I am sure you guys must have heard lately that markets went ahead of themselves too quickly and should experience some correction. Although there is lots of storytelling in the media but I never saw any fundamental valuation of SENSEX. So i though you may find this SENSEX valuation report interesting that I just finished that *only works with numbers and no story-telling*. This is a pure fundamental valuation of SENSEX that you may, if interested, want to play with the underlying assumptions and see how SENSEX will behave in future. You can use this model for any other index like nifty.. Send me your feedback or any questions

To download in word doc

http://www.scribd.com/full/20584628?access_key=key-di0w6tj1vuu7xxhn2f6

http://www.scribd.com/doc/20584733/SENSEX-fundamental-valuation-model

Media is inundated with the news of expected correction in the markets, having rallied too high too quickly. Some say the rally is driven by liquidity, while others claim the optimism in the global market.

Without doing any more storytelling (abundant in media), I will delve into how much SENSEX is valued intrinsically. (Readers can do the similar exercise for NIFTY or any other index)

Intrinsic value of any asset is the present value of future cash flows, generated by the asset. Therefore, SENSEX, backed by 30 stocks, should also have an intrinsic value derived from the future cash flows of its 30 constituent securities. If one can identify these future cash flows and calculate the present value, one can conclude the degree of SENSEX over/undervaluation based on fundamentals.

There is enough literature on the web that does a good job of explaining. In summary, SENSEX is calculated using a free-floating market cap of its 30 stock constituents. Free-floating market cap is the product of stock price and the number of shares that can trade in the market (shares held by promoters or other strategic investors are not included in calculating the free floating market cap). One can download the free floating multiplier from BSE web site, to calculate free-floating market cap. I have used the excel file downloaded from BSE website to do the same.

Lastly, the free floating market cap is multiplied by a divisor that references it to the base year. But for our purpose of discussion, we will limit ourselves to the estimation of free-floating market cap, driving the value of SENSEX.

To refresh our memories, I will run you through an example of calculating intrinsic value of a candle making company (started in 2009 with an investment of Rs. 370). The company plans to generate Net income of Rs. 100 next year (2010) and growing hence @15% for next 4 years. At the end of 4 years, we assume that the growth rate reduces to 4% forever.

Let us first identify the future Net Income of the company.

2010 : 100

2011: 100*(1+.15)=115

2012: 100*(1+.15)^2=132.25

2013: 100*(1+.15)^3=152.08

2014: 100*(1+.15)^4=174.9

After year 5(2014), Net income grows at 4% forever. Therefore, 2015 Net income will be 174.90*(1+.04) =181.89

2010 2011 2012 2013 2014 2015 2016

NI(Rs) 100 115 132.25 152.08 174.9 181.89 189.17

Growth 15 15 15 15 4 4

(Net income will continue to grow@4% forever after 2015. In the interest of space, I omitted more years in the table)

Now that we have identified future Net income, let us bring in the concept of Return on capital. A candle company must invest in the business to drive growth. As mentioned above, the company started with an investment of Rs 370 in 2009 and is expected to generate Net income of Rs. 100 in 2010, resulting in return on capital of 100/370=27.00%. The return on capital (increase/decrease) may change in future years, driven by several factors such as competition and efficiency. But in our example, we will assume that the company manages to maintain same ROE forever. In 2011, company’s net income grows by 15% to 115, requiring reinvestment driven by the formula G=ROC*B

G – Growth in Net income

ROC – Return on capital

B – How much of Net income to retain/reinvest to generate G growth

In our example, G=.15 and ROC=.27 resulting in B of 55.55%. The owner should reinvest 55.55% of Net income every year in its business to generate 15% growth rate. So in year 2010, owner should re-invest 55.55% of 100 =Rs. 55.55 in business leaving a cash flow of Rs. 44.44 to owner. As mentioned above, after year 5 (2014), the growth rate decreases to 4%, resulting in B of .04/.27=14.81%. After 2014, owner should reinvest only 14.81% of Net income in the business to generate 4% growth. Now we can identify the cash flow available to owner after all the reinvestments.

