Finance Essentials: Present Value (“PV”) Equity Valuation's Concepts and Basic Tools

The ability to benefit from identifying on a mispriced equity depends on the market price converging to the estimated intrinsic value. If estimated value is greater than market price, then the equity is perceived to be overvalued.  If estimated value is less than market price, then the equity is perceived to be undervalued. If estimated value equals market price, then the equity is perceived to be fairly valued. 

Overview
In PV models, benefits are defined in terms of cash expected to be distributed, such as dividend discount models (“DDM”) or cash flows available after CAPEX and working capital needs (FCFE models). This analysis requires significant historical data and reasonable assumptions to be meaningful. In practice, individuals prefer to use a FCFE valuation model as it is a measure for dividend paying capacity and may also be used for non-paying dividend stocks. DDM specifies cash flows from a common stock investment to be dividends. The terminal stock value is the expected value of a share at the end of the investment horizon. Note callability on preferred shares slightly decreases intrinsic values.

The Many Assumptions of the Gordon Growth Model
· Dividends are the correct metric to use for valuation purposes,
· Growth rate is forever
· Constant required rate of return over time
· Growth rate is strictly less than the required rate of return

Alternatives to the “Many Assumptions”
· More robust DDM that allows for varying patterns of growth
· Use a cash flow measure other than dividends 
· Other approach like multi-stage DDM Models: For instance, two stage DDM makes use of two growth rates of (i) a high growth rate for an initial finite period and (ii) followed by a lower sustainable growth period for perpetuity.  It can be extended to as many stages deemed appropriate. For instance, we may assume growth for publically traded companies will ultimately fall into three stages (growth, transition, and maturity) where there would different finite growth periods for the first two stages followed by a slower perpetuity growth phase for the last stage.

PV Models Formulas
· Dividend Discount Model: Vo = ∑ (Dt/(1+r)t) + (Pn/(1+r)n); 
Variables: Dt = Dividend at time t, Pn = expected price at time n, and n  in this case would be the last year of the analysis. 
· FCFE Discount Model: Vo = ∑ (FCFEt/(1+r)t)
Variables: FCFE is Free Cash Flow to Equity
· Capital Asset Pricing Model (CAPM): rf + β(rm-rf)
Variables: rf = risk free rate, rm = market return, rm-rf = market risk premium, β = beta. 
·  g = b * ROE
Variables: b = earnings retention rate = 1 – Dividend Payout Ratio
· Gordon Growth Model: Vo = ∑ Do (1+g)t/ (1+r)t or Vo = D1/r-g 
Variables: As D1= Do (1+g); where g = dividend growth rate, Do = current paying dividends, D1 = dividends the first period.  Do note that D2 could equal either (i) D1(1+g) or Do(1+g)2.
· Two-stage DDM: Vo = ∑ Do (1+gS)t/ (1+r)t + Vn/(1+r)n 
Variables: Vn = Dn+1/r -gL; Dn+1 = Do(1+gS)n(1+gL); where gS = short term growth rate, gL = long term growth rate. 
· Preferred Stock paying a level dividend at a constant required rate of return: Vo = Do/r