiplied by the FCF growth rate, which is actually the first Cash Flow in the Terminal period, right?
Hi, Is fascinating, i didnt know that. But 1 question, i think the reason why it reached a point where theres no growth is because discounting factor is bigger than growth rate, but what if a company growth rate is bigger than discounting factor, does it mean that terminal value formula cannot apply to calculate DCF? because the growth is gonna be perpetual already
"Net Present Value" means "Present Value minus the Asking Price or Purchase Price." "Present Value" means what some future cash flow or amount of money is worth today, discounted at the appropriate discount rate. If you're asking the difference between Present Value of FCFs and Present Value of Terminal Value in a DCF, the Present Value of FCF refer to the cash flows in the explicit forecast period over 5-10 years and what they are worth in today's dollars. The Terminal Value is for everything *after* that period, and what the cash flows in that period are worth in today's dollars.
How do you COME UP with the formula for the common ratio starting at 18:04. I understand what the common ratio is, but not how the formula emerges from what is shown in the seconds before? Can you explain? Thank you :)
As an example, assume that we're in Year 3. PV of FCF in Year 3 = FCF in Year 3 / ((1 + Discount Rate) ^ 3) Now, move to Year 4. PV of FCF in Year 4 = FCF in Year 4 / ((1 + Discount Rate) ^ 4) FCF in Year 4 = FCF in Year 3 * (1 + FCF Growth Rate) Therefore: PV of FCF in Year 4 = FCF in Year 3 * (1 + FCF Growth Rate) / ((1 + Discount Rate) ^ 4) PV of FCF in Year 3 = FCF in Year 3 / ((1 + Discount Rate) ^ 3) So, to move from Year 3 to Year 4, we could simply multiply the Year 3 term by (1 + FCF Growth Rate) / (1 + Discount Rate)
Ah, so in the second last function we can just take out the components of the last function, since we already used them in the PV Year 3 formula. So only ((1+FCF Growth Rate) / (1+Discount Rate)) remains (which we can simply multiply with the result of PV Year 3)? Correct me if I am wrong. Thank you!
I think we can all agree the concept is fluid when the targeted yield, which in reality is the estimated inflation rate, is higher than the cash flow growth that a terminal value makes sense. However, most often the cash flow growth is HIGHER than the target yield, and dividing it by some positive growth rate above its inflating cost structure doesnt make sense. If I think my casfhlows are going to grow in excess of the cost to 4%, dividing it to solve for when it zeroes makes no sense. Which yes, this is obvious...but we are describing something in perpetuity, so of course in some infinite series our required rate of return in the market must at the very least match the growth rate, and more certainly will beat it. Otherwise one stock would eventually be the economy.....but the fact is that many businesses are bought to outperform the average growth rate of their peers for short periods of times, and that is why the model is goofy. Arbitrary multiples are least valuable in some relatable context that could practically occur.
???? One of the conditions for using this formula is that the Growth Rate must be less than the Discount Rate since the denominator of the formula is (Discount Rate - Growth Rate). So I don't understand your comment. It's like saying, "Aha! Newtonion physics fails to work when you move at the speed of light. It's wrong!" Well of course, relativity comes into play then and the rules change. That situation doesn't meet the conditions for one set of rules to work. With this formula, there is no way that the Cash Flow Growth Rate could be higher than the Discount Rate or Targeted Yield for obvious reasons. If it is, then your inputs are wrong or your assumptions in the final few years are far off. A formula is only as good as its constraints.
Because the Gordon Growth Formula also uses the cash flow in the first year of the Terminal Period. The numerator in that formula is usually written as Final Year FCF * (1 + FCF Growth Rate), whcih gives you the cash flow in the first year of that Terminal Period by assuming that cash flow continues growing at the terminal FCF growth rate.
What if Growth Rate is higher than Discount Rate? Will it work? Can you explain with a quick example? Is it a valid case to have growth rate greater than Discount Rate?
The Growth Rate cannot exceed the Discount Rate. For the formula to be valid, the Growth Rate must be less than the Discount Rate. Otherwise, you run into a strange contradiction/circular logic because you would be receiving a Growth Rate higher than what is possible in other opportunities elsewhere... which means that your Discount Rate needs to be higher to match that.
???? I am confused by your question. You use a normal DCF analysis; there are no statistics involved unless you use a Monte Carlo simulation, which has some benefits, but is not something most analysts use all the time.
