Take a look at the table and graph given below. Company A earns $10 every year and has a payout ratio of 100%. Company B earns $10 and has a payout of 50%. It reinvests the remaining 50% to engender its growth. Company A doesn’t grow at all and B grows at a constant rate of 5% forever. Here are some questions that I have for you **(1)** how much would you pay for A and B today? **(2)** does B’s growth add any value to its owners?

If you concluded that B is more valuable than A then you flunked the growth test. In order to value a constant earnings stream, both no-growth and growth, you can use the gordon’s growth model. I wrote about it in detail here. The value of A comes to $83.33 [ $10 / 0.12 ] compared to its invested capital of $100. Why is the valuation of A less than its invested capital? This is because A earns 10% on its capital which is less than its cost-of-capital of 12%. The key point to remember is that an asset is worth less than its book if it earns less than its cost-of-capital.

The value of B comes to $71.43 [ $5 / (0.12 – 0.05) ] compared to its invested capital of $100. As B earns less than its cost-of-capital it should be worth less than its book value. But what surprised me was that B which is growing at 5% is worth less than A which is not growing at all. How’s that possible? In order to answer this question we need to do a little bit of algebra. Don’t worry the math is not hard. And we’ll get a deeper insight from this effort.

Let C = Invested capital ROIC = Return on invested capital R = Cost of capital G = Growth rate I = Reinvestment back into the business to engender growth CF = Distributable cash flow to shareholders

The key insight to derive from the above equation is the ratio [ ( ROIC – G) / ( R – G) ]. This ratio can result in three different conditions **(1)** when ROIC < R; under this condition the ratio goes below 1 and any investment in growth will destroy value. This is what happened to B. And this is the reason why it was valued less than A which didn’t invest anything in growth. **(2)** when ROIC = R; under this condition the ratio equals 1 and investment in growth neither adds nor destroys value. **(3)** when ROIC > R; under this condition the ratio goes above 1 and this is the only condition where growth adds value to its owners. This concept is beautifully summarized by Greenwald in his fantastic book.

**ROIC < R:** Growth may be worse than neutral; it may actually destroy value. This occurs whenever the return on capital is less than the cost of capital. Returning to our growth value factor F, if ROIC = .10, and R = .12, then F = (.10 – G)/(.12 – G). In this situation, F will (a) always be less than one no matter what the rate of growth, (b) get smaller as the rate of growth increases, and (c) fall to zero when G reaches 10 percent annual growth. As long as it costs us more for each dollar of new investment than that dollar will produce in increased earnings, growth destroys value. Higher growth rates require more investment and thus destroy value even faster.

**ROIC = R:** Growth requires additional investment, and although this investment produces a return on capital, the financiers who supply it demand payment for the use of their funds, which is the cost of capital. When ROIC = R, the entire proceeds from the investment go to compensate the providers of the new funds; there is nothing left to pay to the existing owners of the firm. Therefore, no matter how much the new investment generates in increased revenue and earnings, the value of the firm to its existing owners does not change.

**ROIC > R:** Growth, it is now clear, only adds value when the return on capital is greater than the cost of capital (ROIC > R). *Only in markets where a company enjoys a sustainable competitive advantage, protected within its franchise by barriers to entry, will returns on capital be greater than the cost of capital. So the basic principle of growth valuation comes down to this: Only growth within the franchise reliably creates value.*

Don’t blindly buy a stock because it’s growing its sales and earnings. The most important question to ask is: What Is Growth Worth? Growth is worth more for businesses that earns more than its cost-of-capital. And this only happens to those with durable competitive advantage; moats.

Awesome work SIr……… #respect

Thanks Aravind.

Regards,

Jana

excellent article sir…………..one small request from my side it would be very helpful for us lay investors if can elaborate this concept by using real examples..

Thanks and will do.

Regards,

Jana

Great post Sir! There is a book by Tim Koller (from Mckinsey) called ‘Valuation’. Sometimes your posts remind me of his concepts. Wonderfully explained!

Thanks Rohan.

Regards,

Jana

Hi Sir,

Good post as usual. The DCF- Gordon growth post was excellent, but I have a small problem with his one.

