In my last post, I looked at the price being paid for growth by valuing the assets in place in a business. To make this judgment, I assumed that the business would pay its entire operating income to claim holders (as dividends to stockholders and interest expenses to lenders). The value of assets in place then becomes the value of the earnings in perpetuity, discounted back at the cost of capital.

So, what is the effect of growth on value? To grow in the long term, you have to reinvest some or a big portion of your earnings back into the business, and the amount you have to reinvest will depend upon the return on capital you earn on your new investments:

Growth, in summary, does not yield itself easily to rules of thumb or broad generalizations. In some firms, it can be worth nothing, as is argued by strict value investors, whereas in others, it can be worth a great deal, lending credence to the arguments of growth investors.

So, what is the effect of growth on value? To grow in the long term, you have to reinvest some or a big portion of your earnings back into the business, and the amount you have to reinvest will depend upon the return on capital you earn on your new investments:

Reinvestment Rate = Expected Growth rate/ Return on Capital

Thus, a firm with a return on capital of 15% that wants to grow 3% a year will have to reinvest 20% (= 3%/15%) of its operating income back each year. Investors will thus get less in cash flows up front but have higher cash flows in future years.

Consider an example. A firm that generates $ 10 million in after-tax operating income, and has a cost of capital of 10%, will have a value of assets in place of $100 million, if it pursues a "no growth" policy:

Value of assets in place = $10 million/ .10 = $100 million

If it decides to pursue a 3% growth rate and invest 20% of its after-tax income (based upon the

__return on capital__of 15%), its value can be computed as follows:
Value of firm = 10 million (1-.20) / (.10-.03) = $114.28 million

The difference between the two values then becomes the value added by growth:

The difference between the two values then becomes the value added by growth:

Value of growth = Value of firm – Value of assets in place = $114.28 - $100 = $14.28 million

*Determinants of the value of growth*

If you accept the proposition that growth creates a trade off of lower cash flows today for higher ones in the future, you have the three ingredients that determine the value of growth. The first is the

__level of growth__, with higher growth rates in the future generating higher earnings over time. The second is__how long these high growth rates can be sustained__before the company becomes too big to keep growing (at least at rates higher than that of the economy). The third and most critical is the__return on capital you generate on new investments__.
To see why the last ingredient is so critical, revisit the last example and make the return on capital = cost of capital. If you do so, the reinvestment rate has to be 30% to sustain the expected growth rate of 3%. The value of growth then becomes zero:

Value of firm = 10 million (1-.30) / (.10-.03) = $100 million

Value of growth = Value of firm – Value of assets in place = $100 - $100 = $ 0

In fact, if the return on capital generated on new investments is less than the cost of capital, growth can destroy value.

The process of valuing growth does get a little more complicated when you set higher growth rates, but the logic and conclusions do not change. If the return on capital > cost of capital, the value of growth will increase as the growth rate increases and the length of the growth period expands. If the return on capital = cost of capital, neither the growth rate nor the length of the growth period affect value and if the return on capital < cost of capital, the value will move inversely with the growth rate and the length of the growth period. If you want to take this concept out for a trial run, this spreadsheet can help you.

*Comparing the value of growth to the price paid for growth*

If you are paying a price for growth, it is always useful to know the value of this growth. If you accept the reasoning in the last section, it follows that it is not growth that you should be paying a premium for but “quality growth”, with quality defined as the excess return you generate over and above the cost of capital. To illustrate this concept, we compute “intrinsic” PE ratios at varying growth rates for three firms, all of which share a cost of capital of 10% but vary in the returns on capital that they earn on new investments (one has a return on capital of 8%, the second has a return on capital of 10% and the third has a return on capital of 12%).

The PE ratio for just the assets in place is 11.63 and remains unchanged, even if you introduce growth, for a firm that earns its cost of capital. For the firm that generates a return on capital < cost of capital, the PE ratio decreases as growth increases, reflecting value destruction in action. For a firm that generates a return on capital > cost of capital, the PE ratio does increase (the growth premium) as growth increases. It is this premium that you would compare to what you actually pay to make a judgment on whether the added PE you are paying for growth is justified.