Wait how come to find NPV of FCF with 3% growth rate, you just divided initial FCF by discount rate - growth rate, so you didn't have to go through the tedious work of dividing all the projected values and terminal values by (1+discount rate) to the power of the year and them all up?
Because that is how you value any company or asset... Company Value = Cash Flow / (Discount Rate - Cash Flow Growth Rate), where Cash Flow Growth Rate < Discount Rate. Terminal Value is just another application of that concept.
@@giovannipoliti8315 ??? I don't understand your question. You only need to discount a cash flow or value if it occurs in the future. If it's at time zero, its present value equals the value shown in the analsis.
+Mike Lim Look at the GDP growth, the growth rates of comparable mature companies, how other companies have grown far into the future when they've reached maturity...
i was banging my head all day on trying to understand how terminal value works. Thanks a lot!
Thanks for watching!
Thanks so much. finally, find a video explaining the intuition behind the formula - like the algebra proof.
Thanks for watching!
wow, thanks so much. I have asked many profs about this and no body was able to explain it properly!
+Jiaming Qiu Thanks for watching!
The reason (at minute 7:03) for the small variance between initial FCF/discount rate and the value generated from the excel NPV function is that when using the NPV function in excel when selecting the range of values that are to be discounted in the second argument of the formula, excel treats the values in the range as occurring at the end of period values and applies a discount factor to each value selected in the range. As the initial value in range is in the current period it does not require discounting. To correct the issue when using the NPV function select a range that excludes the initial value and then add the initial value to the value calculated by the NPV.
Gajen Dhayanathan Yes, that is true, thanks for adding that. The issue is that the NPV function in Excel does not actually calculate the NPV but rather the PV, so it's better to do it the way you suggested. I didn't want to get into this as it was already quite a long tutorial, but it's worth pointing out.
Thanks for shwoing the algebra!
This is amazing. I understand it now. Thank you very much!
Thanks for watching!
Can you do another video for DFC - Terminal Value - Multiples Method Intuition?@@financialmodeling
@@JiHoonPark-n2k There isn't really much to say because... you take the forward multiple from the public comps and then cross-check it to make sure the implied growth rate is reasonable. But there is no real intuition, as it's just taking the multiple from another data set.
the tutorial is just exceptional. but i cant find the excel sheet or practice sheet in the description please practice sheet as well so we could practice along with the tutorial.
If you click "More" or "Show More" below the video, you can scroll down and find links to the files and resources where applicable (we don't have them for every video in this channel).
Thanks for the Brilliant Explanation. I had been trying understand the anatomy of the equation. I am glad i came across your video.
Thanks for watching!
Me too, amazing!
Excellent explanation. Thanks.
Thanks for watching!
thank your perfect explanation
+herp derp Thanks for watching!
Hi, Thanks for the video!
But I have one question:
In the excel file, what you actually do is 100/0,07=1429, I get that. But in the formula it says final year times 1+growth rate divided by 7% = 1471. Can you please explain to me what I miss?
In the Excel file, we assume that the "Initial Free Cash Flow" of $100 *IS* the Final Year FCF * (1 + Growth Rate), in other words it is the first Free Cash Flow received IN the terminal period. So that entire portion from Year 1 onward is actually the Terminal Period of a DCF, which extends out from the first year beyond the end of the projection period. If you use $100 * (1 + 7%) instead, now you're 2 years after the Final Year in the DCF projection period rather than 1 year after the Final Year in the DCF projection period.
Mergers & Inquisitions / Breaking Into Wall Street Ok, now it's clear! thanks for the quick reply!
Hi, Really thank you for the video.
Im confused in part of "Discount rate - fcf growth rate"
If, discount rate : 10%, FCF growth rate : 5%
FCF*(1+growth rate)*(1-discount rate)
FCF*0.945 comes that we have finally discount rate of 5.5%
If we just subtract fcf growth rate from discount rate we have 5%
Is there any part i confused? thank you.!!!
Sorry, but I don't understand your question. You use (Discount Rate - FCF Growth Rate) in the denominator because you're willing to pay more for a company that is growing more quickly, and you're willing to pay less if you have higher-returning alternatives elsewhere (i.e., a higher Discount Rate).
is their a rule of thumb for the time frame before you calculate terminal value? for high growth startups 10 years? stable businesses 5 years?
would like your insight. thanks
It depends greatly on the company and its current growth rate. If it's a super-high-growth startup, maybe as long as 20 years. If it's an average company growing at a moderate pace, maybe 10 years. If the business is already very stable and barely changing from year to year, maybe 5 years. We almost always use 10 years, and more like 20 for younger/higher-growth firms.
