Final Exam-Equity Valuation Part 1-4
Gordon Growth Model (2)
assumptions: 1. dividends are approp measure of shareholder wealth 2. constant dividend growth rate, g, and required return on stock, k are never expected to change 3. k must be greater than g. If not, math will not work
Company X is expected to have EPS in the upcoming year of $6. The expected ROE is 16%. An appropriate required return on the stock is 14%. If the firm has a plowback ratio of 60%, calculate its dividend in the upcoming year.
b = 1-60% = 40%
approaches to valuation
discounted cash flow models (or present value models) 2. multiplier models (or mkt multiple models) 3. Asset-based models
Stock Price-Implied Growth Rate
for stk w/mkt value = intrinsic value g = P1/P0 - 1 -therefore DDM implies that in case of constant expected growth of dividends, expected rate of price appreciation in any yr will equal that constant growth rate, g
Estimate Growth Rate in Dividends (3)
g = ROE x b ROE = return on investment or equity b = plowback ratio or earnings retention ratio = 1-dividend payout ratio
Green, Inc., is expected to pay dividends equal to 25% of earnings. Green's ROE is 21%. Calculate and interpret its sustainable growth rate.
g = ROE x b b = 1-25% = 75% g = 21% (1-25%) = 15.75%
Question 2 Consider a stk w/dividends that are expected to grow at 20% per yr for four yrs, after which they are expected to grow at 5% per yr, indefinitely. The last dividend paid was $1.00, and k=10%. Calculate the value of this stk using the multistage growth model
g1=20% g=5% D0=1 D1=1(1.2) =1.2 D2 =1.2(1.2) = 1.44 D3=1.44(1.2)=1.728 D4=1.728(1.2)=2.0736 D5=P=(2.17728/.05) = 43.5456 V4=D5/(k-g) = 2.17/(.10-.05) =$43.40
Estimate Next Period Dividend
if dividend just paid D0 is given, the expected dividend in the next period can be calculated as: D1 = D0 (1+g) the analyst can also be estimated as: D1 = E1 (1-b) E1=expected earnings per share in next period b = plowback ratio or earnings retention ratio = 1-dividend payout ratio
Market Capitalization Rate (k)
market-consensus estimate of appropriate discount rate for firm's cash flows
Free Cash Flow Models
models used to value a firm's stk by forecasting free cash flow to the firm (FCFF) or free cash flow to equity (FCFE) and discounting these cash flows back to present at approp required rate of return
Residual Income Models
residual income is the amt of earnings during the period that exceeds the investors' required return
One-Period DDM
simple case: -buy share of stock today -plan to sell in one yr -stock pays $10 dividend at year end -stk will be worth $70 at that time -require 25% return on invstmt How much is stock worth today?
Constant Growth DDM (2)
so V0 = (D1/(k-g)) -this is constant growth DDM -constant growth DDM is also called gordon growth model or infinite period DDM
FCFF
the cash available to all of the firm's investors, including stockholders and bondholders, after the firm buys and sells products, provides services, pays its cash operating expenses, and makes short-and long-term invtment
FCFE
the cash available to common shareholders after funding capital requirements, working capital needs, and debt financing requirements
Zero Growth DDM...So
the formula for multiple period DDM eventually becomes D/k similar to value of a perpetuity this is preferred stk valuation model
1. dividend discount model (DDM)
the intrinsic value of stock is the present value of its future dividends V0 = sum of (Dt)/(1+k)^t V0= current stk rate Dt = dividend at time t k = required return rate
Valuation
the process of estimating the value of an asset by 1. using a model based on the variables the analyst believes influence the fundamental value of the asset 2. comparing it to the observable mkt value of "similar" assets
Price Multipliers
the ratio of stock price to such fundamentals as earnings, sales, book value, or cash flow per share
Estimate Growth Rate in Dividends (1)
to estimate growth rate in dividends, analyst can use three methods: 1. use historical growth in dividends for firm 2. use median industry dividend growth rate 3. estimate sustainable growth rate
Question 4 The free cash flow to the firm is $250 million in perpetuity, the cost of equity equals 14%, and the WACC is 10%. If the mkt value of the debt is %0.5 billion, what is the value of the equity using the free cash flow valuation approach?
value of firm = FCFF1/(WACC-g) = (250/10%) =$2.5 billion value of equity = $2.5 billion - .5 billion = $2 billion
Limitations of Gordon Growth Model
-valuations are vary sensitive to estimates of growth rates and required rates of return, both of which are difficult to estimate w/precision -model cannot be easily appliesd to non-dividend-paying stks -unpredictable growth patterns of some firms would make using hte model difficult and the resulting valuations unreliable.
