### Stock Valuation Method - Discounted Cash Flow

This is the 5th part of my stock valuation series and I've previously covered the Graham Number, average dividend yield, average price-to-earnings ratio, and average price-to-sales ratios. The previous 4 posts all looked at a historical trends but didn't really look into the future which is what we're interested in. This week we'll take a more in depth look at the discounted cash flows of the earnings for a company. Forgive me now, but this post will be a bit long and quite dry. Such is the nature when talking math. All my fellow math nerds though, enjoy.

Essentially a discounted cash flow analysis takes the future cash flows, or earnings per share, and discounts them back to now to get a net present value. Discounting is just the opposite of a growth rate. It's a way to calculate how much money you would need now to have a certain amount in the future if you can compound it at the specified discount rate. The formulas in this are all very simple and it's easy to create a spreadsheet to do all the work for you. The basic formula we'll use is:

For example, if I offered to give you $1,000 a year from today, how much would you accept today so you had the same $1,000 in the future? If you assume that you can grow whatever dollar amount you receive by 10% in one year, then you would need me to give you at least $909.09 today to have $1,000 one year from now. How did I come up with the $909.09? Just rearrange the above formula to solve for PV. The formula becomes:

Now that the basics are out of the way, let's go through the whole discounted cash flow process. First off, let's figure out all the information we'll need and define a few more terms. We need to figure out the starting EPS value to use. You can use the TTM EPS or the current fiscal year estimate. Next, we need to figure out what kind of growth rate to use. For simplicity, I use the analyst estimate for the next 5 years, although that's subject to debate as to whether that should be used. If it's a small or mid cap company that has a higher expected growth rate then I would expect a higher EPS growth rate, for large blue chip companies such as JNJ, PG, KO, CLX and the like, I would expect growth rates in the 5-10% range for the next 5-10 years. Next come up with a safe assumption for how long that growth can last. Typically I won't use more than 5 years for my growth rate before swapping to the perpetuity rate.

Speaking of perpetuity rate, what is that? It's just the expected EPS growth rate every year afterwards. I would safely expect that the companies mentioned above can at least grow EPS at the rate of inflation, which in the long-term has been around 3.50%. The last bit of information we need is the discount rate. As covered earlier, the discount rate is essentially your required rate of return. This is the value that every dollar of earnings will be discounted every year to calculate the net present value of those earnings. Some people like to use the risk free rate of return which is typically taken as the rate of the 10 year US Treasury bond, although I prefer to use a discount rate closer to 10% since this is a built in margin of safety and why would you take the risk of equity ownership if you can get a guaranteed return from T-bills.

Since we now have all of the inputs I'll go over the steps. Take the starting EPS figure that you came up with and using formula 1 from above input the growth rate and EPS to calculate the FV EPS using N = 1. This gives you the future year's EPS based on your expected growth rate. Now to calculate the NPV we swap over to formula 2 from above. Input the FV that you just calculated and use the discount rate as the GR in the formula with N = 1. Now you have the 1st year's net present value, or discounted value.

To calculate the 2nd year, use formula 1 from above, but instead of the starting EPS you'll use the FV EPS that you calculated in the previous step for year 1. Once you calculate the 2nd year EPS, swap back to formula 2 using the same discount rate except this time N = 2.

Repeat this process until you get to whatever year you want to crossover from the initial growth rate to the perpetuity or long-term growth rate. Once you get to that year, then start using the long-term rate instead of the higher growth rate for formula 1. Nothing changes in the process for formula 2 however. You then repeat the steps for several years, I'd go at least 30. Adding up the NPV of the EPS will give you the fair value price of the stock. If you pay no more than the fair value price and the EPS growth rates play out like you estimated, assuming a constant P/E ratio you would grow your investment at the discount rate or expected rate of return.

Our inputs will be Starting EPS of $1.00, 9% growth rate for 5 years, followed by 4% in perpetuity, with a discount rate of 10%.

