CHAPTER 8 Basic Stock Valuation

Topics in Chapter Valuing preferred stock Valuing common stock Dividend growth model Free cash flow valuation model 1

Preferred Stock Hybrid security. Similar to bonds in that preferred stockholders receive a fixed dividend which must be paid before dividends can be paid on common stock. 33

Value of Preferred Stock (Dividend = $2.10; rps = 7%) V ps = Dividend r ps = $2.10 7% = $30

Different Approaches for Valuing Common Stock Dividend growth model Constant growth Nonconstant growth Free cash flow model

Value of dividend-paying stock = PV of dividends discounted at required return ^ (1 + rs)1 (1 + rs)2 (1 + rs)3 (1 + rs)∞ D1 D2 D3 D∞ + + … + Conceptually correct, but how do you find the present value of an infinite stream?

Suppose dividends are expected to grow at a constant rate, gL, forever. D1 = D0(1 + gL)1 D2 = D0(1 + gL)2 Dt = D0(1 + gL)t What is the present value of a constant growth Dt when discounted at the stock’s required return, rs?

Constant Dividend Growth Model (gL<rs) If gL is constant and less than rs, then P 0 = D 1 r s − g L = D 0 1+ g L r s − g L

Estimated Intrinsic Stock Value: D0 = $2.00, rs = 13%, gL = 6% D1 = D0(1+gL) D1 = $2.00(1.06) = $2.12 P 0 = D 0 1+ g L r s − g L = D 1 r s − g L P 0 = $2.12 0.13−0.06 = $30.29

Expected Stock Price in 1 Year In general: P t = D t+1 r s − g L D2 = D1(1+gL) D1 = $2.12(1.06) = $2.2472 P 1 = D 2 r s − g L P 0 = $2.2472 0.13−0.06 = $32.10

Expected Dividend Yield and Capital Gains Yield $2.12 $30.29 D1 P0 CG Yield = = P1 – P0 ^ $32.10 – $30.29 = 6.0%. 14

Total Return at Year 1 Total return = Dividend yield + Capital gains yield. Total return = 7% + 6% = 13%. Total return = 13% = rs. For constant growth stock: Capital gains yield = 6% = gL.

Rearrange model to rate of return form Then, rs = $2.12/$30.29 + 0.06 = 0.07 + 0.06 = 13%. ^ P0 = D1 rs – g to P0 rs = + g.

Nonconstant Growth Stock Nonconstant growth of 30% for Year 0 to Year 1, 25% for Year 1 to Year 2, 15% for Year 2 to Year 3, and then long-run constant gL = 6%. Can no longer use constant growth model. However, growth becomes constant after 3 years. 17

Example of Estimating Current Stock Value (D0 = $2.00, rs = 13%) gL = 6% Year 1 2 3 4 Dividends D0(1+g0,1) ↓ $2.600 D1(1+g1,2) $3.250 D2(1+g2,3) $3.7375   $2.301 ← $2.600/(1+rs)1 PVs of divs. $2.545 ← $3.250/(1+rs)2 $2.590 ← $3.7375/(1+rs)3 $39.224 $56.596/(1+rs)3 ← $46.661

The Free Cash Flow Valuation Model: FCF and WACC Free cash flow (FCF) is: The cash flow available for distribution to all of a company’s investors. Generated by a company’s operations. The weighted average cost of capital (WACC)

Sources of Corporate Value Value of operations Nonoperating assets Short-term investments and other marketable securities Ownership of non-controlling interest in another company

Claims on Corporate Value Debtholders have first claim. Preferred stockholders have the next claim. Any remaining value belongs to common stockholders.

Estimated Intrinsic Value of Equity (VEquity) Voperations + ST Inv. + Ownership in other co. VTotal −Debt − Preferred Stk. VEquity

Value of Operations (Vop) The PV of expected future FCF, discounted at the WACC, is the value of a company’s operations (Vop): Vop = Σ ∞ t = 1 FCFt (1 + WACC)t

Value of Operations (Vop) V op = FCF 1 (1+WACC) 1 + FCF 2 (1+WACC) 2 + FCF 3 (1+WACC) 3 +…+ FCF ∞ (1+WACC) ∞ Conceptually correct, but how do you find the present value of an infinite stream?