Equity Valuation Part 3
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Equity Valuation Part 4
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Equity Valuation Part II
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Factors in Discounted Cash Flow Models
NPV plays essential roll 1. cash flows 2. invtmt horizons 3. mkt required returns (discount rate)
Steps in Equity Valuation Process
-understand business -forecast company performance -select appropriate valuation model -convert forecasts into valuation -apply valuation conclusions
1. Discounted Cash Flow Models (or present value models)
-Dividend Discount Models -Free Cash Flow to equity models -Residual income models
Gordon Growth Model vs Multistage Growth Models
-GGM is most approp for valuing stable and mature, non-cyclical, dividend-paying firms -Multistage DGM can be applied: -->to firm w/high current growth that will drop to stable rate in future -->to firm that is temporarily losing mkt share and growing slowly or getting smaller, as long as its growth is expected to stabilize to a constant rate at some point in future
2. Multiplier Models (or mkt multiple models)
-Price Multipliers -Enterprise value multipliers
Life Cycles and Multistage Growth Models
-Two-stage DDM -Multistage Growth Models
Multistage Growth Models
-allow dividends per share to grow at several different rates as firm matures V0 = D1/(1+k) + D2/(1+k)^2...+Dn/(1+k)^n + Pn/(1+k)^n =where Pn = (D(n+1))/(k-g) is the terminal stk value, assuming that dividends at t=n+1 and beyond grow at a constant rate of g
Estimate Cost of Equity
-analyst can use CAPM to estimate RRoR by shareholders for investing in stk (cost of equity) E(ri) = rf+B[E)rm)-rf] -Beta can be estimated as slope of linear regression of excess return of stk on excess returns on mkt -beta can also be Bi = (Cov(Rm,Rf)/(VarRm) = σmi/σm^2
Applications of Gordon Growth Model
-applicable to value stable, mature, dividend paying firms -approp for valuing mkt indices -easily communicated and explained bc of straightforward approach -used to determine price implied growth rates, required rates of return, and value of growth opportunities -can be used to suppliment other, more complex valuation methods
3. Problems with DDM
-companies that do not pay dividends -no clear relationship bet. dividends and profitability
4. DDM is suitable when
-company is dividend paying -board of directors has a dividend policy that has an understandable relationship to profitability -investor has a non-control perspective
Stock Price-Implied Required Rate of Return
-for stk w/mkt price = intrinsic value (V0 = P0) expected holding period return -E(r) = dividend yeild + capital gains yeild = k k = D1/P0 +g -this equation is also known as the discounted cash flow (DCF) formula
Gordon Growth Model w/ Historical Data
-get data from internet -estimate exp growth rate in dividends -estimate exp dividends in next period -estimate cost of equity -equity valuation using GGM
3. Asset-Based Models
-intrinsic value of comm stk is est as total asset value minus liabilities and pref stk -analysts typically adjust the book values of the firm's assets and liabilities to their fair values when est the mkt value of its equity w/ an asset-based model
Why use Free Cash Flow Models (instead of dividend-based valuation)
-many firms pay no, or low, cash dividends -dividends are paid at discretion of board of directors -if a company is viewed as acquisition target, free cash flow is more approp measure -free cash flows may be more related to long-run profitability of the firm as compared to dividends
Absolute Valuation Models
-model that est an asset's intrinsic value, (its value arising from its invtmt characteristics) w/o regard to the value of other firms -discounted cash flow models -asset-based models
Multiple Period DDM comments
-no matter what the stk price is, the present value is ESSENTIALLY zero, if we push the sale of the stock far enough away? -therefore, what we EVENTUALLY are left with is a series of dividend payments? SO V0 = (D1/(1+k)^1)) + (D2/(1+k)^2)) + (D3/(1+k)^3))...
Stock Prices and Investment Opportunities
-present value of growth opportunities (PVGO) -price = no-growth value per share +PVGO P0 = (E1/k) +PVGO
Intrinsic Value (aka Fundamental Value)
-rational value investors would place on the asset if they had full knowledge of the asset's characteristics -difference between analyst's estimate of intrinsic value and the current mkt price: IVanalyst - Price = (IVactual - Price) + (IVanalyst-IVactual)
Applications of Equity Valuation
-stock selection -reading the mkt -projecting value of corporate actions -fairness opinions -planning/consulting -comm w/analysts and investors -valuation of private business -portfolio mgmt
Enterprise Value Multipliers
-the ratio of enterprise value to either earnings before interest, taxes, depreciation, and amortization (EBITDA) or revenue -enterprise value is the mkt value of all a firm's outstanding securities minus cash and short-term investments
Relative Valuation Model
-to determine the value of an asset in relation to the values of other assets -multiplier models
A firm currently pays no dividend but is expected to pay a dividend at the end of year 4. year 4 earnings are expected to be $1.64, and the firm will maintain a payout ratio of 45%. Assuming a constant growth rate of 5% and a required rate of return of 10%, estimate the current value of this stock.
