The Math of Intrinsic Value

Transcription

1 The Math of Intrinsic Value Introduction: In India and across the world, the most commonly found investment options are bank fixed deposits, gold, real estate, bonds and stocks. Since over a hundred years now, numerous books have been published on the topic of various investment opportunities. A couple of them are valuable and have been helpful in assisting common investors and investment professionals in developing their skills in this regard. As an ordinary yet passionate investor, I have read many such interesting books and articles in a span of about ten years. During these years, I ve researched, studied and understood business models, accounting standards, fundamental analysis, long-term investment approach and related subjects. Among the many books I ve read that covered different investment options, books written particularly about equity investments interested me a lot. Eventually, I realized that learning the intrinsic value concept is very crucial for a business or stock purchase. Numerous methods have been followed by investors for business valuation. Among those, valuation based on historical price earnings ratio, price to book value, discounted cash flow method, and asset based model is common in the investors community. After using these metrics for my investment decisions for many years, I felt these methods didn t convince me enough with regards to the perfect business valuation approach. None of these methods explained the exact math behind the business valuation. I did a comprehensive study from various sources (on-line and off-line) but nothing really helped me in finding the right answers. Well that didn t stop me from trying harder, so I just kept pushing ahead and began my research with an objective to formulate a mathematical equation to calculate the intrinsic value of any business. It took seven years to complete the research and find the right answers, and strongly I believe they could help others who re looking for meaningful answers as well. This book is loaded with content that s concentrated and gets you to the point. I recommend you to pay attention to every single chapter to truly benefit from this book. I have focused primarily on how a business is valued, the math behind the business valuation and how one can justify the intrinsic value of the business from a private owner s perspective. Using this equation, one can value private companies, public listed companies, start-ups and any business ownership. I sincerely hope this book benefits you in making a well informed and successful investment decision. All the best! Intrinsic value- the all-important concept: Business valuation comes into the picture when business ownership transaction takes place. Business owners, venture capitalist, private equity, investment bankers are those who commonly into business ownership transaction for various reasons. Business owners dilute the stake in the company for multiple purposes like business expansion, reducing the debt, general corporate requirement, etc. Often the present owner of the business wants to exit his ownership partially or entirely for various reasons. Mergers and acquisition is another place where business ownership transaction takes place. Apart from bulk business ownership transaction, common stocks (or pieces of business ownership) transaction is very common in stock exchanges. Retail investors, high net worth individuals, mutual funds, 1

2 insurance firms, private equity, foreign institutional investors and various investment companies actively do the stock transaction on every stock exchange. In all the cases, fair value of the business is the most critical factor in deciding the deal. Both buyer and seller want to make the transaction at a fair value of the business. There are many methods currently available to help the investors in deciding whether the business is fairly valued. Some commonly followed business valuation methods are asset based valuation, discounted cash flow method and market based valuation (using historical PE ratio or Price to book value). Most commonly accepted method by investors and analyst are historical PE ratio method for non-finance based companies and historical price to book value method for finance based companies. However, even these two methods don t really explain to an investor how these numbers are mathematically arrived and justifiable at respective prices. It is evident in the stock market companies with more promising future trades at a high PE ratio and companies with uncertain future trades at a low PE ratio. For example, a stable FMCG company in India trades at a valuation about 40 times the present earnings, and a Tyre manufacturing company trades at a valuation about 12 times the present earnings. The different is very significant. An analyst might explain the reason for such high difference in PE ratio between FMCG and Tyre industry as FMCG companies are very stable in their future earnings and tyre manufacturing companies are comparatively less stable in their future earnings. In other terms, it can be said: FMCG companies are less riskier than tyre manufacturing companies. Even I agree the risk plays a huge role in arriving intrinsic value of any business. The risk is an essential factor in valuation. However the question comes naturally, is the risk quantifiable? If yes, whether the risk can be plugged into value equation to arrive the intrinsic value of a given business? If it can be plugged into value equation, can one quantify how the risk factor affects the present value of future earnings with respect to time? I believe the answer is Yes to all three question and I will explain it in detail in upcoming chapters. Next comes the growth of the business. Most analysts believe that different earnings growth rate projection would result different business valuations; in other words, companies with high growth rate projection in earnings deserve a higher valuation (high price to earnings ratio), and companies with low growth rate projection in earnings deserve a lower valuation (low price to earnings ratio). Here is where my results differed from most analyst. I agree growth is a positive factor and one of the crucial element in value equation, however my results showed different earnings growth rate projection doesn t change the intrinsic value of a business. My definition of growth differs from many analysts. I will explain this in more detail in the upcoming chapters. Business A perpetual bond: To understand the business valuation, I feel it is necessary that one should first understand the character of a perpetual bond. I believe the value of a business is similar to the value of a perpetual bond. The reason why business ownership should be viewed similarly to a perpetual bond is both business ownership and perpetual bond don t have a maturity date, however they do have future coupons forever. A business owner always wants the business to retain the earnings and reinvest them at an attractive rate of return. The business will retain the earnings as long as the business finds opportunities to reinvest the earnings 2