2010 2011 2012 2013 2014 2015 2016

NI(Rs) 100 115 132.25 152.08 174.9 181.89 189.17

Reinv(%) 55.55 55.55 55.55 55.55 55.55 14.8 14.8

Reinv(Rs) 55.55 63.82 73.39 84.40 97.06 26.92 27.99

FCF 44.5 51.17 58.85 67.67 77.83 154.97 161.17

(FCF is the cash flow available to the owner that he/she can withdraw from business. This cash flow is also called at times free cash flow)

To estimate the intrinsic/fundamental value of candle business, we need to calculate the present value of all future cash flows. Let us assume that the discount rate for this business is 12%. (Discount rate is driven by the riskiness of business, identified by Beta). The discount factor for 2010 will be 1/(1.12) and for 2011 be 1/(1.12)^2 and so on.

Putting back the discount rate into the table, the table looks like:

2010 2011 2012 2013 2014 2015 2016

NI(Rs) 100 115 132.25 152.08 174.9 181.89 189.17

Reinv(%) 55.55 55.55 55.55 55.55 55.55 14.8 14.8

Reinv(Rs) 55.55 63.82 73.39 84.40 97.06 26.92 27.99

FCFF 44.5 51.17 58.85 67.67 77.83 154.97 161.17

DF 0.89 0.79 0.71 0.63 0.56 0.50 0.45

PV 39.73 40.79 41.88 43.01 44.16

(Omitted years after 2016)

DF - Discount factor

PV - (available cash*disc)

Let us introduce the concept of terminal value. As mentioned above, it is assumed that starting 2015, Net income will grow @4% forever. The value of such annuity in year 2014 is:

(annuity cash flow in 2015)/(discount rate – annuity growth rate) ---- This is formula of infinite Geometric progression series

Annuity cash flow in 2015=154.97

Discount rate=12%=.12

Annuity growth rate=4%=.04

Annuity value in 2014=154.97/(.12-.04)=1937.19

This annuity value is also referred to as Terminal Value.

We need to discount terminal value to calculate its PV today (2009), so we will multiply by 0.56 resulting in 1099.21 . This is the present value of annuity, starting in 2015.

Therefore, the intrinsic value of candle business is the sum of terminal value( 1099.21) and the present value of first 5 years cash values.

Intrinsic value=39.73+40.79+41.88+43.01+44.16+1099.21=1308.81

Assuming owner has no debt and there are 100 shares in the company, the price of 1 share=1308.81/100=Rs.13.08

Because SENSEX is composed of 30 stocks, we will need to identify future cash flows resulting from these 30 stocks, adjusted for free floating factor. (SENSEX is calculated using free-floating method).

We need to identify below mentioned parameters to calculate present value of SENSEX:

- Growth rate for next 10 years and Terminal growth rate.

- Return on Equity during next 10 years and in Terminal growth period.

There are 2 ways one can identify the next 10 years growth rate:

1. Using predictions for Indian economy growth rate – Mckinsey in its recent research report estimated Indian economy to grow at a CAGR of 10-12% in the next 10 years. Because SENSEX represents the Indian market, Indian growth rate can be a good substitute for SENSEX growth rate.

2. Using analyst EPS growth rate estimates of SENSEX companies - Analysts estimate the long term growth of public listed companies. Using the mean value of such estimates, one can derive the SENSEX long term/10 year growth rate. Because SENSEX uses free floating multiplier, index growth rate is the free-floating earnings weighted average of growth rate of 30 index components. For example, let us assume that SENSEX is composed of only 2 stocks: A and B. Analyst estimate for forward EPS for A and B is 10 and 12 respectively. Also, analysts’ long term growth rate estimates for A and B are 10% and 12% respectively. Additionally, we are given the outstanding shares of A and B to be 100 and 200, and the free-floating multiplier to be .5 and .4, resulting in a free-floating number of shares of 50 and 80. The growth rate of SENSEX will be (10*50*0.1+12*80*0.12) /(10*50+12*80)=11.3%.

If one does the similar exercise for 30 SENSEX stocks using estimated forward EPS for next year and their long term growth rates, SENSEX long term growth rate comes out to 13.72 %.

This is determined by the risk free rate or GDP growth rate in the terminal period. Indian 10 year yield on Sep 30, 2009 is 7% and the country holds a BBB- Moody’s credit rating, resulting in country risk premium of ~3.5%. This results in Indian risk free rate of 7-3.5=3.5%, or the terminal growth rate of 3.5%.

We calculate ROE of SENSEX for last 5 years and use the maximum ROE in the last 5 years as an estimate of ROE for the next 10 years. The max ROE for SENSEX is 23.06% in 2007.

ROE for SENSEX is calculated using the Book Value weighted average of ROE of index components.