(1) Calculate the FV EPS for Year 1 using Formula 1. FV = $1.00 * (1+0.09)^1 = $1.09

(2) Calculate the NPV of the Year 1 FV EPS using Formula 2. PV = $1.09 / (1 + 0.10)^1) = $0.99

(3) Calculate the FV EPS for Year 2 using Formula 1. FV = $1.09 * (1+0.09)^1 = $1.19

(4) Calculate the NPV of the Year 2 FV EPS using Formula 2. PV = $1.19 / (1 + 0.10)^2 = $0.98

Continuing these steps for 30 or more years and then summing up the NPV EPS = $21.42.

This means that $21.42 is the most you should pay per share of the stock in order to have a 10% rate of return.

Since I'm so nice, I've created a Google spreadsheet to calculate the Discounted Cash Flow for you guys to make your life easier. All you need is the same inputs from before, but the spreadsheet will calculate everything else, including using different discount rates with the same inputs. Feel free to look at the spreadsheet and try it out for yourself. All calculations should be protected but you can save the spreadsheet to your own Google drive if you want to make changes to the spreadsheet. If you happen to notice something that isn't quite right or it won't let you input your data, please let me know.

A Discounted Cash Flow Analysis is great for several reasons. One being that it's forward looking as opposed to backward looking. The previous methods that have been covered look at historical trends, however there's nothing written in the rules of investing that says a company must continue to trade in its' historical ranges for P/E, dividend yield, or P/S. Another thing I like about the Discounted Cash Flow analysis is that it allows you to see how fast a company must grow to be supported by the current share price. Just use the spreadsheet and change the inputs until the fair value price for your chosen discount rate equals the current price.

Like any valuation method, there's limitations. For one, trying to forecast earnings per share into the future is a tough task from year to year, let alone decades into the future. The calculations are also very sensitive to the inputs. In the example used above, using an 11% discount rate changes the fair price to $18.30, a 14.5% lower price. While using a 9% discount rate changes the fair price to $25.80, a 20.4% higher price. Changing any of the inputs by small amounts can drastically change the fair value price. This leads to the "garbage in, garbage out" conundrum. If your assumptions for the inputs are way off base, then your fair price will be useless.

Is using earnings per share the best route to go with the discounted cash flow? Ideally you'd start with revenues and subtract the capital expenditures to determine the actual free cash flows. However all we can go off of is the historical norms for revenue growth, tax rates, capital expenditures, and depreciation. That just introduces more variables to make assumptions on, which introduces more sources for error. There's just too many variables to try and make assumptions, a company's tax rate my significantly change, a new unforeseen product could be introduced or any other number of changes. Using EPS is a good enough metric for me when calculating the discounted cash flow for its simplicity.

For all of the inputs I try to be pretty conservative in my growth rate estimates to have a built in margin of safety in the calculations. If I was going to use the discounted cash flow analysis as my main valuation method, I'd further decrease the final value by at least 15% to have additional margin of safety due to the limitations listed above. Remember, in the end we're trying to forecast the growth of a company over several years using assumptions, and you know what the say about when you assume. A discounted cash flow analysis works best for large-cap stocks where you can have a higher degree of confidence in their yearly growth. I think it's pretty safe to say that almost all of the consumer staple giants will be able to at least grow earnings on par with inflation over the long term.

Once again, no valuation method can possibly encompass everything about a company to determine a fair value. This is why I like to look at several different valuation methods to come up with a fair value price and to be able to compare across multiple methods. If all of the valuation methods I've covered show that the company is undervalued, then there's a much better chance that it truly is undervalued.

Here is the link to the Discounted Cash Flow spreadsheet.

