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7.22 Verifying the Calculations for Intrinsic Value

In the above grid the red numbers are the estimated inputs, expressed on a per share basis, into the 2-Stage FCFE valuation model.  That is, FCFE 10.395 which was computed from cash flow from operations, adjusted CAPEX and the estimated debt ratio as described earlier.   The stage 1growth was 0.10, normal growth 0.045 and cost of equity capital 0.084.  The two stage growth model computes the intrinsic value as the PV of future economic dividends (i.e., FCFE) that the stock is assessed to generate.

Stage 1 covers 2010, 2011, … , 2014.  The FCFE for 2010 is 10.395*1.10, 2011 = 10.395*1.10^2 and so on.  Alternatively this can be computed from the projected growth in cash flows from operations, projected CAPEX, and the assessed debt ratio.  Thus for 2010 11.434 = 15.503 – 5.347 + 0.239*5.347 (FCFE = FCFF + Debt Ratio*CAPEX).  The projected 2010 cash flow from operations is 14.094*1.10 = 15.503 and similarly for CAPEX.

Present Value of FCFE Stage 1

The PV FCFE for Stage 1 equals the sum of FCFE2010/(1.0837)+ FCFE2010/(1.0837^2) + FCFE2010/(1.0837^3) + FCFE2010/(1.0837^4) + FCFE2010/(1.0837^5 ) = $54.36

Present Value of FCFE Stage 2 (Going Concern)

IBM is presumed to be a going concern in this exercise.  As a result, at the end of the Stage 1 IBM’s FCFE is assumed to grow in perpetuity at the constant normal growth rate (0.045).  As a result, at the end of 2014 IBM’s stock price is assumed to be computed from Gordon’s constant growth model.

Terminal Price2014  = 16.740*1.045/(0.0837 – 0.045) = 452

PV Continuing Value = 452.036/(1.0837^5) = $302

Important Note:  The majority of the intrinsic value of a stock comes from the PV of continuing value.  In other words events impacting the stock beyond the stage 1 growth phase of the stock and which is well beyond any reasonable estimate for a recession to last.  The actual stock market would appear to be much more myopically focused such that the events from the labor figures released to the market Friday June 4, 2010 for the month of May triggered a large market response. 

Intrinsic Value for IBM

Intrinsic Value = PV FCFE Stage 1 + PV Continuing Value (Stage 2) = 54 + 302 = $356

As an immediate comment this spot price prediction is well above the current market value for IBM.  From the above analysis one could question whether the projection of $452 is realistic for the end of 2014!  In other words the normal growth assumption in perpetuity of 0.045 appears to be much higher than what is implied in the market for IBM now.  As a result, in sensitivity analysis we will reduce normal growth as one of the variables to assess the impact of this on IBM’s assessed intrinsic value.

Decomposing the Intrinsic Value of IBM Further

Consider the following re-arrangement of IBM’s assessed intrinsic value:

In the above arrangement we have broken up intrinsic value into three major components:

PV of FCFE2010 in perpetuity assuming zero growth = $136.606

PV FCFE Stage 1 in Excess of FCFE2010 = $9.155

PV Continuing Value beyond Stage 1 in Excess of the zero growth FCFE perpetuity = $211.036

The sum of the above two PV’s = $356.797

What this illustrates that if the assessed FCFE is correct and the cost of equity capital is reasonable then IBM is being currently priced below is zero growth perpetuity value.