2009 2008 2007 2006 2005

SENSEX-ROE (%) 18.32 20.36 23.06 22.42 21.00

No company can continue to maintain excess returns forever, as it will encourage competition and hence whittle away the excess returns. Similarly, Indian markets can’t continue to maintain excess returns forever, as it will encourage more FIIs to invest in India, increasing the valuations and reducing the excess returns. According to Mckinsey school of thought, terminal excess return should be zero, resulting in ROE equal to cost of equity. The SENSEX valuation will assume terminal excess return of zero, resulting in terminal ROE of 10% equal to cost of Equity.

This is determined by the Indian risk free rate, Indian country risk premium and the equity market risk premium. India holds a BBB- Moody’s rating corresponding to 3.5% country risk premium. The Indian 10 year yield at the time is 7% and the average historical market risk premium is 5%. Because SENSEX beta is 1, the cost of equity=7+5=12%.

It is estimated that India’s Moody’s rating will improve 10 years from now, attributed to improved country’s economy. In terminal period, India’s risk premium will reduce by 200bp resulting in cost of equity of 10%.

Using analysts estimates of 30 index components, free-floating weighted average of forward EPS is calculated resulting in next year earnings of Rs. 628264.71m. (Free-floating earnings= fwd EPS*free-floating-multiplier*shares-outstanding)

Earnings are not the free cash flow because growth is driven by reinvestment. Using G=ROE*B, we can calculate the retention ratio for high growth phase and terminal growth period. Using growth rate of 13.72% and ROE of 23.06% in high growth phase, SENSEX needs to retain 60% of its earnings resulting in a payout ratio of 40%. In terminal growth phase, payout ratio is 65%.

With future EPS, growth rates and pay-out ratio of SENSEX, we can calculate the Free-cash flow to equity generated by SENSEX. Calculating the present value of these cash flows will give us the intrinsic value of SENSEX, indicating SENSEX is overvalued by 14.10%

I couldn't get the final DCF model table in correct format so you can download it from -

http://www.scribd.com/full/20584628?access_key=key-di0w6tj1vuu7xxhn2f6

http://www.scribd.com/doc/20584733/SENSEX-fundamental-valuation-model

To download in word doc

**Word document**http://www.scribd.com/full/20584628?access_key=key-di0w6tj1vuu7xxhn2f6

**Excel valuation model- click below and download as excel**http://www.scribd.com/doc/20584733/SENSEX-fundamental-valuation-model

**Is BSE-SENSEX over/undervalued as of Sep 30, 2009?**Media is inundated with the news of expected correction in the markets, having rallied too high too quickly. Some say the rally is driven by liquidity, while others claim the optimism in the global market.

Without doing any more storytelling (abundant in media), I will delve into how much SENSEX is valued intrinsically. (Readers can do the similar exercise for NIFTY or any other index)

**What do I mean by the intrinsic value of SENSEX?**Intrinsic value of any asset is the present value of future cash flows, generated by the asset. Therefore, SENSEX, backed by 30 stocks, should also have an intrinsic value derived from the future cash flows of its 30 constituent securities. If one can identify these future cash flows and calculate the present value, one can conclude the degree of SENSEX over/undervaluation based on fundamentals.

**How is SENSEX CALCULATED?**There is enough literature on the web that does a good job of explaining. In summary, SENSEX is calculated using a free-floating market cap of its 30 stock constituents. Free-floating market cap is the product of stock price and the number of shares that can trade in the market (shares held by promoters or other strategic investors are not included in calculating the free floating market cap). One can download the free floating multiplier from BSE web site, to calculate free-floating market cap. I have used the excel file downloaded from BSE website to do the same.

Lastly, the free floating market cap is multiplied by a divisor that references it to the base year. But for our purpose of discussion, we will limit ourselves to the estimation of free-floating market cap, driving the value of SENSEX.

**How do you calculate intrinsic value of an asset?**To refresh our memories, I will run you through an example of calculating intrinsic value of a candle making company (started in 2009 with an investment of Rs. 370). The company plans to generate Net income of Rs. 100 next year (2010) and growing hence @15% for next 4 years. At the end of 4 years, we assume that the growth rate reduces to 4% forever.

Let us first identify the future Net Income of the company.

