I appreciate your efforts in educating individuals.
You are taking estimated market value after end of 3 years for calculating intrinsic value of the company which I think is wrong. When we are saying that market value and intrinsic value both are different than MV should not go into calculation of IV. Further, estimation of MV after a certain period is highly subjective. I suggest to take book value of the company as liquidation value in calculating IV.
@rskothari I largely agree with most of your contentions, but I have to slightly disagree with you on a couple of points.
Firstly, I was trying to use a Terminal Value which is different from a Liquidation Value.
A terminal value is the value at which we expect to sell off our investment at the end of our investment period. A liquidation value on the other hand, is the value at which the company itself is expected to be sold off at the end of its lifetime. Further, we cannot guarantee that the company will go into liquidation, exactly at the end of our investment period, at which point of time, it is more than likely that the company will be alive. So it makes more sense to use a terminal value rather than a liquidation value.
Secondly, market value and market cap are also two entirely different concepts. Market value is the price at which the stock of a company sells on the market. Market cap, on the other hand, reflects the worth of the entire company. In other words it shows for how much the entire company can be bought.
In my example, I was estimating the market cap and not the market value of the company. So in my example I was buying a company worth 23,000 odd crore for just 14,000 odd crore which represents a good deal. I only had to estimate the market price because the market cap is given by the formula market price * number of outstanding shares. So I was trying to find the future market cap, or the future worth of the company to bring it back to its present value and see how much the entire company is worth today.
And I agree with you when you when you say that estimating beyond a certain period is futile, but every valuation, even the best one, is just that, an estimate so there will always be an inevitable degree of subjectivity to valuation.
My point was that we are calculating Intrinsic Value of the Company and not our Investment and in that case terminal value at which we expect to sell off our investment has no point (in my view). Further, i think we have to include expected liquidation value (may be book value) to calculate intrinsic value of the company which is part of future cash flows of the company.
@rskothari Since we have initially calculated Free Cash Flows To The Firm and discounted these cash flows and the estimated future market cap of the company at the cost of capital we have effectively ended up at the intrinsic value of the company as a whole.
As far as discounting the liquidation value is concerned, I am of the opinion that it is not required, since it is not guaranteed that we will receive the liquidation cash flow during our investment period.
Please mull over your thinking on calculation of Intrinsic value.
If we can estimate market cap after our intended holding period, then where is the need to calculate IV. Also, as mentioned by you only that we should not have any liking for any stock before calculation of IV and estimated Market Cap will be as per our liking only.
You have started a very good topic but I think you made some gross error in example. This may lead to wrong understanding by learners. Instead of justifying it, please come with a new good example.
Thank you, you have initiated a good thread on valuation.
However I would like to suggest that while calculating the intrinsic value of the company, terminal cash flow should be identified based on discounting of perpetual cash flow and it should not be replaced by market cap. As the idea behind to calculate the value of the company based on its inherent capabilities, not on market sentiments. Using estimated market cap in intrinsic valuation makes it totally flawed as more than 95% of your value is just based on your estimation of market cap which itself may be questionable due to market sentiments.
Second point I want to highlight is that cost of capital of the company may keep on changing if debt equity ratio keeps on changing. What is your view on it, kindly share.
@rskothari I understand what you are trying to say. I have now come back with a better example. I will be expanding on the Graphite India Limited example with the assumption that the company will ultimately be going into liquidation.
Continuing with the same data where Graphite India Limited has a present free cash flow of 174.57 crore with a free cash flow growth rate of 5% per annum, assuming a 10 year investment period, we get the following cash flows:
Year 0 (today): 174.57
Year 1: 174.57 + 5% = 183.3
Year 2: 183.3 + 5% = 192.46
Year 3: 192.46 + 5% = 202.90
Year 4: 202.90 + 5% = 212.20
Year 5: 212.20 + 5% = 222.80
Year 6: 222.80 + 5% = 233.94
Year 7: 233.94 + 5% = 245.63
Year 8: 245.63 + 5% = 257.91
Year 9: 257.91 + 5% = 270.81
Year 10: 270.81 + 5% = 284.35
Further discounting these cash flows at the cost of capital which is 10%, we get the following following present value cash flows:
Year 0 (today): 174.57
Year 1: 183.3 x 0.909 = 166.61
Year 2: 192.46 x 0.826 = 158.97
Year 3: 202.90 x 0.751 = 151.76
Year 4: 212.20 x 0.683 = 144.93
Year 5: 222.80 x 0.620 = 138.13
Year 6: 233.94 x 0.564 = 131.94
Year 7: 245.63 x 0.513 = 126
Year 8: 257.91 x 0.466 = 120.18
Year 9: 270.81 x 0.424 = 114.82
Year 10: 284.35 x 0.385 = 109.47
Now, adding these present value cash flows we get an NPV of 1537.38 crore.