*Price of Growth versus Value of Growth*

Using the spreadsheet on growth as a device for deconstructing growth (and its value), I looked at Microsoft, Kraft, Google and Linkedin. In the table below, I have listed my base assumptions for each company and the value of assets in place and expected growth in each one:

This table can be used to address several issues relating to growth:

__a. Price of growth versus value of growth__: You can compare the price you are paying for growth with the value of growth, and you come to different conclusions. For Microsoft, where the value of assets in place covers the market price you are paying, the value of growth is a pure bonus. For Kraft, the value of growth is negative, since the firm earns less than its cost of capital, and the price you are paying for growth is therefore too high. For Google, the price of growth is almost exactly equal to the value of growth, making it the only fair priced stock in this grouping. Finally, for Linkedin, the price paid for growth is more than twice the value of that growth, making the stock over valued. For investors who believe in growth at a reasonable price (GARP), this is the statistic worth watching.

__b. Implied growth rates__: An alternative approach is to solve for that growth rate (Look at the spreadsheet and follow the instructions), holding the return on capital and length of growth period fixed, that would yield the price you paid for that growth. Linkedin, for instance, would have to maintain a compounded growth rate of 73% a year (instead of the estimated growth rate of 60% a year) for the next ten years to justify the price you are paying for the growth. (The spreadsheet provides instructions on how to back out the implied growth rate using the Goal seek function in Excel.)

Growth, in summary, does not yield itself easily to rules of thumb or broad generalizations. In some firms, it can be worth nothing, as is argued by strict value investors, whereas in others, it can be worth a great deal, lending credence to the arguments of growth investors.

Enjoy reading your posts. I think there is a typo in the third para "(based upon the return on capital of 15%)" - should that be 10%?

ReplyDeleteExcellent and an insightful article...Always amazed by your knowledge..Thanks professor...

ReplyDeleteI don't think that there is a typo. The cost of capita is 10% but the return on capital is 15%. That is why growth adds value in the first example.

ReplyDeleteGood Post. Do you still come to XLRI sometimes to teach ?

ReplyDeletehave you considered posting your blog as short video clips aka Khan academy?

ReplyDeleteI have never been to XLRI and I am thinking of putting up video clips.

ReplyDeleteTime and hackwork are ingredient in achieving a worthy growth.

ReplyDeleteI might be wrong (the formula is quite extensive) but it seems to me that in your calculation of Value added by future growth for MSFT you have mixed up the Length of growth period (there is hard coded 10 instead of reference to cell B16) in one place, please see below:

ReplyDelete=-B10*(1-B11)*(B14/B15)+B10*(1-B11)*(1-B14/B15)*(1+B14)*(1-(1+B14)^(B16-1)/(1+B19)^(B16-1))/(B19-B14)+B10*(1-B11)*(1+B14)^10*(1-B20/B19)/(1+B19)^B16+(B10*(1-B11)*(1+B14)^B16*(1+B20)*(1-B20/B19)/(B19-B20))/(1+B19)^B16-B23

It wouldn't change the outcome considerably though. Thank you

This is really helpful. I have been trying to think about valuation intuitively for a long time, and this process makes sense. One question, your valuation of future growth in the example, doesn't quite gel to my simple mind with how the spreadsheets calculate the value of future growth. Can you express the equation you use in cell b25 of the growthbreakdown spreadsheet in simple words, so I can follow how the value of future growth is derived? I think what you are doing is calculating a DCF value of total growth ex the intrinsic value of existing assets. But there seem to be more subtractions, and adjustments for time & reinvestment rates that I don't follow. My simple calc for future growth generates a significantly higher value than yours. I am doing((NOPAT*(1-g)/k-g)/(1+k)^t)-intrinsic value..where am I going wrong? Thanks so much. Will make my life a lot easier when I get my head round this.

ReplyDeleteps I agree with Krystian on the potential error as well, but assumed it was just a typo.

Anonymous,

ReplyDeleteI am trying to cram into one cell what you usually do over dozens, but here is the intuition. I am taking the present value of cash flows growing at a constant rate for your high growth period. The equation you see is the present value of a growing annuity, with the annuity being the cash flow after reinvestment needs have been met.

And Krystian

You are right. I messed up. Thank you for finding the error. I have fixed it now.

Dear Damodaran,

ReplyDeleteIn your post May 17th, “Facebook and "Field of Dreams": Hoodies, Hubris and Hoopla”, you wrote that you would recommend a long term sell for the Facebook IPO, but that you still are searching for the most efficient (and least costly) way to execute this. We find it difficult to interpret if you think this is a feasible strategy or not (to short the the Facebook stock from day one and for three years). Could you please elaborate on what you meant?