3 at an attractive rate of return. It is predicted at the time of business negotiation, frequent management changes will happen in the future, board of directors will represent the owner s interest in the business, at any given moment the management will put their best effort to retain and increase the earnings of the business. Securing the current earnings and increasing the future earnings will be attained through retaining the unit volume, adjusting the company s products nature to the market need, expanding the current business model to new regions and executing the new projects. In general, every business present with the possibility of functioning for many decades from the day of business negotiation generation after generation- virtually forever -to make cash for its owners. As a result of this, it makes sense to say, both business and perpetual bond should be valued based on future coupons from the date of purchase till infinity year. In other words, the number of years to consider the future coupons should not be restricted in the value equation of perpetual bond as well as business. In the perpetual bond, the discount rate denominator reduces the present value of the future coupon and eventually making future coupon value to zero beyond certain years. In case of business, the risk factor reduces the future value coupon to zero beyond some years. Value of perpetual bond: = CF (1 + i) 1 + CF (1 + i) CF (1 + i) = CF 1/i CF- future coupon of perpetual bond i -current treasury bills interest rate The intrinsic value equation: The intrinsic value equation answer to an investor for the question how much it is worth paying today to acquire all the future cash flow of the given business? considering all aspects of the business. Let me first explain the intrinsic value equation and later I will explain how to justify the valuation from a private owner perspective. Variables in intrinsic value equations are, Base cash flow (CF) Risk associated with base cash flow (r) Interest discount factor for time (i) Reinvestment gain (Rg) Intrinsic value of business= = (CF + Rg1) (1 r) (1 + i1) (CF+Rg2) (1 r)2 + (1 + i1) (1 + i2) (CF + Rg ) (1 r) +. + (1 + i1) (1 + i2) (1 + i ) 3

4 CF (1 + Rg1/CF) (1 r) CF (1+Rg2/CF) (1 r)2 = + (1 + i1) (1 + i1) (1 + i2) CF (1 + Rg /CF) (1 r) (1 + i1) (1 + i2) (1 + i ) = CF(1 r) + CF (1 r) 2 + CF(1 r) CF(1 r) = CF {(1 r) + (1 r) 2 + (1 r) (1 r) } = CF {(1/r)-1} (Reinvestment gain Rg and interest discount factor for time dismiss each other in value equation and explanation for the same will be given later) CF= base cash flow r= risk associated with base cash flow (CF) i= risk-free interest rate (after tax) in respective years Rg= (Sum of discounted value of returns) - (Cash input into the business) CF - Base cash flow: CF is simply the net profit or net earnings of the latest four quarters of the business which is under negotiation for sale. The present net profit or net earnings is projected into future as the base cash flow in intrinsic value equation. The net earnings must be adjusted for any extraordinary items. One-time settlement with the government, unusual spend on marketing or R&D, one-time inventory losses, one time losses due to business consolidation or acquisition and any non-repetitive items must be adjusted in the latest four quarters of profit and loss statement for calculating the owner earnings. What an investor must project into the future as base flow is the sustainable net earnings which will be entirely available for business owners to make use of it for reinvesting the amount back to the business, paying out a dividend and shares buyback. Some analyst believes depreciation must be added back to net profit in arriving owner earnings. I disagree. Depreciation expense is a real expense like salary payout, rental cost, and cost of raw material. Even though depreciation expense doesn t cause an immediate cash outflow, eventually the business has to replace the machinery and equipment in future date at a higher price to allocated depreciation cost taking inflation into account. Therefore, the business has to keep aside the amount they allocated as depreciation cost to grow at least the rate of inflation to meet the future capital requirement of replacing the machinery and equipment at a future date. Finally, the goodwill is a subjective topic, and I will not explain it in detail. Usually, goodwill amount deducted from the profit and loss account is added back to net profit in calculating owner earnings. In this document, I have used the terms net profit and net earnings in different places, however, both represent the same. 4