1. D4 = E4(1-b) = $1.64(.45) = $0.738 V4 = D5/k-g = .738(1+.05)/(.10-.05) = $15.498 V0 = D4/(1+k)^4) + V4/(1+k)^4) =.738/(1+.10)^4 + 15.498/(1+.10)^4 =11.09
Basics of Dividend Discount Models
1. dividend discount model (DDM) 2. DDM defines cash flows as DIVIDENDS 3. Problems with DDM 4. DDM is suitable when
Steps in Using Multistage Model
1.determine discount rate, k 2. project size and duration of high initial dividend growth rate, g1. 3. estimate constant growth rate at end of high-growth period, g 4. estimate dividends during high-growth period 5. estimate first dividend that will grow at the constant rate 6. use the constant growth value to calculate stk value at end of high-growth period 7. add PVs of all dividends to the PV of terminal value of stk
A firm currently pays no dividend but is expected to pay a dividend at the end of year 4. year 4 earnings are expected to be $1.64, and the firm will maintain a payout ratio of 45%. Assuming a constant growth rate of 5% and a required rate of return of 10%, estimate the current value of this stock. second way to do it
2. V3 = D4/(k-g) = $.738/(.10-.05) = $14.76 V0 = 14.76/(1.10)^3 = $11.09
Criteria for choosing valuation approaches
Consider whether the model: -fits characteristics of company -approp based on quality and availability of input data -suitable given the purpose of analysis -Note: using multiplier models and examining differences in estimated values can reveal how a model's assumptions and the perspective of the analysis are affecting the estimated values
Calculate the value of a stock that paid a $2 dividend last year, if dividends are expected to grow at 5% forever and the required return on equity is 12%.
D1 = $2(1.05) = $2.10 V0 = $2.10/(.12-.05) = (2.10)/.07 = $30.00 D0 = just paid, paid recently last year D1 = will pay, ie expect to pay
Two-Stage DDM
DDM in which dividend growth assumed to level off only at future date
Question 5 The free cash flow to the firm is reported as $200 million. The interest expense to the firm is $20 million. If the tax rate is 35% and the net debt of the firm increased by $30 million, what is the approximate mkt value of equity if the FCFE grows at 2% and the cost of equity is 10%?
FCFE = $200-20(1-.35) + 30 = $217 million Value of equity = [217(1+.02)]/(.10-.02) = $2.766 billion
FCFF and FCFE
FCFE = FCFF -Int(1-tax rate) + net borrwing Int = interest expense net borrowing = long and short term new debt issues - long and short term debt repayments
Question 3 The free cash flow to the firm is reported as $400 million. The interest expense to the firm is $70 million. If the tax rate is 35% and the net debt of the firm increased by $40 million, what is the free cash flow to the equity holders of the firm?
FCFE = FCFF -Int(1-tax rate) + net borrwing = $400-$70(1-.35) +40 = $394.5 million
When to use Free Cash Flow Models
FCFF or FCFE when: 1. firm doesn't pay dividends at all or pays out fewer dividends than dictated by its cash flow 2. free cash flow tracks profitability or 3. the analyst takes a corporate control perspective
Company has expected earnings of $4.2 per share for next yr. The firm's ROE is 20%, and its earnings retention ratio is 60%. If the firm's mkt cap rate is 14%, what is the present value of its growth opportunities?