Best regards,

Danuka and Olav

Thanks v. much. Understand were you are coming from now, so can reverse engineer a process. Really enjoy the posts. Thanks again.

ReplyDeleteDear Mr. Damodaran

ReplyDeleteFirst, I have realy enjoyed reading your last post (As always). Yet, I must admit that i didn't understand the formula in cell B24 (Value added by future growth). My reverse engeneering was not even close to your figure. Perhaps adding a "Miniature DCF" alongside the formula would help understanding the buildup of that formula.

Regarding your last section of yout formula, you assume that the reinvest ratio should be the risk free rate/cost of capital (B20/B19) - Are you assuming that in the long term the Cost of Capital = Return on Capital? If so, what is the rational behinde it?

Dear Professor

ReplyDeleteGood day to you.

I am completely amazed at your contribution to society. These valuation sheets and podcasts are unparalleled among whatever I have seen on the web. Thanks would be too small a word ! .. Still Thanks a ton

1. I have tried to use your valuation model sp sheets and couldn't understand something about the fcfeginzu.xls sp. sheet

2. I've sent you a mail at the address on your website ... (yeah the same one with XL sheets and models); I'm taking the liberty of posting the question in brief here, because I am NOT sure if that e mail is valid or if it is spammed / closed

3. I decided value the Coal Mining Company, Peabody, listed under the Symbol BTU, using your methods.

4. Using your model.xls sheet I arrived at a conclusion to use the FCFE technique / method and so tried to use fcfeginzu.xls sp. sheet, with following parameters

5. My problem / doubts are with fcfeginzu.xls and so please ignore para 4 above IF that turns out to be a distraction

6. When I use fcfeginzu.xls I see that Cell D 22 on the Sheet titled "Valuation", has the following formula =IF(Inputs!B25=0,D5*(1-D20)*(1+D19)/(D21-D19),MAX(C12:Q12)*(1+D19)*(1-D20)/(D21-D19))

7. In this formulae the denominator is always (D21-D19). (only numerator changes based on the outcome / answer to IFs )

8. The way I see it, the denominator is always the Cost of Equity in Stable phase (- Less) Growth Rate in Stable Phase

9. I feel this formula leads to some un expected consequences

9.1. Sample values for BTU (based on certain assumptions ) in fcfeginsu.xls are

Cost of equity = 10.3%

Net income without interest = $660

Growth rate in net income = 14.5%

Eq. reinv rate for H Growth = 74.7%

Still the price at end of growth phase is -4571 (negative)

10. In the example (BTU) with

- a positive Net Income and

- a growth rate that exceeds cost of equity and

- payout ratio @ 25% of earnings and

- 0 Stable growth period (meaning it takes the current earnings in cell D5 above ....

- I still get a negative price at end of growth phase

11. **I can't understand, where I am wrong**

12. If I am not messing up something on the sp sheet, I can't understand How a company with a positive earning now, growth around 15% could have a negative value at the end of income stream / growth period

13. The negative valuation does not become positive with increasing current earnings or assuming a 5 year stable growth phase or a 10 year stable growth phase , in this model

I'm very curious to know what I am missing .... !!!

Thanks in adv. and Best regards

Subu

You have a fundamental problem. The growth rate in perpetuity cannot exceed the growth rate in the economy, which in turn should be capped at the risk free rate. Thus, if you let growth in perpetuity become too high, your terminal value will be negative, and more important, you are violating simple rules in mathematics and economics. So, cap your growth at the risk free rate, make reasonable assumptions about ROE in perpetuity and the rest will follow.

ReplyDeleteDear Professor :

ReplyDeleteThanks for the reply ! Really Appreciate you taking time and effort to reply

>>>>>>hus, if you let growth in perpetuity become too high, your terminal value will be negative<<<<<

Yes. I see that. You have summarized my question in one line!

>>>>>and more important, you are violating simple rules in mathematics <<<<<<<

Violating rules of mathematics :

-----------------------------------

I see that the numerator becomes negative. So the result becomes negative !!

>>>>>and more important, you are violating simple rules in mathematics and economics<<<<<<<

Violating rules of economics :

-----------------------------------

I can't see where I am violating the rules of economics and IF so which one ?

I understand that discounting terminal value or discounting cash flows beyond the growth period is a problem most value investors have to / have tried to grapple with ......

But I can't quite understand why the firm's growth should always be lower than the economy's growth

and

Why the difference between these should be the best denominator to use ....