5 r - Risk associated with base cash flow (CF) The risk is the possibility of damage that can happen to the base cash flow in the future. The buyer of the business will not pay the full price to base cash flow because he takes a risk today to receive base cash flow in the future. Therefore, it logically makes sense to reduce the base cash flow by potential loss with the hope of receiving potential gain when the loss doesn t occur in future. Risk can be described as what % of projected base cash flow is doubtful on the day of business negotiation? And the risk is more in subsequent years when one looks at the future from the day of business negotiation. Therefore the risk element is compounded in the intrinsic value equation with respect to time. For example, if an investor believes 5% of estimated base cash flow are doubtful, he would pay (1-5%) or 95% of first year estimated base cash flow to acquire it, and he would be pay 95% x 95% of the second year base cash flow to acquire the second cash flow value and this sequence continue till infinite years. High risk: possibility of high damage to base cash flow Low risk: possibility of low damage to base cash flow The risk % vary business to business and industry to industry. Companies with a strong brand, competitive advantage, pricing power and able management come with a low risk %, and companies with no such advantage come with a high risk %. There is no hard rule to calculate risk %. Investors and analysts have to calculate himself the risk % whether it is a private or public company. Common factors come into the picture when one try to arrive the risk% are, Future possibility of, 1. Reduction in unit volume of product either due to competition or less demand for the product 2. Reduction in realization either due to competition or less demand for the product 3. Unable to pass the cost increase to customer (fear of unit loss) 4. Government regulation that impacts unit volume, pricing power, and cost of the product 5. Currency fluctuation that impacts both sales and cost of the product 6. Company internal issues Note that, even though the buyer of business apply a risk% to acquire the future base flow at a discounted price, ideally he expects the business to overcome the entire risk and expects the business to retain the net earnings in future. The difference between estimated earnings discounted to risk and actual earnings the business going to generate through business operation explains the risk premium the buyer hoping to receive it in the future. (Let s call this as risk premium1) Interest discount factor for time (i): Once the present earnings is projected into future for infinite years as base cash flow, the discount must be applied to calculate the present value of future coupons using risk-free interest rate (return on treasury bills-after tax). The discount is applied to reward the buyer of the business for the time he is going to wait to receive the future value; the risk-free interest rate is kept as variable here to account the future fluctuation in risk-free yield one passive investor will receive in respective years by constantly investing his principal amount in government treasury bills. Let me explain in following paragraphs why it makes sense to consider future return from short-term government treasury bills as risk-free return (even though 5

6 it is not constant and unknown at the time of negotiation) than considering the current yield on long-term government bond as risk-free return (though it is known value at the time of negotiation) What rate of return can be considered as risk-free rate of return? Theoretically, the return that can be attained with zero risk (zero possibility of losing the principal and return value) is risk-free rate of return. However in practical, there is no such investment exist, even the safest investment carry a least amount of risk. The yield on long-term government bonds often referred as risk-free return. I disagree with anyone saying return from the long-term government bond is risk-free. Even though the long-term government bond provides an investor the highest level of safety to future coupons (virtually no default on interest and principal amount), it comes with interest rate risk which means any change in future interest rate will impact the future bond value. Any sharp increase in interest rate will bring down the value of bond significantly in the future. The significant reduction in market value of the bond in such case will be meaningful because when the interest rate increases, an investor then will have the option to invest in a bond which provides a higher interest rate. Therefore to account the loss in the yield, the bond value will be recalculated using revised interest rate to discount the future cash flow. One can argue that the bondholder will receive full amount on the maturity date regardless the reduction of bond value in the market- it is true the bondholder will be served with full payment regardless the decrease in market value of bond- however yield received on bond lesser to market yield must be considered as a loss. The flipside of this is true as well, the bondholder has the possibility of receiving an additional yield compared to market yield when the future interest rate falls. In such event, the additional yield one receives over the future market yield should be treated as risk premium for the risk taken on interest rate risk. However, the interest rate risk present with longterm government bonds doesn t go anywhere. More the extended period of maturity, higher the risk the bond carries with it. As a result of this circumstance, return one get from the long-term government bond can t be considered as risk-free return. If the returns from the long-term government bonds can t be considered as risk-free returns, then which return can be considered as risk-free return? Though the risk factor can t be eliminated entirely, the return that can be attained from short-term maturity government treasury bills can be considered as risk-free return (or return with least risk) because, the short-term maturity nature of treasury bills provides an investor negligible interest rate risk (Fluctuation in future interest rate will have insignificant impact on present value of future coupon as the maturity is very near) and extreme low default risk (possibility of default is extremely low compared to long-term bonds). In other words, a long-term investor who wants to receive risk-free return should always invest in shortterm government treasury bills and keep reinvesting end of every cycle to receive risk-free return. In such case, the return an investor going to receive in the long term is unknown at the time of the investment; however, the future return will always match to future market return and so the investor will virtually receive no risk premium or a loss. Treasury bills are available with different maturities. I consider here yield on 364 days (just less than a year) treasury bills as risk-free return in all intrinsic value calculation. The treasury bills here represents the treasury bills of the currency in which the net earnings of the 6