The present book value per share of Graphite India Limited is 94.78. Assuming that Graphite India Limited goes into liquidation at the end of the 10 year period, with no significant change in book value per share, we get the following liquidation value:
94.78 x 19.53 crore shares outstanding (this figure has been obtained from Graphite India Limited’s 2017 annual report.) which gives us a liquidation value of 1851.05 crore. Discounting this liquidation value to present value we get:
1851.05 x 0.385 = 712.65
Adding the discounted liquidation value to our cash flow NPV we get:
1537.38 + 712.65 = 2250.03 crore
This value compared to Graphite India Limited’s current market cap of 15141.61 crore clearly shows that Graphite India Limited is intrinsically overvalued at this point of time.
With respect to your query regarding the discrepancy in the intrinsic valuation, I have shared an updated example above.
With regard to your query regarding the fluctuations in the cost of capital, you are absolutely right when you say that they keep fluctuating.
These fluctuations can invariably be traced back to the the stage of the company life cycle at which the individual company is.
It is important to remember that the cost of debt is lower than the cost of equity, because interest on debt is a tax deductible expense. As the proportion of debt in the capital structure increases, the cost of capital decreases, because of the tax benefit availed on the interest cost of debt.
Younger companies are predominantly financed primarily by equity, because they do not possess adequate debt capacity. This leads to younger companies having higher rates of cost of capital.
As companies start to grow and mature, their capacity to handle debt increases, leading to these companies borrowing more, thereby bringing down the cost of capital.
You can therefore keep calculating the cost of capital of the company at regular intervals as it grows and matures and calculate a new intrinsic value at regular intervals based on the latest cost of capital rates.
Being from non-commerce background, I have been struggling with the valuation concepts, your explanation and example is really helpful to understand it.
In your example, I am able to understand till deriving of FCFF values for year 0 and for future years, however unable to understand how you derived 0.909 for 1st year, 0.826 for 2nd year and so on for calculating present value using 10% discount rate. can you please help?
@malayruparel First off, I’m really happy that my pieces have been able to help you understand these concepts better.
Those decimal figures you’re trying to figure out are the discount factors which are used to discount the cash flows to their present values. And let me assure you calculating these discount factors is an absolute piece of cake.
Since you are from a non commerce background, I will share a very easy shortcut with you which will help you calculate the discount factors. Just follow these very easy steps and you’ll be calculating those discount factors in next to no time:
Convert the discount rate into decimals. For example, 10% becomes 0.1, 15% becomes 0.15, 20% becomes 0.2 and so on depending on what your discount rate is.
Add the decimal figures to 1. So for example, you get 1.1, 1.15, 1.2 and so on, depending on what your discount rate is.
On a regular calculator, type 1/the added up figure. So for example, type 1/1.1, 1/1.15, 1/1.2 and so on
Hit the ‘=’ (equal to) button. Each time you hit the button you get the discount factor for each successive year. Press it once to get the discount factor for the first year, twice for the factor for the second year, thrice for the third year and so on. So in this case, when you press the = button once you get 0.909, twice you get 0.826, thrice you get 0.751 and so on.
Write each individual factor down on a piece of paper so that you don’t lose track.
And that’s all there is to it. Hope you find this technique useful.
Thank you Akshay for your reply.
Yes one should be careful in evaluating cost of capital, specially in the business which is high on Debt is or high on equity as any debt repayment or increase in debt can impact the valuation. Because of this reason value of shares calculated by FCFF - Debt and directly from FCFE would be different.
Here I would like to know what would you prefer value of equity calculated from FCFE or FCFF?
Second - I checked you example, and I am of the view that you should calculate terminal value based on minimum terminal growth rate, because market most of the time values the company based on perpetual going concern, our investment horizon might be limited but not market’s. As new investors will keep on coming. It is very rare that market would value a company based on liquidated value, be it 10 years down the line in future or early.
Thanks. Personal economics/account tutor event would not have been so clear. Based on DCF, I tried finding intrinsic value of Lupin for holding period of 3 years.