__The Basics__Essentially a discounted cash flow analysis takes the future cash flows, or earnings per share, and discounts them back to now to get a net present value. Discounting is just the opposite of a growth rate. It's a way to calculate how much money you would need now to have a certain amount in the future if you can compound it at the specified discount rate. The formulas in this are all very simple and it's easy to create a spreadsheet to do all the work for you. The basic formula we'll use is:

Formula 1

*where FV = future value, PV = present value, GR = growth rate, and N = number of years*For example, if I offered to give you $1,000 a year from today, how much would you accept today so you had the same $1,000 in the future? If you assume that you can grow whatever dollar amount you receive by 10% in one year, then you would need me to give you at least $909.09 today to have $1,000 one year from now. How did I come up with the $909.09? Just rearrange the above formula to solve for PV. The formula becomes:

Formula 2

If you plug in FV = $1,000, GR = 10% = 0.10 and N = 1, the PV is calculated to be $909.09.__The Guts:__Now that the basics are out of the way, let's go through the whole discounted cash flow process. First off, let's figure out all the information we'll need and define a few more terms. We need to figure out the starting EPS value to use. You can use the TTM EPS or the current fiscal year estimate. Next, we need to figure out what kind of growth rate to use. For simplicity, I use the analyst estimate for the next 5 years, although that's subject to debate as to whether that should be used. If it's a small or mid cap company that has a higher expected growth rate then I would expect a higher EPS growth rate, for large blue chip companies such as JNJ, PG, KO, CLX and the like, I would expect growth rates in the 5-10% range for the next 5-10 years. Next come up with a safe assumption for how long that growth can last. Typically I won't use more than 5 years for my growth rate before swapping to the perpetuity rate.

Speaking of perpetuity rate, what is that? It's just the expected EPS growth rate every year afterwards. I would safely expect that the companies mentioned above can at least grow EPS at the rate of inflation, which in the long-term has been around 3.50%. The last bit of information we need is the discount rate. As covered earlier, the discount rate is essentially your required rate of return. This is the value that every dollar of earnings will be discounted every year to calculate the net present value of those earnings. Some people like to use the risk free rate of return which is typically taken as the rate of the 10 year US Treasury bond, although I prefer to use a discount rate closer to 10% since this is a built in margin of safety and why would you take the risk of equity ownership if you can get a guaranteed return from T-bills.

Since we now have all of the inputs I'll go over the steps. Take the starting EPS figure that you came up with and using formula 1 from above input the growth rate and EPS to calculate the FV EPS using N = 1. This gives you the future year's EPS based on your expected growth rate. Now to calculate the NPV we swap over to formula 2 from above. Input the FV that you just calculated and use the discount rate as the GR in the formula with N = 1. Now you have the 1st year's net present value, or discounted value.

To calculate the 2nd year, use formula 1 from above, but instead of the starting EPS you'll use the FV EPS that you calculated in the previous step for year 1. Once you calculate the 2nd year EPS, swap back to formula 2 using the same discount rate except this time N = 2.

Repeat this process until you get to whatever year you want to crossover from the initial growth rate to the perpetuity or long-term growth rate. Once you get to that year, then start using the long-term rate instead of the higher growth rate for formula 1. Nothing changes in the process for formula 2 however. You then repeat the steps for several years, I'd go at least 30. Adding up the NPV of the EPS will give you the fair value price of the stock. If you pay no more than the fair value price and the EPS growth rates play out like you estimated, assuming a constant P/E ratio you would grow your investment at the discount rate or expected rate of return.

__An Example__Our inputs will be Starting EPS of $1.00, 9% growth rate for 5 years, followed by 4% in perpetuity, with a discount rate of 10%.

(1) Calculate the FV EPS for Year 1 using Formula 1. FV = $1.00 * (1+0.09)^1 = $1.09

(2) Calculate the NPV of the Year 1 FV EPS using Formula 2. PV = $1.09 / (1 + 0.10)^1) = $0.99

(3) Calculate the FV EPS for Year 2 using Formula 1. FV = $1.09 * (1+0.09)^1 = $1.19

(4) Calculate the NPV of the Year 2 FV EPS using Formula 2. PV = $1.19 / (1 + 0.10)^2 = $0.98

Continuing these steps for 30 or more years and then summing up the NPV EPS = $21.42.