7 business is reported. In case treasury bills are not available in the currency in which earnings is reported, returns from short-term government bonds shall be considered as risk-free return. In the intrinsic value equation, every year risk-free interest rate is kept distinct to account the fluctuation in the future treasury bills interest rate (i1, i2, i3, i4, i5 ). Reinvestment gain (Rg): Reinvestment gain (Rg) can be defined as The gain an investor has the possibility of receiving through future reinvestment of earnings. Reinvestment gain (Rg) factor is positive in the value equation as every business inherently has the possibility of retaining a significant portion of business earnings inside the business and reinvest them at an above-average rate of return (over the risk-free rate of return). This possibility of event provides an investor to find value over the reinvestment capital into the business. Value of reinvestment capital can be explained by the following equation, Value of capital= {R1/ (1+i1)} + {R2/ (1+i1)*(1+i2)} + {R3/ (1+i1)*(1+i2)*(1+i3)} + + R- Return or cash flow from the reinvestment capital i-risk-free interest rate in respective years through treasury bills (after tax) Explanation: The equation to calculate the value of reinvestment capital into the business is formulated based on comparing the returns from reinvestment capital against the returns that can be achieved through investing the same capital into risk-free earning instrument (treasury bills) Assume capital X is reinvested into a business and that reinvestment capital is producing returns (cash flow) like below sequence, [Capital X into business]r1, R2, R3, R4, R5.. Now, assume the same capital X is invested in one-year treasury bills; end of the first year, the return (i) received through treasury bills is taken out, and the principal amount (X) is reinvested to purchase new treasury bills. Assume this event is being repeated forever; therefore, in this case, one can virtually forgo the capital (X) forever and receive risk-free return every year forever like a below sequence, [Capital X into treasury bills] i1, i2, i3, i4, i5. Now, applying discounted cash flow calculation will provide relative valuation of capital into the business against treasury return, Value of capital= {R1/ (1+i1)} + {R2/ (1+i1)*(1+i2)} + {R3/ (1+i1)*(1+i2)*(1+i3)} + + Therefore, reinvestment gain (Rg) can be calculated as, Reinvestment gain (Rg) = (Sum of discounted value of returns) - (cash input into the business) = (Value of capital) - (capital input) 7

8 From the above equation, it can be understood that reinvestment gain to be a positive in value equation, the sum of the discounted value of return from the reinvestment capital should be higher than the reinvestment capital input into the business. In other words, reinvestment gain (Rg) to attain a positive value, ROE% of reinvestment capital into the business should be above the risk-free interest rate% for the very long time from the initial year of capital investment into the business. If reinvestment capital is going to lag in initial years in producing above-average return, the capital should generate extraordinary returns in later years to compensate higher discount rate applied in later years to achieve a positive reinvestment gain (Rg). Therefore, one can calculate the net potential value the buyer of the business expects at the end of every year from the business through the following equation, = (net profit) - (cash input into business) + (sum of discounted value of return of capital input into business) =net profit + {(sum of discounted value of return of cash input into business) - (cash input into business)} =net profit + Reinvestment gain =CF + Rg Let me explain the reinvestment gain (Rg) with few examples. (Download the excel file from the link or from the link and refer to the tab value of capital ) Scenario1: Assume a business earned a net profit of $200 at the end of the first year after business is acquired. Management of business decides to payout $100 to business owners and chooses to reinvest remaining $100 into the business which is producing an additional cash flow of $10 from next year. Assume risk-free interest rate stays constant at 5% (after tax return) in the long run. The following cash flows sequence can be imagined for reinvestments of $100 into business and $100 into risk-free treasury bills [$100 reinvestment capital] 10, 10, 10, 10, 10, 10.. [$100 treasury bills] 5, 5, 5, 5, 5, 5 Now one can calculate the value of the $100 reinvestment capital into business equal to $200 based on the value of capital equation. =10/(1+5%)^1 + 10/(1+5%)^2 + 10/(1+5%)^3.. Based on this scenario, it is appropriate to say, the buyer of the business will receive net value of $300 = $100 (through dividend payout) + $200 (through reinvestment gain) end of the first year which is 150% of the first year reported earnings. In this case, every 1$ reinvested into the business created a value of 2$, otherwise, the value created = 2x capital into the business. Business with average return on equity will produce lesser times the value invested capital and similarly business with high return on equity will produce higher times the value invested capital (sometimes as much as five times the capital into the business because of an attractive rate of return). 8