I'm still hoping you have some *other* great solution to this "terminal value" question

regards

Subu

Thanks for the great post! The table summarizing Price of Growth versus Value of Growth is a great tool.

ReplyDeleteThere are only two ways that a terminal value can be negative and they are both in conflict with either mathematics or economics. The first is to set the growth rate higher than the risk free rate, which will make the denominator negative. The second is if you set the ROE or ROC way below the cost of capital, in fact, below your growth rate, in which case your firm is contenting to take projects that destroy value in perpetuity. In either case, the problem is not with the terminal value computation, it is with one of these assumptions.

ReplyDeleteAnd if you are wondering why a firm's growth has to be less than the growth rate in perpetuity, think about what happens to a firm growing at a rate higher than the growth rate of the economy in perpetuity.

ReplyDeleteDear Damodaran

ReplyDeleteFirst, I have realy enjoyed reading your last post (As always). Yet, I must admit that i didn't understand the formula in cell B24 (Value added by future growth)altough my reverse engeneering was close to your figure. Perhaps adding a "Miniature DCF" alongside the formula would help understanding the buildup of that formula.

Regarding your last section of yout formula, you assume that the reinvest ratio should be the risk free rate/cost of capital (B20/B19) - Are you assuming that in the long term the Cost of Capital = Return on Capital? If so, what is the rational behind it?

I think there are some great tips for market, on web, just like this article, great stuff

ReplyDeleteI am assuming that the return on capital = cost of capital in perpetuity. To earn more than the cost of capital, you have to have barriers to entry and it is tough to maintain those barriers forever. So, the safest assumption in the terminal value is to assume that the return on capital = cost of capital.

ReplyDeleteAnd I will add a mini-DCF with the detailed cash flows so that the valuation part becomes more transparent.

Hi!

ReplyDeleteI tried the following inputs in your spread sheet AND in a spread sheet I made on my own since I too didn’t really follow your calculations in B24 (Value added by future growth):

EBIT: 2000

Tax rate: 30%

NOPLAT 1400

Growth: 25%

ROC: 30%

WACC: 8%

Riskfree rate (long term growth): 2%

Period length: 10 years

Long term ROC = WACC = 8%

Based on these input numbers I came up with an intrinsic value of firm of 80 040 in my sheet, whereas your sheet returned a value of 85 044. I also did set up a DCF just to check and this confirmed my number.

What I do is that I calculate the total firm value by using the formula of a growing annuity and then add the discounted value of the terminal value. By subtracting the “value of assets in place (1400/0.08 = 17 500) I get the value of future growth (65 540 compared to your (67 544).

I’ve been going over the calculations over and over again and can’t seem to find any error which is why I would love to see some further explanations on your calculations, preferably including a DCF.

I really like the approach of separating value from growth from value from assets in place.

Thank you for a great blog!

Prof Damodaran

ReplyDeleteIn your first valuation comparison, you assumed that the cost of capital remains the same when you move from a no-growth scenario to a positive growth scenario. n general that is not a fair assumption because changing a business plan to capture growth when previously a company operated with a no-growth plan usually involves taking on more risk. As a result, the cost of capital should be higher in that case, which would reduce your calculated growth value.

Excellent point. I did consider allowing for two different costs of capital (it is a simple adjustment to the model) but decided against it in the interests of keeping the inputs under control. Since the excel spreadsheet is an open one, why don't you modify the spreadsheet.

ReplyDeleteAs for the prior post, here is why why our numbers may deviate, I think one big factor is what I am assuming about reinvestment. In most DCF valuations, you assume for convenience that growth and reinvestment are contemporaneous. In other words, you assume that you if reinvest 40% and have a return on capital of 20% in year 1, you will have a growth rate of 8% in year 1. In reality, reinvestment has a lagged effect on growth. If you reinvest 20% in year 1, you drive growth in year 2. Thus, I have an upfront reinvestment in time 0 to get growth in year 1 and my reinvestment in my final year of high growth is based upon my stable growth rate.

Prof Damodaran

ReplyDeleteThe idea of separating value generated by existing assets from value generated from growth assets has also been addressed in another interesting way. Marty Leibowitz and Stan Kogelman wrote a number of papers (which ultimately got collected in a book) which introduced the Franchise Factor Model. This model decomposes the P/E ratio of companies into a value multiple coming from earnings from the existing book of business and a separate value multiple coming from growth assets that are expected to generate returns in excess of the cost of capital. They define the ability to maintain a positive spread to the cost of capital as a company's Franchise Factor, and the ability to identify and deploy growth opportunities that contain this Franchise Factor is called the Growth factor. The FFM makes clear that growth without a franchise or a franchise without growth creates no incremental value (or equivalently, no premium valuation multiple).