‘I’ should equate the sum of maintenance capex and the capex required for growth. How have you derived ‘I’ by multiplying capital with profit growth rate? Please elaborate on that.

I agree with everything else. Thanks for sharing your knowledge.

Rahul,

For majority of the companies increase in sales requires proportional increase in both fixed and working capital. For Company B I made an assumption of 5% increase in investments (fixed + working capital) to increase sales and earnings by 5%.

Regards,

Jana

hello sir, How to decide the Cost of capital?

if it is an assumption, then what is the basis behind it..

Thanks fr sharing ur work.

Prateek,

Assuming that the company has negligible debt, the cost-of-capital comes what returns new equity investors would expect for providing capital. This should be a function of current risk free rates plus some alpha. With the current 10 year government bonds of under 8% and an alpha of 4% you can get a cost-of-capital between 11-12%. This is an approximation but in my mind it’s better than CAPM – Beta adjustment.

Regards,

Jana

Great Post Jana, How do you estimate future “g” value for different companies/sectors? Thanks for the answer on cost of capital.

Keyur,

Read the last part of this post: https://goo.gl/rnkSxX. Gordon’s formula is used to calculate terminal value of a company. And it’s really hard to come with a right value for g. I think in terms of exit multiple & yields and keep it as conservative as possible. In other words I keep g at almost 0.

Regards,

Jana

hi nice article. So we should watch out for incremental returns on capital a company makes to assess how well it is investing its capital both for maintainance and growth

Ayaz,

Yes.

Regards,

Jana

This is an interesting problem. At first glance, a system 1 vs system 2 solution (within the definition of Thinking Fast, Thinking Slow). In real life, I suspect this example is unrealistic. A company producing either of these returns will end up with a low cost of capital. They will end up with considerable debt on the balance sheet, which they can well handle, within the described parameters. this will change the dynamics.

In this particular example, I guess we could say that investing for growth with a return below the cost of capital is a bad idea. Now that should be understood a priori. The chance for change is embedded in the effect of predictable returns on the cost of capital. It is that dynamic that can create disparity between price and value.

It is a nice problem. Thank you for posting.

HI jana………I have a question not related this post………..recently i have been reading value investing from from buffet and graham ………………how do u calculate selling admin and general expenses for a company as they r not separately stated in financial statements….it would be really helpful for me if u can post an article on EARNINGS POWER VALUE valuvation on ur blog………hoping for ur reply……..thnx

Narsing,

Are you referring to US or Indian companies. If it’s US they do break it out and by reading the Notes you’ll find it there. For Indian companies the only hope is to the schedules.

Regards,

jana

thnx for the reply……………was refering to indian companies

Hi Jana,

Adding to what you’ve said, when you first pointed out that B is worth $71.43[$5/(0.12-0.05)], did you notice, that the payout ratio, can substantially change the company’s worth? For instance, if it paid out $7 instead of $5, it would be worth $100[$7/(0.12-0.05)]. If it instead paid out all of $10, then it would be worth $142[$10/(0.12-0.05)]! No?

What you’ve conveniently done, is to arrange retained earnings (50% of $10), in the same proportion as growth (5%). However, the company would do better to paint an optimistic picture by paying everything out, thereby presenting a higher networth, and then perhaps raise funds based on the higher valuation!

Hi,

In discounting the cash flows should we keep our required return as the discount factor or a more general rate ie : Rf + Equity Risk Premium.

Using Equity risk premium method, discount factor could be between 12-14% while my required return from stocks would not be less than 20%.

While calculating the terminal value of a stock can we lower the required rate than that used in the earlier phase.(Due to the company having achieved a bigger scale and maturity in operations.)

Regards,

Vivek Gupta

Vivek,

For calculating cost-of-capital I think in terms of opportunity cost. Currently fixed deposit yield 8% and after tax it comes to around 5.5%. Adding another 400 basis points I arrive at an after tax cost of capital of 10%.

This is the rate at which you will discount the free cash flow. Your IRR depends on how much discount the stock price is selling below the intrinsic value. If price = intrinsic-value then your after tax return is going to be 10%.

Regards,

Jana

Thanks for replying.

Regards,

Vivek