Quiz 3 dividend discount models to value stocks

Multi stage growth models, and different life cycles of dividends

Dividend is $3.00 for the next 3 years (0 growth), and then it will grow to 5% thereafter. K= 13.6% Po= 3 / 1.136 + 3 / (1.136)^2 + 3 / (1.136)^3 + 3 (1.05) / (.136 - .05) / (1.136) ^3 see how after the third year, changes the equation to reflect the growth to 5% but still making sure it shows that it happens after the 3rd year.

Expected holding period return,(HPR)

E(r)= D1 +[E(P1) - P0] / P0 expected return = expected dividend + (Last - beginning price on purchase of stock) / beginning price. Example: =$4 + (52 - 48) / 48 = 16.7% return

Present value of growth opportunities PVGO

Grott Perrin expects earnings of $3 per share next year. ROE=.20, b= .70 therefore Div p=.30, k = .15, what is the present value of its growth opportunities? g=.20 x .70 = .14 No growth present value= 3 / .15= $20 Constant growth = 3 ( 1- .70 ) / (.15 - .14) = $90 that was earnings * (dividend payout ratio) / (k - g) PVGO= $90 - $20= $70

Example of constant growth DDM

High flyer just paid its annual dividend of $3 per share. the dividend is expected to grow at 8% indefinitely. The beta for the stock is 1. The risk free rate is 6%. and the market risk premium is 8%. what is the intrinsic value of the stock? what about a beta of 1.25? (it must be wrong because .08 -.06 =.02) ANSWER: because a $3 dividend was just paid and the growth rate is 8%, the forecast for the year end dividend is $3 x 1.08 = $3.24. The market capitalization is .06 + 1.0 ( .08) = .14. therefore the value of the stock is: Vo= $3.24 / (.14 - .08) = $54 If the value is perceived to be riskier (higher beta of 1.25) its value must be lower. market capitalization: .06 + 1.25 (.08) = .16, so the stock is worth: Vo= $3.24/ (.16 - .08) = $40.25

P/E ratio: multiples of companies where growth, risk of stock, shareholders earnings, and dividends are counted to come out with a multiple of how much a company it's worth in the future. high P/E means a company is a high growth opportunity. but books could be cooked.

It refers to multistage dividend discount model with EPS

No GROWTH: (preferred stock per example)

Po= D1 / K (simplified). Vo= $2 / (.08 - 0) = $25

Intrinsic value

Vo= (D1) + E (P1) / 1 + K (required return) =$4 + $52 / 1 + 0.12 = $50, where D1 is expected dividend 1 (in a year), E (P1) is the price of the stock in a year(projected), and K is the market capitalization or expected return.

Dividend discount model equation: states the stock price should equal the present value of all expected future dividends into perpetuity. ignores capital gains. Horizon value

Vo= D1 / (1 + K) + D2 / (1 + K)^2 + D3 / (1 + K)^3..... last D + final P / (1 + K)^ last period we use dividend discount models where Vo= value of stock. D1= dividend year 1. D2=dividend year 2. and so on. h= the year the stock is sold. Ph= sell price of stock in year h. K= required return.

Dividend discount model Horizon value (basic equation)

Vo= D1 / 1 + K, where Vo= value of stock, D1 expected dividend in a year, K required return or market return (minimum)

The constant growth Dividend Discount model: dividends are expected to grow in payments giving a future price of the stock today. The Gordon model, terminal value.

Vo= Do (1+ g) / (1+K) + Do (1 + g) ^2 / (1 + K) ^2... simplified to = D1 / (K - g). D1= expected dividend, K= market return, g= growth rate on dividend. example : $4 / .12 - .05 = $57.15

dividend discount models are used as

a fundamental way to know the book value of companies so we as investors can make a "reasoned" investment decision given from financial information available, by searching mis priced stocks with opportunities for growth to make a return on our money. These were used by stock analysts when computers were not around, and it is the base for fundamentals for valuation of stocks. We use dividend discount models where definitions are Vo= value of stock. D1= dividend year 1. D2=dividend year 2. and so on. n= the year the stock is sold. Pn= sell price of stock in year n. K= required return. CAPM= capital asset pricing model, where we use beta of the stock, market return Rm, and the Risk free rate Rfr. CAPM is referred to the cost of equity or what the investor expects to earn on a security measured by beta (volatility). CAPM= Rf+ B (Rm-Rf)

Another example of constant growth best one

dividend $3.00 dividend is expected to grow at 5% every year Beta: 1.2 Return on market: 12% Risk free rate: 4% Discount rate: .04 + 1.2 (.12 -.04) = .136, then it's plugged in on constant growth equation: $3.00 (1.05) / .136 - .05 = $36.63

Determine g (growth)

g = ROE x plowback ratio or retention on earnings percentage. ROE is usually given, plowback ratio is found in b or by subtracting dividends out of earnings, so we know how much the company retains (b). per example: earnings 5 million and dividends are 3 million 3/5= 60% in dividends, so they retained 40%, that is b. ROE=20%, b= 40% g= .20 x .40 = 8% growth