9 Scenario2: In scenario1, both cash flow from reinvestment capital and risk-free interest rate are kept constant for easy understanding purpose; but in real, both return from the reinvestment capital and the risk-free interest rate from treasury bills will fluctuate in future; hence let s assume the second scenario like below sequence [$100 reinvestment capital] 7, 3, 8, 6, 10, 9, 5.. [$100 treasury bills] 5, 4, 6, 8, 5, 7, 6 Here one can still calculate the value of capital that exceeds the capital invested into the business using the value of capital equation. It is important to understand that, few years business return (ROE %) may underperform with respect to treasury bills yield (i) still the reinvestment capital can produce a value excess to reinvestment capital into the business due to other year s outperformance. Scenario3: Let s modify the assumption in scenario1 and see how the reinvestment gain works, assume the reinvestment capital of $100 into the business is producing a return of $10 every year for the initial 20 years and the capital is not making any return from 21st year; now assume a constant risk-free interest rate of 5%. One can arrive a discounted value of return to be $124.6 which is well above $100 investment into the business. Scenario4: Finally let s look at the case where the reinvestment gain can be negative. When the business is reinvesting the earnings back into business at a poor rate of return (ROE% is lesser than the risk-free return %), the reinvestment gain will be negative. Consider the following cash flow sequence from reinvestment capital in the business and treasury bills [$100 reinvestment capital] 3, 3, 2, -5, 0, -2, 5.. [$100 treasury bills] 5, 4, 6, 8, 5, 7, 6 In this scenario, the capital input into the business will exceed the value created by the incremental capital into to the business; in other words, the reinvestment gain is a negative value; From the above scenarios, it can be understood, business with a high return on equity will find it easy to create a value above the reinvestment capital and business with a low return on equity will find it difficult to a create value above the reinvestment capital. Overall it can be said, every business will try to attain a value exceeding the reinvestment capital. Reinvestment gain (Rg) a risk premium: Reinvestment gain (Rg) is truly a risk premium amount an investor receives for the reinvestment risk that he takes reinvestment capital into business has the possibility of not producing a value above the reinvested capital into the business. Importantly, this risk premium (let s call it risk premium2) is not an immediate payout to owners; it will be paid out to the owner over a period of time as an excess return to risk-free rate of return for the given reinvestment capital into the business. Every risk factors (explained under the topic r - Risk associated with base cash flow (CF) ) applicable to base cash flow are applicable to reinvestment capital as well. These risk factors will make the business 9

10 difficult to create value above the reinvestment capital. The business has to overcome the risk inherent in the reinvestment capital to make a positive reinvestment gain (Rg) It is impossible to predict future movement in risk-free rate of return, and it is unpredictable whether the future reinvestment capital into the business will create a rate of return excess to the future risk-free rate of return; if so, then what factor drives reinvestment gain (Rg) variable to become a positive component by default in intrinsic value equation? It is positive because of the possibility existence; every business has the possibility of making a rate of return excess to future risk-free rate of return for the given reinvestment capital into the business. In other words, every business comes with the possibility of creating a value above the reinvestment capital into the business despite the dynamic nature in the future risk-free rate of return and unknown circumstance of business operation in the future. The magnitude of reinvestment gain (Rg): It is essential to understand that the activity of reinvestment is not only adding an additional value to particular year earnings but also increases the future cash flow available for future reinvestment in subsequent years. Therefore, the potential magnitude of reinvestment gain increases year on year as the business has possibility of having more capital to reinvest in following years; i.e. Possibility exists for Rg1<Rg2<Rg3<Rg4<Rg5 Reinvestment gain is an additional value to every year net earnings as the reinvestment gain value is a derivative from net earnings; reinvestment gain added with net earnings can be seen as a following sequence, (CF+Rg1), (CF+Rg2), (CF+Rg3), (CF+Rg4), (CF+Rg5).. One might ask when the second year and subsequent year s earnings are revised based on first-year reinvestment, why it is not reflected in above sequence. The answer stays inside the sequence. Even though the second year and subsequent year s cash flow is revised based on first-year reinvestment, Rg1 takes into account of all additional cash flow through first year reinvestment starting from second year. Therefore, additional cash flow can t be added again in subsequent years. Similarly Rg2, Rg3, Rg4, Rg5 reflects the additional cash flows from their respective years through reinvestment. Now let s try to imagine the magnitude of reinvestment gain (Rg) factor in the intrinsic value equation in following years. It is not difficult for one to understand that more the capital business going to consume in future, more the reinvestment gain a business can produce in the future; to know how much capital a business can consume back into the business, let s understand what will drive the reinvestment capital requirement. The following points explains the factors that will drive the future capital requirement of business every year. 1. Inflation a significant portion of earnings will be reinvested back to business in order to meet the additional capital requirement caused by inflation for maintaining the same unit sales 2. Expansion of existing product unit volume- capital will be invested for making more units sales of existing product portfolio in the same and new regions 3. New product unit volume- capital will be invested for making more units sales of innovated net products in the same and new regions 10