This means that $21.42 is the most you should pay per share of the stock in order to have a 10% rate of return.

Since I'm so nice, I've created a Google spreadsheet to calculate the Discounted Cash Flow for you guys to make your life easier. All you need is the same inputs from before, but the spreadsheet will calculate everything else, including using different discount rates with the same inputs. Feel free to look at the spreadsheet and try it out for yourself. All calculations should be protected but you can save the spreadsheet to your own Google drive if you want to make changes to the spreadsheet. If you happen to notice something that isn't quite right or it won't let you input your data, please let me know.

__Conclusions:__A Discounted Cash Flow Analysis is great for several reasons. One being that it's forward looking as opposed to backward looking. The previous methods that have been covered look at historical trends, however there's nothing written in the rules of investing that says a company must continue to trade in its' historical ranges for P/E, dividend yield, or P/S. Another thing I like about the Discounted Cash Flow analysis is that it allows you to see how fast a company must grow to be supported by the current share price. Just use the spreadsheet and change the inputs until the fair value price for your chosen discount rate equals the current price.

Like any valuation method, there's limitations. For one, trying to forecast earnings per share into the future is a tough task from year to year, let alone decades into the future. The calculations are also very sensitive to the inputs. In the example used above, using an 11% discount rate changes the fair price to $18.30, a 14.5% lower price. While using a 9% discount rate changes the fair price to $25.80, a 20.4% higher price. Changing any of the inputs by small amounts can drastically change the fair value price. This leads to the "garbage in, garbage out" conundrum. If your assumptions for the inputs are way off base, then your fair price will be useless.

Is using earnings per share the best route to go with the discounted cash flow? Ideally you'd start with revenues and subtract the capital expenditures to determine the actual free cash flows. However all we can go off of is the historical norms for revenue growth, tax rates, capital expenditures, and depreciation. That just introduces more variables to make assumptions on, which introduces more sources for error. There's just too many variables to try and make assumptions, a company's tax rate my significantly change, a new unforeseen product could be introduced or any other number of changes. Using EPS is a good enough metric for me when calculating the discounted cash flow for its simplicity.

For all of the inputs I try to be pretty conservative in my growth rate estimates to have a built in margin of safety in the calculations. If I was going to use the discounted cash flow analysis as my main valuation method, I'd further decrease the final value by at least 15% to have additional margin of safety due to the limitations listed above. Remember, in the end we're trying to forecast the growth of a company over several years using assumptions, and you know what the say about when you assume. A discounted cash flow analysis works best for large-cap stocks where you can have a higher degree of confidence in their yearly growth. I think it's pretty safe to say that almost all of the consumer staple giants will be able to at least grow earnings on par with inflation over the long term.

Once again, no valuation method can possibly encompass everything about a company to determine a fair value. This is why I like to look at several different valuation methods to come up with a fair value price and to be able to compare across multiple methods. If all of the valuation methods I've covered show that the company is undervalued, then there's a much better chance that it truly is undervalued.

Here is the link to the Discounted Cash Flow spreadsheet.

Hello Pip!

ReplyDeleteAlways enjoy your informative posts and am trying to learn about valuation. I have a "dumb" question about the discounted cashflow approach. I understand that basically you are trying to determine today's value of all future cashflows but are you not omitting some valuation of today's assets/book value? So if a company was only going to be in business for 5 years and then close down its operations, the stock value should be the discounted future cashflows PLUS any cash the company would get for its assets on dissolution. What am I missing? Is there no other value to the company than its future dividend payouts? Or does the valuation approach assume that the dividends would not be payable without the company's assets? Hmmm....

Please let me know what you think.

Thanks.