2010 : 100

2011: 100*(1+.15)=115

2012: 100*(1+.15)^2=132.25

2013: 100*(1+.15)^3=152.08

2014: 100*(1+.15)^4=174.9

After year 5(2014), Net income grows at 4% forever. Therefore, 2015 Net income will be 174.90*(1+.04) =181.89

2010 2011 2012 2013 2014 2015 2016

NI(Rs) 100 115 132.25 152.08 174.9 181.89 189.17

Growth 15 15 15 15 4 4

(Net income will continue to grow@4% forever after 2015. In the interest of space, I omitted more years in the table)

Now that we have identified future Net income, let us bring in the concept of Return on capital. A candle company must invest in the business to drive growth. As mentioned above, the company started with an investment of Rs 370 in 2009 and is expected to generate Net income of Rs. 100 in 2010, resulting in return on capital of 100/370=27.00%. The return on capital (increase/decrease) may change in future years, driven by several factors such as competition and efficiency. But in our example, we will assume that the company manages to maintain same ROE forever. In 2011, company’s net income grows by 15% to 115, requiring reinvestment driven by the formula G=ROC*B

G – Growth in Net income

ROC – Return on capital

B – How much of Net income to retain/reinvest to generate G growth

In our example, G=.15 and ROC=.27 resulting in B of 55.55%. The owner should reinvest 55.55% of Net income every year in its business to generate 15% growth rate. So in year 2010, owner should re-invest 55.55% of 100 =Rs. 55.55 in business leaving a cash flow of Rs. 44.44 to owner. As mentioned above, after year 5 (2014), the growth rate decreases to 4%, resulting in B of .04/.27=14.81%. After 2014, owner should reinvest only 14.81% of Net income in the business to generate 4% growth. Now we can identify the cash flow available to owner after all the reinvestments.

2010 2011 2012 2013 2014 2015 2016

NI(Rs) 100 115 132.25 152.08 174.9 181.89 189.17

Reinv(%) 55.55 55.55 55.55 55.55 55.55 14.8 14.8

Reinv(Rs) 55.55 63.82 73.39 84.40 97.06 26.92 27.99

FCF 44.5 51.17 58.85 67.67 77.83 154.97 161.17

(FCF is the cash flow available to the owner that he/she can withdraw from business. This cash flow is also called at times free cash flow)

To estimate the intrinsic/fundamental value of candle business, we need to calculate the present value of all future cash flows. Let us assume that the discount rate for this business is 12%. (Discount rate is driven by the riskiness of business, identified by Beta). The discount factor for 2010 will be 1/(1.12) and for 2011 be 1/(1.12)^2 and so on.

Putting back the discount rate into the table, the table looks like:

2010 2011 2012 2013 2014 2015 2016

NI(Rs) 100 115 132.25 152.08 174.9 181.89 189.17

Reinv(%) 55.55 55.55 55.55 55.55 55.55 14.8 14.8

Reinv(Rs) 55.55 63.82 73.39 84.40 97.06 26.92 27.99

FCFF 44.5 51.17 58.85 67.67 77.83 154.97 161.17

DF 0.89 0.79 0.71 0.63 0.56 0.50 0.45

PV 39.73 40.79 41.88 43.01 44.16

(Omitted years after 2016)

DF - Discount factor

PV - (available cash*disc)

Let us introduce the concept of terminal value. As mentioned above, it is assumed that starting 2015, Net income will grow @4% forever. The value of such annuity in year 2014 is:

(annuity cash flow in 2015)/(discount rate – annuity growth rate) ---- This is formula of infinite Geometric progression series

Annuity cash flow in 2015=154.97

Discount rate=12%=.12

Annuity growth rate=4%=.04

Annuity value in 2014=154.97/(.12-.04)=1937.19

This annuity value is also referred to as Terminal Value.

We need to discount terminal value to calculate its PV today (2009), so we will multiply by 0.56 resulting in 1099.21 . This is the present value of annuity, starting in 2015.

Therefore, the intrinsic value of candle business is the sum of terminal value( 1099.21) and the present value of first 5 years cash values.

Intrinsic value=39.73+40.79+41.88+43.01+44.16+1099.21=1308.81

Assuming owner has no debt and there are 100 shares in the company, the price of 1 share=1308.81/100=Rs.13.08

**Intrinsic valuation of BSE SENSEX**Because SENSEX is composed of 30 stocks, we will need to identify future cash flows resulting from these 30 stocks, adjusted for free floating factor. (SENSEX is calculated using free-floating method).

We need to identify below mentioned parameters to calculate present value of SENSEX:

- Growth rate for next 10 years and Terminal growth rate.