Facts as on 31-Mar-2017 (in Cr)
Net cash flow from operations 4115
Interest expenses 152.53
Tax rate % 30.00
Net capital expenditure 1663.00
Post tax interest expense 106.77
FCFF 2558.77
Year Cash flow DCF PV
Year 0 2558.77 1
Year 1 2686.71 0.91 2442.463
Year 2 2821.045 0.83 2331.442
Year 3 2962.097 0.75 2225.468
NPV (A) = PV of Year 1 + Year 2 + Year 3 = 6999.373 Crore
Present book value 316.61 Crore
No. of outstanding shares in crores 45
Liquidation at end of 3 years 14294.9415 Crore Present liquidation value (B) 10721.2061 Crore
Current Intrinsic value = A + B = 17720.5791 Crore
@Rounak_Maheshwari In response to your first query, to my common sense it is always better to value using FCFF rather than FCFE, because FCFF values the firm as a whole and FCFE values only the equity. And when you buy the stock of a company, you buy a part of the business, and not just a part of the equity. Therefore, FCFF is better.
Coming to your second query, yes a terminal value after a certain number of years can also be found without assuming that the company goes into liquidation. The formula for the same can be given as follows:
Terminal Value = [FCFFn (1+g)]/(r-g)
Where,
FCFFn - Free Cash Flow To The Firm for the nth year basically the last year of our investment period
r - Discount Rate converted into decimals
g - Free Cash Flow Growth Rate converted into decimals
When we use this formula we are assuming that the company will continue to exist and cash flows will continue to grow at the end of our investment period.
So, if this is applied to our Graphite India Limited example, we get the following terminal value:
FCFF in year 10 = FCFFn = 284.35
Discount rate in decimals = r = 10% or 0.1
Free Cash Flow growth rate in decimals = g = 5% or 0.05
Therefore,
Terminal Value = [284.35 (1+0.05)]/ (0.1-0.05)
= [ 284.35 * 1.05]/ 0.05
= 298.56/0.05
= 5971.35 crore
Remember not to use the discounted value for the FCFFn figure, because the discounting will be done when we apply the Terminal Value formula.
Above is more logical approach in calculating Intrinsic Value. Thanks.
As regards discounting rate, I think we can take a rate which is acceptable to us for return on our investment. For a risky business, we can consider higher discount rate say 12% to 15% and for a normal business we can consider 10% to 12%. What is others views.
@malayruparel A fantastic attempt at an intrinsic valuation for someone from a non commerce background. You are absolutely right until the calculation of present FCFF and FCFF calculation for years 1 2 and 3.
However, there are a few errors in the discounted cash flows and the liquidation value. Hence I have worked it out below:
Year 0: 2558.77
Year 1: 2686.71 x 0.91 = 2444.91
Year 2: 2821.045 x 0.83 = 2341.46
Year 3: 2962.097 x 0.75 = 2221.57
Coming to the liquidation value, 316.61 x 45 crore shares = 14247.45. Discounting to present value we get:
14247.45 x 0.75 = 10685.58 crore
This added to the cash flow NPV gives a final intrinsic value of:
10685.58 + 9556.71 = 20242.2975 crore
But nothing to take away from your fabulous effort. I am personally an MBA in finance and I keep making mistakes in my valuations, so for someone from a non commerce background to do this much is unbelievable.
@rskothari First off, I should be the one thanking you for alerting me to my erroneous approach to intrinsic valuation which gave me the chance to learn how to do it right.
Secondly coming to your query on having higher discount rates for riskier businesses, that is definitely the right way to go, because the riskier the business, the more uncertain it is that the future cash flows will actually accrue to the firm. So a higher discount rate will definitely make the valuation more realistic.
Thank you for correcting the error of not adding year 0 cash value. Other mistakes were rounding up error and corrected it.
I have attempted to find terminal value of Lupin
Assumptions
Lupin will continue to grow at 3% after 3rd year
Discount rate continue to be at 10%
Terminal Value = [FCFFn (1+g)]/(r-g)] =(2962.097*(1+0.03))/(0.1-0.03) = 43585.14 crore.
Current market cap of Lupin is around 40,000 crore meaning Lupin is available 10% cheaper than intrinsic value. Can you correct for any errors in this?
@malayruparel Your calculation of the terminal value is absolutely right. Well done!!
But before you compare with the market cap, you must first add the terminal value to the cash flow NPV. Doing this we get:
43585.14 + 9566.71 =53,151.85 crore
So when compared with the market cap of Lupin, which stands at 40000 crore, we can see that Lupin is still undervalued, but the discount is actually 32.879% ([13151.85/40000] * 100) rather than 10% as estimated earlier.