11 4. Capital consumption towards optimization of process (will cut down the cost and will increase the future cash flow) 5. Capital consumption towards quality improvement and revamping the existing product portfolio will help the business to attain better realization in sales 6. Capital investment in brand building and investment towards discounts with the intention of acquiring more customers in future (through which increase in unit sales can be attained) 7. Capital investment in R&D to develop new products/service for the incremental future sales 8. Capital investment on joint venture to produce more unit sales and profit 9. Capital investment towards acquiring other business with the aim of a) Expanding the existing products of acquired company b) Expanding the parent company products through acquired company s channels c) Reducing the overlapping cost between two companies d) Accessing intellectual properties -technology, trademarks, patterns and skilled people, etc. available in acquired company To approximately measure the magnitude of reinvestment gain in value equation, one needs to visualize the future from the day of business negotiation. Almost every business will work towards increasing the future earnings of the business at a healthy rate by continuously reinvesting a significant portion of every year future earnings. Among all the points discussed above, the first three points are the primary factors which help one to understand the magnitude of reinvestment gain over the years. Business with low return on equity will require very high % of profit back into business and business with a very high return on equity will require less % of profit back into business to grow their earnings at the inflation rate. Apart from cash inputs into business to meet the additional capital requirement caused by inflation, business will also consume a significant portion of every year profit back into business for expansion of existing products unit volume and for producing incremental sales of innovated new products. Overall every business has the possibility to grow the future profit at a healthy rate (over the inflation rate), and so the possible magnitude of the reinvestment gain (Rg1, Rg2, Rg3,.) in the future also increases roughly at the same rate. How far can one imagine the future reinvestment gain from now? 10 years or 20 years or 50 years or 100 years? I believe the answer is forever or till infinity year because there is going to be always some opportunity exist for business to expand or reinvest their earnings at an attractive rate of return. Future management and board of directors of the business will decide then what would be the best possible way to use the capital; in general, the business is expected to expand in the same industry in which they already operate in, through organic and inorganic growth; however the management and the board of directors will decide to invest in a different industry when they find an attractive investment opportunities to invest the capital in a different industry. The capital that the management believe can t be reinvested back to business at an above-average rate of return are expected to paid out to the owner as a dividend or will be kept inside the business for future investments opportunities. Of course an investor can t predict on the day of business negotiation where the business will expand in future down the line many years from now, what will be the return on equity on those future reinvestment capital and what would be the risk associated with those incremental cash flow; however what rationally can be said is, there is possibility exist for business to find value above the reinvestment capital (reinvestment gain) regardless of the industry that the business are going to operate in the future, and 11

12 there is possibility exist for receiving incremental reinvestment gain (Rg) value following years through incremental capital consumption into business" The Reinvestment gain (Rg) factor in intrinsic value equation is sharing the risk associated with base cash flow as well as the interest discount factor for time along with the base cash flow; the following statements explains the reason, Any damage to base cash flow in the future will impact the future reinvestment gain (any permanent reduction in base cash flow will reduce the net capital available to reinvest and so reduces the magnitude of reinvestment gain); therefore the risk that applies to base cash flow is also applicable to future risk premium (reinvestment gain) Reinvestment gains are arriving late (must be discounted for time using risk-free interest rate) Arriving the final intrinsic value equation: We shall now discuss arriving the final equation to calculate the intrinsic value of the business. Value of a business is always negotiated for the entire lifetime of the business as the buyer of the business acquiring the ultimate ownership to receive entire future cash flow that the business is going to produce in the lifetime from the date of purchase. Here comes a complexity in arriving an exact value for a business; both buyer and seller of the business don t know the future; it is impossible to predict the future cash flow of the business and future risk-free rate of return; therefore both buyer and seller negotiating the value based on all aspects of the business. Subsequently buyer and seller considering all positive and negative factors that will impact the future cash flow for arriving a negotiated value; primary variables taken into consideration are Base cash flow (CF) Risk associated with base cash flow (r) Interest discount factor for time (i) Reinvestment gain (Rg) Intrinsic value of business= = (CF + Rg1) (1 r) (1 + i1) (CF+Rg2) (1 r)2 + (1 + i1) (1 + i2) (CF + Rg ) (1 r) +. + (1 + i1) (1 + i2) (1 + i ) CF (1 + Rg1/CF) (1 r) CF (1+Rg2/CF) (1 r)2 = + (1 + i1) (1 + i1) (1 + i2) CF (1 + Rg /CF) (1 r) (1 + i1) (1 + i2) (1 + i ) 12

13 CF= base cash flow r= risk associated with base cash flow (CF) i= risk-free interest rate (after tax) in respective years Rg= (Sum of discounted value of returns) - (Cash input into the business) Now let s take a look at the value of business in graphical form. This diagram explains what buyer and seller visualizing inside the business in future years from the date of business negotiation. Intrinsic value The future value of the business can be picturized as three areas Line Present earnings (CF) explains the base cash flow Area under the curve CF discounted to risk explains the sum of (base cash flow discounted to risk inherent in base cash flow) Area between two curves Present earnings (CF) and CF discounted to risk explains the sum of risk premium in base cash flow (risk premium1) Area between two curves Present earnings (CF) and Expected net value (CF+Rg) explains the sum of all future reinvestment gain the business expected to generate in future (risk premium2) 13