That's perfect video, and if the related excel files uploaded is better!
Thanks! The Excel files are not available here but will be made available as part of our bonus case studies on the BIWS site.
Hi Brian,
First of all thank you for all your videos, it's amazing!
For this video, I had a question: I understand the logic behind the Gordon Growth Rate method, however I was wondering why we get a different amount by simply using the formula: FCF*(1+Growth Rate)/(Discount-Growth) - that is 100*(1+3%)/(10%-3%) which equals 1471.43EUR? Thanks !
Sorry, I'm not sure which part you're referring to here. Both Terminal Values in this Excel file are the same.
Discount Rate : 5% , Growth Rate : 3% Initial : $100 NPV : $5000 Excel NPV:$4269. It is quite different.Which should i use?
Why does the yield i intend to get is decreasing, the price is upping in the formula?(The longer time i would get back my invest $, the higher the npv)
Is the rate is using the long-term Treasury Bond for each country?
What is the formula when the Growth Rate is beyond discount rate?
Is the terminal value is intrinsic value?
$5,000 is correct because that is what the NPV is if you go out into "infinity." The Excel version here only goes out 100 years.
I'm not sure I understand your second question, but when the discount rate is lower, the NPV goes up because you can afford to pay more and still get the same amount of cash flows because you're targeting a lower yield.
The discount rate is typically based on WACC or Cost of Equity, depending on the analysis. You can't make the growth rate higher than the discount rate or the formula doesn't make sense. Terminal Value is one component of the company's implied value, but there's more to it than that.
Mergers & Inquisitions / Breaking Into Wall Street Correct.Thanks for reply
Love from india, nice explaination
Thanks for watching!
Thanks a lot. In the right formula for the Gordon growth model, the numerator is actually the final year cash flow in the forecast period multiplied by the FCF growth rate, which is actually the first Cash Flow in the Terminal period, right?
Yes
Hi, Is fascinating, i didnt know that. But 1 question, i think the reason why it reached a point where theres no growth is because discounting factor is bigger than growth rate, but what if a company growth rate is bigger than discounting factor, does it mean that terminal value formula cannot apply to calculate DCF? because the growth is gonna be perpetual already
That can't happen. To use the Perpetuity Growth formula, the Terminal Growth Rate must be less than the Discount Rate.
What if the FCF Growth Rate is bigger than discount rate?
Then you need to re-think your assumptions because the analysis won't work if the FCF growth rate exceeds the discount rate.
Awesome
Thanks for watching!
Hi, great video!
Can you please explain what the difference is between net present value of FCF and present value of terminal value?
"Net Present Value" means "Present Value minus the Asking Price or Purchase Price." "Present Value" means what some future cash flow or amount of money is worth today, discounted at the appropriate discount rate.
If you're asking the difference between Present Value of FCFs and Present Value of Terminal Value in a DCF, the Present Value of FCF refer to the cash flows in the explicit forecast period over 5-10 years and what they are worth in today's dollars. The Terminal Value is for everything *after* that period, and what the cash flows in that period are worth in today's dollars.
How do you COME UP with the formula for the common ratio starting at 18:04. I understand what the common ratio is, but not how the formula emerges from what is shown in the seconds before? Can you explain? Thank you :)
As an example, assume that we're in Year 3.
PV of FCF in Year 3 = FCF in Year 3 / ((1 + Discount Rate) ^ 3)
Now, move to Year 4.
PV of FCF in Year 4 = FCF in Year 4 / ((1 + Discount Rate) ^ 4)
FCF in Year 4 = FCF in Year 3 * (1 + FCF Growth Rate)
Therefore:
PV of FCF in Year 4 = FCF in Year 3 * (1 + FCF Growth Rate) / ((1 + Discount Rate) ^ 4)
PV of FCF in Year 3 = FCF in Year 3 / ((1 + Discount Rate) ^ 3)
So, to move from Year 3 to Year 4, we could simply multiply the Year 3 term by (1 + FCF Growth Rate) / (1 + Discount Rate)
Ah, so in the second last function we can just take out the components of the last function, since we already used them in the PV Year 3 formula. So only ((1+FCF Growth Rate) / (1+Discount Rate)) remains (which we can simply multiply with the result of PV Year 3)? Correct me if I am wrong.