Suppose FCFs are expected to grow at a constant rate, gL, starting at t=1, and continue forever. FCF2 = FCF1(1 + gL)1 FCF3 = FCF1(1 + gL)2 FCFt = FCF1(1 + gL)t-1

Constant Growth Formula for Value of Operations If FCF are expected to grow at a constant rate of gL from Time 1 and afterwards, and gL<WACC: Vop,0 = FCF1 (WACC - gL)

Constant Growth Formula for Value of Operations Vop,0 = FCF0 (1+gL) (WACC - gL)

Data for FCF Valuation FCF0 = $24 million WACC = 11% FCF is expected to grow at a constant rate of gL = 5% Short-term investments = $100 million Debt = $200 million Preferred stock = $50 million Number of shares =n = 10 million

Find Value of Operations Vop = FCF0 (1 + gL) (WACC - gL) $24(1+0.05) (0.11 – 0.05) = $420

Total Value of Company (VTotal) Voperations $420.00 + ST Inv. 100.00 VTotal $520.00

Intrinsic Value of Equity (VEquity) Voperations $420.00 + ST Inv. 100.00 VTotal $520.00 −Debt 200.00 − Preferred Stk. 50.00 VEquity $270.00

Intrinsic Stock Price per Share, P 0 Voperations $420.00 + ST Inv. 100.00 VTotal $520.00 −Debt 200.00 − Preferred Stk. 50.00 VEquity $270.00 ÷ n 10 P 0 $27.00

Expansion Plan: Nonconstant Growth Finance expansion financed by owners. Projected free cash flows (FCF): Year 1 FCF = −$10 million. Year 2 FCF = $20 million. Year 3 FCF = $35 million FCF grows at constant rate of 5% after year 3. No change in WACC, marketable securities, debt, preferred stock, or number of shares of stock.

Estimating the Value of Operations Free cash flows are forecast for three years in this example, so the forecast horizon is three years. Growth in free cash flows is not constant during the forecast, so we can’t use the constant growth formula to find the value of operations at time 0.

Time Line of FCF Year 1 2 3 4 5 … t FCF   −$10 $20 $35 FCF3(1+gL) FCF4(1+gL) FCFt(1+gL) Growth is constant after the horizon (Year 3), so we can modify the constant growth formula to find the value of all free cash flows beyond the horizon, discounted back to the horizon. This is called the “horizon” value.

Vop at time t = HV = FCFt(1+g) (WACC - g) Horizon Value Year 1 2 3 4 5 … t FCF   FCF3(1+gL) FCF4(1+gL) FCFt(1+gL) HV3 ←↵ Horizon value is also called terminal value, or continuing value. Vop at time t = FCFt(1+g) (WACC - g) HV =

Horizon Value Application (FCF3 = $35, WACC = 11%, gL = 5%) HV3 = Vop,3 = FCF3(1+g) (WACC - g) HV3 = $35(1+0.05) (0.11 – 0.05) =$612.50 This is the value of FCF from Year 4 and beyond discounted back to Year 3.

Current Value of Operations gL = 5% Year 1 2 3 4 FCF −$10 $20 $35   ↓ FCF 4 WACC− g L −$9.009 ← −$10/(1+WACC)1 PVs of FCF $16.232 ← $20/(1+WACC)2 FCF 3 (1+ g L ) WACC− g L $25.592 ← $35/(1+WACC)3 PV of Vop,3 $447.855 $612.5/(1+WACC)3 ← Vop,3= $612.5 ← $36.75 0.06    Vop = $480.67

Intrinsic Stock Price, P 0 Voperations $480.67 + ST Inv. 100.00 VTotal $580.67 −Debt 200.00 − Preferred Stk. 50.00 VEquity $330.67 ÷ n 10 P 0 $33.07

Comparing the FCF Model and Dividend Growth Model Can apply FCF model in more situations: Privately held companies Divisions of companies Companies that pay zero (or very low) dividends FCF model requires forecasted financial statements to estimate FCF

ROIC vs. WACC If ROIC<WACC/(1+g), then operation value will be less than the investment in total net operating capital (NOWC+net PP&E) If ROIC<WACC/((1+WACC), the any growth makes the company less valuable.

Assignment Review slides of chapter 9 in FINC3131. Chapter 8 problems: 1,2,4,6,7,17,18.