Is the curent market cheap? Part II – what does DCF model tell us.

Is the current market cheap or expensive? Let us use two stage growth Discount Cash Flow (DCF) model to calculate the intrinsic value of SP500 in order to answer this question.

On December 2^nd, 2001, the price of S&P 500 index was 1244.28. The dividend yield on the index was 1.84% (based on div yield of 06/30/2011 data). By including stock buybacks, the modified dividend yield will increase to 1.84% + 3.04%= 4.88%. Historical S&P 500 Dividend and buyback data can be found at: SP500-buyback-09202011 or through SP500 web site.

The earnings growth of SP500 from 1988 to 2011 is 7.63% (arithmetic average), or 5.96% (linear extrapolation growth rate), or 6.20% (log linear extrapolation growth rate). To be conservative, we adopt 5.96% growth rate as today’s average growth rate. The earnings growth rates of SP500 Historical are calculated from historical earnings of SP500 data which can be found at: SP500EPSEST-11222011 or through SP500 web site.

By using two-stage growth Discount Cash Flow (DCF) model, we assume the index would increase 5.96% for the next 5 years (high growth rate stage). Afar 5 years, the expected growth rate is assumed to be 5%, the nominal growth rate in the economy (=GDP growth rate ~2% + inflation rate ~3%).

The 30 year treasury bond rate was 4.37% and we adopt a market risk premium of 4%, leading to a cost of equity of 8.37%. i.e. Cost of equity = 4.37% + 4% = 8.37%. The current treasury bond rates can be found at here.

The expected modified dividends (dividend plus stock buybacks) on the index for the next 5 years can be estimated from the current dividends and expected growth of 5.96%.

Current dividends plus buybacks = 4.88% of 1244.28 = 60.72, Expected modified dividends for the next 5 years are

Year 1: =60.72*(1+5.96%)^1= $64.34

Year 2: =60.72*(1+5.96%)^2 = $68.17

Year 3: =60.72*(1+5.96%)^3= $72.24

Year 4: =60.72*(1+5.96%)^4 = $76.54

Year 5: =60.72*(1+5.96%)^5 = $81.10

The Present Value of Expected modified dividends, by discounting the expected modified dividend at 8.37%, for the next 5 years are

Year 1: =64.34/(1+4.37%+4%)^1 = $59.37

Year 2: =68.17/(1+4.37%+4%)^2 = $58.05

Year 3: =72.24/(1+4.37%+4%)^3 = $56.76

Year 4: =76.54/(1+4.37%+4%)^4 = $55.50

Year 5: =81.10/(1+4.37%+4%)^5 = $54.26

To estimate the terminal value, we estimate dividends in year 6 on the index:

Expected modified dividends in year 6 = $81.10 *(1+4.37%) = $84.64

Terminal value of the index = expected modified dividends at year 6 /(8.37%-4.37%) = $2116.00

Present value of Terminal value of the index = 2116.00/(1+8.37%)^5= $1415.81

The value of the index can now be computed: Value of index = Present value of modified dividends during high growth + Present value of terminal value = $59.37+$58.05+$56.76+$55.50+ $54.26+ $1415.81 = $1699.75. Based on this, we could have concluded that the index is underpriced at 1244.28.

To have a clearer perspective of SP500 valuation using DCF model, I will present sensitivity studies and intrinsic value comparison with historical SP500 index prices in my follow-up posts.