MG

MG,

DeleteYes the remaining assets upon closing shop would be liquidated and returned to the debt/shareholders. Now cash and equivalents are easy to value, but as far as plants/equipment/office furniture...you won't get par value for those so you'd have to apply some kind of discount to those values. The more in depth DCF analysis where you look at actual cash flows by projecting tax rates, revenue growth, operating margin, depreciation/amortization...does go through the process of adding the current assets back into the final value. The DCF analysis I presented shows more of an assumed constant valuation metric based on the EPS (P/E ratio) and a long-term buy/hold/monitor investor. It goes through the DCF process by looking at the future EPS and getting the NPV of those. If a constant P/E is assumed then if you can purchase at a lower price than the fair value from this process and the EPS grow at the same rate as you assumed, then theoretically with a constant P/E ratio you'll earn your discount rate or better on the investment. I'm already thinking of a follow up post to cover the more in-depth process of running through a DCF analysis where you look at the actual cash flows, so that might be in the works.

Thanks for stopping by and thanks for the compliment! There's no dumb questions as long as you're sincere in asking them. I'm a self-taught investor and also human, so I'm bound to make mistakes. Anything to get the conversation going is always welcomed by me.

Hi PIP,

DeleteThank you for your considered response. I actually missed the fact that you were performing a NPV analysis on EPS and not dividends - which I believe some other folks do. Seems that I need to do some more thinking on the subject.

Cheers,

MG

MG,

DeleteNo problem. I think going through the DDM analysis, dividend discount model, you shouldn't add the current assets into the value because you're looking for the cash flow from the dividends and not necessarily the growth of the company, at least for a buy/hold/monitor investor. Although a growing dividend should mean a growing company. I'll be covering the DDM next week so stay tuned.

Thanks for stopping by!

Good write up here. DCF is one of the methods I use to figure out buy prices. I like to use a 10% discount rate except for utilities and telecoms. Glad you mention that inputs are sensitive! It is best to be conservative. DCF is useful although there is too much room for error to use it exclusively.

ReplyDeleteWow your spreadsheet is actually very nice! I think I will use that instead of the site I normally go to. Cool!

CI,

DeleteLooking back through the post, I probably need to go add something about discount rates and target ranges. I like the DCF although it does have it's limitations, but what method doesn't? The historical p/e, dividend yield, p/s are exactly what they say historical averages and unfortunately I've never come across something that says the company must trade within those ranges in the future. The DCF gives you a chance to do a bit of looking toward the future.

Glad you like the spreadsheet. It actually didn't take that long to set up and I think it turned out pretty nice. I think you should be able to save it in case you want to make any changes, but I'm not positive if the share settings are right. If you notice anything about that let me know and I'll see what I can do.

Thanks for stopping by!

Pursuit,

ReplyDeleteAwesome series here. I like your approach to use multiple valuation methods and then try to average them together. The DDM and DCF models are particularly sensitive to input, as you mention...so they are prone to error. I always try to use them fairly conservatively and even then shoot for a number below what they spit out as a fair value.

Great work. Keep it up!

Best wishes.

DM,

DeleteThanks. After having a comment somewhere else on my blog asking about valuation I figured I should start a series covering the valuation techniques. I think to get a good estimate of the price it's important to look at several different methods of valuing a company and if it looks cheap compared to most of the methods then it's a good bet that it's currently unloved by the market.

It's a shame that the the DDM/DCF are so sensitive because I think they're two of the better ways to value a company since it's forward looking. But growth estimates one year out are hard enough to guess so going multiple years/decades out is exponentially harder. You bring up a good point about trying to still have a margin of safety despite the built in conservative estimates going into the formulas. Most of the time I look to buy at my target entry price from my stock analysis posts since that price is based off the averages of the low historical ranges and the DCF/DDM which I also use fairly conservative estimates. Especially for the long-term growth. I think even companies as large as KO, PG...will still be able to grow faster than the historical rate of inflation (~3.5%) but I typically use that as the terminal growth rate.

Thanks for stopping by!