The other interesting result from the FFM model is that it is not the perpetual growth rate that matters but rather the present value of all future investment opportunities ( as a % of existing investment. Thus the FFM can account for irregular investment opportunities that come along over time.

Thanks for reply. I see what you mean but don't get it exactly right anyway.

ReplyDeleteAgain, It would be very helpful if you would want to illustrate further in a simple DCF so one can follow exactly how you're doing :-)

If u have enough time, of course.

If the stable growth rates of some firms are below the growth rate of the economy,shouldn't the stable growth rates of other firms be slightly above the growth rate of the economy? (Based on law of average)

ReplyDeleteThanks.

That works only if all companies in an economy are stable growth firms. Since some firms are high growth firms, the stable growth firms collectively should grow at a rate less than the growth rate of the economy.

ReplyDeleteGreat post professor! It would be interesting to see the proportion of the S&P 500's or the DJIA's value from growth. I wish I had the time to go through this exercise.

ReplyDeleteThis comment has been removed by the author.

ReplyDeleteGrowth stock investing is all about buying future expectations. While value investing is all about buying a company thats worth twenty dollars for just ten dollars. I am not a big fan of growth stock investing. What if I own shares in a high growth company thats currently only really worth twentyfive dollars a share but its trading at fifty dollars a share. Whats going to happen to the price of that stock if the future prospects are severely downgraded by analysts. Say growth of revenue and earnings are projected to decrease from 20% a year to just 8% a years. That stock will sell off like a hot potato. How many companies are their that can grow their earnings and revenues by 20% a year for ten years very few indeed.

ReplyDeleteThank you for your blog post and spreadsheet. I have a couple of observations/questions:

ReplyDelete1. If you assume that return on capital = cost of capital in perpetuity (beyond the high growth period) then any further growth will create no value, so an equivalent assumption when calculating the terminal value is just to set the perpetuity growth rate to zero and assume no further growth reinvestment.

2. Also, if you want to reflect the fact that return on capital is going to be competed down over time because barriers to entry can't be maintained forever, what does that imply for returns on the capital that has been invested during (and prior to) the high growth phase? Aren't you implicitly assuming that capital invested prior to your final period will earn the high initial rate of return into perpetuity? In the spreadsheet it seems as though returns are only competed down on incremental capital invested beyond the high growth phase - i.e. the company seems to enjoy perpetual barriers to entry with respect to certain of its activities (those corresponding to capital invested prior to the final period).

Thank you in advance for any follow-up comments you might offer.

The real problem when investing in growth stocks is your not buying growth your buying future expectations. How many companies are their out their that can increase earnings and sales by 20% a year for ten years. Very very few.

ReplyDeleteDear Aswath, thanks for the post. You mention this: "For the firm that generates a return on capital < cost of capital, the PE ratio decreases as growth increases, reflecting value destruction in action. For a firm that generates a return on capital > cost of capital, the PE ratio does increase (the growth premium) as growth increases." How did you come up with this relationship or where is this relationship from or the mechanism by which this relationship comes about?

ReplyDeleteMany thanks in advance

Is there a general equation that calculations value based on PE and ROC?

ReplyDeleteMoody's at PE 15 with ROC 30% is obviously worth more than a GM at PE 15 with ROC 10%. But it becomes unclear to me if Moody's PE is 30 and GM PE is 10. Now which is more valuable?

Is there a equation to normalize this problem?

Another concept about your Terminal Value that I don't understand is that you use Growth = NetInvestment * ROC. The NetInvestment basically equals TotalInvestment subtracted by Depreciation.

ReplyDeleteConceptually, shouldn't the growth be tied to the Total Investment? The actual amount of new investment the firm makes is the factor that determines the growth. The depreciation from previous CAPEX shouldn't have an effect on new investments.

However, maybe the past depreciation is a good indicator of the "maintenance" re-investment a firm needs to make into R&D or CAPEX to sustain the current rate of profits. Maybe the TotalInvestment should be separated into a maintenance portion and a growth investment portion.

My concern is that by subtracting depreciation from the Total Investment, the Terminal Value will be underestimated because the actual amount of money being invested will not be given proper weight. Do you think this concern is legitimate?