14 Reinvestment gain (Rg) factor as compensation for interest discount factor for time (i): There are two factors in value equation act in a different direction. Interest discount factor for time (i) is negative impact in value equation as buyer of the business receives the return in later years from the date of purchase; therefore every year future estimated value is discounted by risk-free interest rate in order to compensate buyer with risk-free interest amount in future for the delay in receiving future returns Reinvestment gain (Rg) is positive impact on value equation as business can find more value on return it is going to produce every year by reinvesting a significant portion of profit at high rate of return; therefore buyer of the business has the possibility of receiving additional value to future net profit every year in the future Reinvestment gain (Rg) is not quantifiable at the same time it is not ignorable on the day of negotiationthere is a strong possibility exist for huge untapped value attached to every subsequent year profit from the day of business negotiation; therefore seller of the business demands for future reinvestment gain that the business is going to produce in the future during the price negotiation. Even buyer of the business agree that there is a possibility of receiving enormous reinvestment gain in future through future reinvestment actions yet the value is not quantifiable on the day of negotiation; In the final negotiation, buyer of the business agrees to take all future reinvestment gain as compensation to interest amount that he supposed to receive for delay in receiving future earnings; buyer and seller believe that reinvestment gain (Rg) can compensate buyer more than the interest amount that the buyer supposed to receive in future. Here comes the question, is it worth trading interest amount for future reinvestment gain from the buyer perspective? To answer this question, we need to understand the characteristic of two variables that we are discussing in the intrinsic value equation, 1.) Characteristic of discount factor for time (i)- the denominator value is compounded every year at the rate of future risk-free interest rate 2.) Characteristic of reinvestment gain (Rg) factor- the numerator value is compounded every year at a healthy rate (expected) One thing is clear; the risk-free interest rate here refers the risk-free interest rate of the same currency being used to purchase the business. And the reinvestment gain (Rg) will be influenced by various currencies as the business can operate globally. The magnitude of future reinvestment gain values (Rg1, Rg2, Rg3..) is explained by future growth potential in the earnings of the business. Despite many countries in which the business operates and different currency risk involved with future earnings, the business inherently has the possibility to achieve a long term average growth rate in earnings above the long term average of the future risk-free interest rate by continuously reinvesting earnings back to business. If the business has the possibility of growing the future earnings over the long term average of future risk-free interest rate, it makes sense to say that the future reinvestment gain (Rg) value also has the possibility to grow over the long term average of future risk-free interest rate; If the future reinvestment gain value can grow over the rate of future risk-free interest, it can be considered as compensation value to discount factor for time in the intrinsic value equation. 14

15 Right from the first year reinvestment gain Rg1 as percentage of CF is sufficiently expected to cover the first year interest rate i.e. (1+Rg1/CF) > (1+i1); then, the expectation of growth rate in reinvestment gain (Rg) above the future risk-free interest rate in subsequent years (Rg1<Rg2<Rg3<Rg4<Rg5.. ) is helping one to understand the following sequence that both buyer and seller picturizing it in future, (1+Rg1/CF)> (1+i1), (1+Rg2/CF)> (1+i1)*(1+i2), (1+Rg3/CF)> (1+i1)*(1+i2)*(1+i3), (1+Rg4/CF)> (1+i1)*(1+i2)*(1+i3)*(1+i4), (1+Rg5/CF)> (1+i1)*(1+i2)*(1+i3)*(1+i4)*(1+i5),. Of course, it is understood between buyer and seller at the time of negotiation Not every year the reinvestment gain (Rg) factor will compensate the interest rate discount factor for time but overall the reinvestment gain factor (Rg) is expected to compensate well above the interest discount factor for time in the long run. The future operation of the business will validate the above sequence. If business s future earnings is growing over the future average risk-free interest rate in the long term, the magnitude of reinvestment gain (Rg) will exceed the magnitude of interest discount factor for time (i) in the intrinsic value equation, and the above sequence will become true; As a result of this possibility, the buyer agrees to take the entire future reinvestment gains as the compensation for interest amount that he supposed to receive in the future. One thing is clear here; the interest amount is traded for reinvestment gain considering the possibility not for the certainty. The future is really not predictable; if the future reinvestment is going to be unsuccessful, it will disappoint the buyer of the business. Therefore, in the final negotiation, reinvestment gain (Rg) factor and interest discount factor for time (i) dismiss each other in the intrinsic value equation, and the final equation ends with two variables, 1. Base cash flow (CF) 2. Risk associated with base cash flow (r) Intrinsic value= = CF(1 r) + CF (1 r) 2 + CF(1 r) CF(1 r) = CF {(1/r)-1} The following graph explains the final negotiated value between buyer and seller of the business. The base cash flow discounted to the risk associated with base cash flow and then summed all discounted value provides the final intrinsic value. 15

16 VALUE Intrinsic value Present earnings (CF) CF discounted to risk YEAR Justifying the intrinsic value from private owner perspective: In this chapter, I will be explaining how intrinsic value of a business is justified from a private owner perspective. If the price paid for purchasing business has to be justified from a private owner perspective, then the historical price to earnings ratio, price to book value, industry price to earnings ratio and similar metrics can t be considered. In other terms, the private owner should assume that he and his generation will own the business forever and he must find value inside the business to arrive a conclusion whether the price is worth paying. To arrive a conclusion whether the price paid for purchasing the business is worth, it is essential to answer the question what is the maximum return that can be produced with the given amount? Now imagine two wealthy persons present with an equal amount of cash in hand. The first person is a passive investor who doesn t want to take any risk. Therefore he is investing the entire amount in 364 days treasury bills (core currency). End of the first year he is reinvesting in new 364 treasury bills the entire amount that he received from first year investment (principal + interest). Imagine he is repeating this activity forever and he is not taking out any amount for himself from this investment activity. Therefore the passive investor will receive risk-free return every year and the principal amount in net value term will 16