P0 = D1/(k-g) = E1(1-b)/(k-ROExb) = $4.21(1-16%)/[14%-20%(16%)] =$84 V0 = P0 = E1/k +PVGO PVGO = P0-E1/K =$84-$30 =$54
Price Multiples
Price multiples used for valuation include: →Price-earnings (P/E) ratio →Price-sales (P/S) ratio →Price-book value (P/B) ratio →Price-cash flow (P/CF) ratio
Free Cash flow
Starts with Cash Revenues ↓ inventory (working capital invstmt), PP&E (fixed capital invstmt), Salaries (Cash operating expenses (including taxes, but not interest expense) ↓ FCFF (to shareholders and bondholders) ↓ FCFE, to shareholders, interest pmts to Bondholders
Question 1 What would the expected price today be, if g=25% for 2 yrs before achieving long-run growth of 7%? Assume last dividend was $1.60 and required rate of return is 12%. Step 1
Step 1: Calculate dividends at end of each yr for first 2+1 yrs D1 = D0(1+g) = 1.60(1+25% = $2.00 D2 = D1(1+g) =2.00(1+.25) = $2.50 D3 = D2(1+g) =2.50(1+.07) =$2.675
Question 1 What would the expected price today be, if g=25% for 2 yrs before achieving long-run growth of 7%? Assume last dividend was $1.60 and required rate of return is 12%. Step 2
Step 2: Calculate stk value at end of yr 2 using GGM V2 = D3/(k-g) = (2.675)/(.12-.07) = $53.50
Question 1 What would the expected price today be, if g=25% for 2 yrs before achieving long-run growth of 7%? Assume last dividend was $1.60 and required rate of return is 12%. Step 3
Step 3: Find total PVs of dividends at end of yr 1 and yr 2 and stk value at end of yr 2 V0 = D1/(1+k) + D2/(1+k)^2 + V2/(1+k)^2 =2.00/(1+.12) + 2.50/(1+.12)^2 +53.5/(1+.12)^2 =$46.43
Estimate Growth Rate in Dividends (2)
Sustainable Growth Rate -rate at which equity, earnings, and dividends can continue to grow indefinitely assuming that ROE is constant, the dividend payout ratio is constant, and no new equity is sold
Constant Growth DDM (1)
assume the dividend grows at a steady rate, g. Let D0 be the dividend just paid, then: D1 = D0(1+g) D2 = D1(1+g) = D0(1+g)(1+g) = D0(1+g)^2 Dt = D0(1+g)^t
A company's $100 par preferred stk pays a $5.00 annual dividend and has a required return of 8%. Calculate the value of the preferred stock.
V0 = (5/.08) = $62.50
Multiple Period DDM
V0 = (D1 + P1) / (1+k) P1 = (D2 + P2) / (1+k) V0 = (D1/(1+k)) + (d2/(1+k)^2) + P2/(1+k)^2)
Gordon Growth DDM (1)
V0 = (D1)/(k-g) D1 is exp dividend in next period g is expected growth in dividends k is cost of equity. this is required rate of return required by shareholders for investing in the stock
Question 2 Consider a stk w/dividends that are expected to grow at 20% per yr for four yrs, after which they are expected to grow at 5% per yr, indefinitely. The last dividend paid was $1.00, and k=10%. Calculate the value of this stk using the multistage growth model Part 2
V0=(1.2/1.1)(1.44/1.12)(1.728/1.12)(2.0736/1.14)(43.5456/1.15) = $35.74
Zero Growth DDM
We assume D1 = D2 = D3...=D = constant
2. DDM defines cash flows as DIVIDENDS
an investor who buys and holds a share of stock receives cash flows only in the form of dividends
Price-book value (P/B) ratio
a firm's stock price divided by book value of equity per share
Price-cash flow (P/CF) ratio
a firm's stock price divided by cash flow per share, where cash flow may be defined as operating cash flow or free cash flow
Price-sales (P/S) ratio
a firm's stock price divided by sales per share
Price-earnings (P/E) ratio
a firm's stock price dividend by earnings per share and is widely used to by analysts and cited in the press
Dividend Discount Models
a stock's value is estimated as the present value of cash distributed to shareholders
Free Cash Flow to Equity Models
a stock's value is the present value of cash available to shareholders after the firm meets its necessary capital expenditures and working capital expenses
FCFF Constant Growth Model
→ single-stage constant-growth FCFF model Value of Firm = FCFF1/(WACC-g) = FCFF1(1+g)/(WACC-g) FCFF1 = exp Free cash flow to firm in 1 yr FCFF0 = starting level of FCFF g = constant expected growth rate in FCFF WACC = weighted average cost of capital Equity Value = value of firm-mkt value of debt
Why use P/E ratio
→earnings power, as measured by earnings per share (EPS), is the primary determinant of invstmt value →the P/E ratio is popular in the invstmt community →empirical research shows that P/E differences are significantly related to long-run average stock returns
FCFE Constant Growth Model
→single-stage constant-growth FCFE valuation model Value of equity = FCFE1/(k-g) = FCFE0(1+g)/(k-g) FCFE1 = exp free cash flow to equity in 1 yr FCFE0 = starting level of FCFE g = constant expected growth rate in FCFE k = required rate of return on equity