Thank you!
Yes
I think we can all agree the concept is fluid when the targeted yield, which in reality is the estimated inflation rate, is higher than the cash flow growth that a terminal value makes sense. However, most often the cash flow growth is HIGHER than the target yield, and dividing it by some positive growth rate above its inflating cost structure doesnt make sense. If I think my casfhlows are going to grow in excess of the cost to 4%, dividing it to solve for when it zeroes makes no sense. Which yes, this is obvious...but we are describing something in perpetuity, so of course in some infinite series our required rate of return in the market must at the very least match the growth rate, and more certainly will beat it. Otherwise one stock would eventually be the economy.....but the fact is that many businesses are bought to outperform the average growth rate of their peers for short periods of times, and that is why the model is goofy. Arbitrary multiples are least valuable in some relatable context that could practically occur.
???? One of the conditions for using this formula is that the Growth Rate must be less than the Discount Rate since the denominator of the formula is (Discount Rate - Growth Rate). So I don't understand your comment. It's like saying, "Aha! Newtonion physics fails to work when you move at the speed of light. It's wrong!" Well of course, relativity comes into play then and the rules change. That situation doesn't meet the conditions for one set of rules to work.
With this formula, there is no way that the Cash Flow Growth Rate could be higher than the Discount Rate or Targeted Yield for obvious reasons. If it is, then your inputs are wrong or your assumptions in the final few years are far off. A formula is only as good as its constraints.
Why did u use first year cashflow for the terminal value instead of final year as initially stated by the Gordon growth formula
Because the Gordon Growth Formula also uses the cash flow in the first year of the Terminal Period. The numerator in that formula is usually written as Final Year FCF * (1 + FCF Growth Rate), whcih gives you the cash flow in the first year of that Terminal Period by assuming that cash flow continues growing at the terminal FCF growth rate.
What if Growth Rate is higher than Discount Rate? Will it work? Can you explain with a quick example? Is it a valid case to have growth rate greater than Discount Rate?
The Growth Rate cannot exceed the Discount Rate. For the formula to be valid, the Growth Rate must be less than the Discount Rate. Otherwise, you run into a strange contradiction/circular logic because you would be receiving a Growth Rate higher than what is possible in other opportunities elsewhere... which means that your Discount Rate needs to be higher to match that.
i wanted to analyse the dcf method and fcfe method and the ratios for valuation which statistical model should i use for this ?
???? I am confused by your question. You use a normal DCF analysis; there are no statistics involved unless you use a Monte Carlo simulation, which has some benefits, but is not something most analysts use all the time.
thanks mate
Hi!
How do I open the excel file for this video, I don't see it on the page?
Thanks
It is not available for this video, but I will see if we can upload it in the future.
Wait how come to find NPV of FCF with 3% growth rate, you just divided initial FCF by discount rate - growth rate, so you didn't have to go through the tedious work of dividing all the projected values and terminal values by (1+discount rate) to the power of the year and them all up?
Because that is how you value any company or asset... Company Value = Cash Flow / (Discount Rate - Cash Flow Growth Rate), where Cash Flow Growth Rate < Discount Rate. Terminal Value is just another application of that concept.
thanks!
@@financialmodeling thats true but why you did not discount it at time zero?
@@giovannipoliti8315 ??? I don't understand your question. You only need to discount a cash flow or value if it occurs in the future. If it's at time zero, its present value equals the value shown in the analsis.
You should have been my finance prof at uni lol
Thanks! One day, one day... just need a Ph.D. or two first.
is (r-g) saying you can pay more because there is growth?
Yes
How does one determine the growth rate?
+Mike Lim Look at the GDP growth, the growth rates of comparable mature companies, how other companies have grown far into the future when they've reached maturity...
Hello BIWS,
So, is the terminal value of using the formula (final year fcf*(1+fcf growth rate) over
(discount rate-fcf growth rate)
27,455.19?
+mark yu That is the formula, yes. I'm not sure what numbers you're using in the formula, so your answer may or may not be correct.
I see, thank you BWIS.
How to Find the FCF Growth Rate ???
For the projection period, forecast it based on past performance. For the terminal period, tie it to long-term GDP growth or the rate of inflation.
Hi for growth rate should I take the average inflation rate for that year or inflation rate of the just the month in which I am doing the analysis