17 grow in future at the rate of future risk-free interest rate which explains the maximum value that can be produced in the long term with zero risks for the given investment amount. Now comes the second person who is an active investor and who is fine accepting a risk to receive a better possible return than the treasury bills return that he could have got with zero risks. Therefore he decides to purchase a business which is having most promising future. The only reason why he chooses to buy a business instead of investing in risk-free treasury bills is Maximum return that he is hopeful of receiving from the business is higher than the maximum return that he is hopeful of receiving from treasury bills investment for the given investment amount. I.e. Maximum potential return through business in lifetime > Maximum potential return through treasury bills investment in lifetime (for an equal investment amount) Note: lifetime here denotes infinite years Let me explain this with an example. Imagine a business with a book value of 8,000 cr. and producing 20% return on equity. Therefore net earnings (after tax) of the business would be 8,000 x 20% = 1600 cr. (Note: 1 cr = 10 million) assume the business present with diversified portfolio of products which is directly linked to consumers, able management operating the business, products protected with strong brand names, don t have any close substitute products by competitor, well established distribution network, tight cost control and healthy research and development department to drive the future sales and profit at significant rate. Considering all these advantages about the business, seller demands an expensive price to the buyer. Let s assume buyer agrees to purchase the entire business ownership at 62,400 cr in the final negotiation. In this case, both buyer and seller believe that there is very low risk present in the business; therefore, they are applying 2.5% risk rate in the intrinsic value equation. The math work like below, Intrinsic value of business= = CF(1 r) + CF (1 r) 2 + CF(1 r) CF(1 r) = CF x (1/r)-1 = 1600 x (1/2.5%)-1 = 1600 x 39 = 62,400 cr. (Reinvestment gain factor compensate for interest discount factor for time; therefore both factors dismiss each other in value equation). The above calculation is detailed in the excel file in the tab Intrinsic value. Here comes the question whether 62,400 cr price paid for purchasing the business is worth and justifiable from a private owner perceptive? To answer this question, we will first understand the maximum return that can be produced with same amount being invested in treasury bills and later we will compare treasury bills returns against the maximum potential return of the business. Consider an investor purchasing 62,400 cr worth of one-year treasury bills, and he is continuously reinvesting every proceeds (principal and return) in treasury bills end of every year and assume he is repeating this investment activity forever. Therefore the value of this amount will grow in the future at the rate of future risk-free interest rate which explains the maximum possible growth rate in value that can be attained by investing the amount in a risk-free earning instrument. 17

18 Now we shall compare the potential return that is expected out of business against the potential return that is expected out of treasury bills investment. Assume the average risk-free interest rate stays close to 5% in the long term. If all earnings from the business are going to be paid out as dividend and if treasury bills yield stays closer to 5% in the long term, then the price can t be justified as maximum dividend yield from the business will be 2.56% which is far lesser than the treasury bills yield of 5%. In such case, obviously buyer of the business will receive far lesser return compared to the treasury bills investor. However, in most cases, every business continuously reinvest a significant portion of earnings back into business to increase their future earnings at a healthy rate, and there is strong possibility exist for it. Imagine, in future 1. If business matches the long term average growth rate in earnings to the long term average of risk-free interest rate by continually reinvesting a significant portion of every year earnings and business is paying some dividend every year (or) 2. If business long term average growth rate in earnings exceeds the long term average of risk-free interest rate by continually reinvesting the entire earnings of business Can you imagine what will happen in 100 years from now? If an equal amount is used to purchase business and treasury bills, the business will outperform the treasury bills in terms of net return in both cases. In other words, the business with dividends accumulated (and reinvested at future risk-free interest rate) + one year net earnings from the business will exceed the net treasury bills value at some date in future. (Refer to the excel file tabs Justification- case1 and Justification- case2 ) Elaborating this further, in this example, If we assume that both business owner and treasury bills holder is accumulating all their respective future returns and in the event of successful business return, the business owner will be able to comfortably buyout the net accumulated treasury bills from the treasury bills holder using dividends value accumulated from business + one year earnings from the business at some point in future (however the maturity date is unknown at the time of business negotiation) and business owner will be receiving excess returns through business operation even after buyout of entire value from treasury bills holder. Every return that business owner will receive after such point of the buyout will work as an additional return to the business owner for the risk he had taken to purchase the business over the treasury bills. These examples prove that business provides an investor the possibility of producing better return than treasury bills return in the life time holding period for a given purchase price. Every business provided with this opportunity/possibility looks expensive at first glance however when one considers the business ownership in a very long-term perspective, it can be understood that the price paid for purchasing business is justifiable or worth paying. The graphical form of this events is shown below, 18