- Return on Equity during next 10 years and in Terminal growth period.

**Growth rate for next 10 years**There are 2 ways one can identify the next 10 years growth rate:

1. Using predictions for Indian economy growth rate – Mckinsey in its recent research report estimated Indian economy to grow at a CAGR of 10-12% in the next 10 years. Because SENSEX represents the Indian market, Indian growth rate can be a good substitute for SENSEX growth rate.

2. Using analyst EPS growth rate estimates of SENSEX companies - Analysts estimate the long term growth of public listed companies. Using the mean value of such estimates, one can derive the SENSEX long term/10 year growth rate. Because SENSEX uses free floating multiplier, index growth rate is the free-floating earnings weighted average of growth rate of 30 index components. For example, let us assume that SENSEX is composed of only 2 stocks: A and B. Analyst estimate for forward EPS for A and B is 10 and 12 respectively. Also, analysts’ long term growth rate estimates for A and B are 10% and 12% respectively. Additionally, we are given the outstanding shares of A and B to be 100 and 200, and the free-floating multiplier to be .5 and .4, resulting in a free-floating number of shares of 50 and 80. The growth rate of SENSEX will be (10*50*0.1+12*80*0.12) /(10*50+12*80)=11.3%.

If one does the similar exercise for 30 SENSEX stocks using estimated forward EPS for next year and their long term growth rates, SENSEX long term growth rate comes out to 13.72 %.

**Terminal growth rate**This is determined by the risk free rate or GDP growth rate in the terminal period. Indian 10 year yield on Sep 30, 2009 is 7% and the country holds a BBB- Moody’s credit rating, resulting in country risk premium of ~3.5%. This results in Indian risk free rate of 7-3.5=3.5%, or the terminal growth rate of 3.5%.

**Return on Equity for next 10 years**We calculate ROE of SENSEX for last 5 years and use the maximum ROE in the last 5 years as an estimate of ROE for the next 10 years. The max ROE for SENSEX is 23.06% in 2007.

ROE for SENSEX is calculated using the Book Value weighted average of ROE of index components.

2009 2008 2007 2006 2005

SENSEX-ROE (%) 18.32 20.36 23.06 22.42 21.00

**ROE in terminal period**No company can continue to maintain excess returns forever, as it will encourage competition and hence whittle away the excess returns. Similarly, Indian markets can’t continue to maintain excess returns forever, as it will encourage more FIIs to invest in India, increasing the valuations and reducing the excess returns. According to Mckinsey school of thought, terminal excess return should be zero, resulting in ROE equal to cost of equity. The SENSEX valuation will assume terminal excess return of zero, resulting in terminal ROE of 10% equal to cost of Equity.

**Cost of Equity**This is determined by the Indian risk free rate, Indian country risk premium and the equity market risk premium. India holds a BBB- Moody’s rating corresponding to 3.5% country risk premium. The Indian 10 year yield at the time is 7% and the average historical market risk premium is 5%. Because SENSEX beta is 1, the cost of equity=7+5=12%.

It is estimated that India’s Moody’s rating will improve 10 years from now, attributed to improved country’s economy. In terminal period, India’s risk premium will reduce by 200bp resulting in cost of equity of 10%.

**SENSEX forward EPS- 2010**Using analysts estimates of 30 index components, free-floating weighted average of forward EPS is calculated resulting in next year earnings of Rs. 628264.71m. (Free-floating earnings= fwd EPS*free-floating-multiplier*shares-outstanding)

**Retention ratio**Earnings are not the free cash flow because growth is driven by reinvestment. Using G=ROE*B, we can calculate the retention ratio for high growth phase and terminal growth period. Using growth rate of 13.72% and ROE of 23.06% in high growth phase, SENSEX needs to retain 60% of its earnings resulting in a payout ratio of 40%. In terminal growth phase, payout ratio is 65%.

**Intrinsic valuation of SENSEX**With future EPS, growth rates and pay-out ratio of SENSEX, we can calculate the Free-cash flow to equity generated by SENSEX. Calculating the present value of these cash flows will give us the intrinsic value of SENSEX, indicating SENSEX is overvalued by 14.10%

I couldn't get the final DCF model table in correct format so you can download it from -

**Word document**http://www.scribd.com/full/20584628?access_key=key-di0w6tj1vuu7xxhn2f6

**Excel valuation model - clock below and download as excel**http://www.scribd.com/doc/20584733/SENSEX-fundamental-valuation-model

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