Discounted Dividend Valuation Flashcards
What is discounted cash flows?
- calculates intrinsic value of company’s common stock as present value of expected future cash flows
What is present value of future cash flows formula?
PV = (CF/ (1+r)^t) + (CF/ (1+r)^t)
What are 3 streams of cash flows that the discounted cash flow model can be used?
- dividends
- free cash flows
- residual income
What 3 conditions met would make it most appropriate to use dividend discount model?
- company is paying dividends.
- dividend policy is consistent with the company’s profitability.
- investor has a non-control perspective.
What are the 3 types of free cash flow methods you can use in discounted cash flow method?
- cash flow from operations (CFO): cash generated from day to day activities (eg. buying & selling products/services)
- free cash flow to firm (FCFF): cash flows available to all capital providers such as bondholders/stockholders
- free cash flow to equity (FCFE): cash flow available to shareholders only
What 4 conditions met would make it most appropriate to use free cash flow discount model?
- company is not dividend-paying.
- company pays dividends that are materially different from the FCFE.
- projected free cash flows are aligned with the company’s profitability.
- investor has a control perspective (or views the company as a likely merger target).
What 2 conditions met would make it most appropriate to use residual income discount model?
- company is not paying dividends (used as an alternative to the free cash flow model).
- company has negative expected free cash flows.
What is the formula for dividend discount model for a single period and multiple periods?
- single period: V0 = (D1 + P1/ (1+r)^1)
- multi period: V0 = (D1 / (1+r)^1) + (D2 / (1+r)^2) + (P2 / (1+r)^2)
V0 = present value
D1 = dividend in one year
P1 & P2 = selling price
r = discount rate
D2 = dividend in two years
What is the present value of a perpetually growing dividend stream that starts at a future time (aka dividend discount formula if dividends are assumed to be paid indefinitely)?
V0 = (dividend when paid/ (r-g) / (1+r)^t
V0 = present value
Dt = infinite dividend
r = discount rate
t = years or time
What does the Gordon growth model assume and what is the formula?
- assumes dividend will grow at constant rate forever
V0 = (D0 (1+g) / r - g) which is also equivalent to D1/ r - g
D0 = dividend at time 0 or now
g = growth rate
r = required rate of return
D1 = dividend in 1 year
What is share repurchase?
- when a company buys back its own shares from the market place
What is the implied dividend growth rate?
- projected growth rate of a company’s dividends.
The value of a stock is the sum of what 2 following? What is the formula?
- value of the company without earnings reinvestment
- the present value of growth opportunities (PVGO)
V0 = E1/r +PVGO
V0 = present value
E1 = earnings per share in 1 year
r = discount rate
PVGO = present value of growth opportunities (valuation that comes from expected growth rather than existing assets & operations. eg. amzn reinvest earnings into future growth opportunities, such as cloud computing, AI, etc)
E1/r = no growth value per share (aka company without positive NPV projects)
What is the formula for P/E derived from the value of a stock sum formula (present value of growth opportunities?
P0 /E1 = 1/r + PVGO/E1
P0 = present value price
E1 = earnings per share in 1 year
r = discount rate
PVGO = present value of growth opportunities
1/r = no growth component of P/E
PVGO/E1 = growth component of P/E
What is the formula for leading P/E ratio and trailing P/E ratio?
leading P/E ratio = P0/E1 = ((D1/E1) / (r-g)) = ((1-b) / (r-g))
trailing P/E ratio = P0/E0 = (D1/ E0) /r-g = ((1+g)*(1-b)) / r-g
P0 = price now or present value
E1 = earnings per share in 1 year
D1 = dividend in 1 year
r = discount rate
g = growth
b = retention rate
1-b = dividend payout ratio
E0 = earnings per share now
D0 = dividend now
What is the formula that can be derived from the Gordon growth model to get stocks required rate of return?
r = (D1/P0) +g
r = required rate of return or discount rate
D1 = dividend in 1 year
P0 = price now or present value
g = dividend growth rate
What are 3 stages that growth usually falls into, describe them.
- growth phase
- transition phase
- mature phase
What is the formula for 2 stage Gordon growth model?
V0 = ((D0 (1+gs)^t)/ (1+r)^t) + (Vn / (1+r)^n)
V0 = value now or present value
D0 = dividend now
gs = short term dividend growth rate
t = time
r = discount rate
Vn = terminal value of second stage of Gordon growth model
N = time
((D0 (1+gs)^t) = future dividend at time t (or end of short term rate before growth rate)
What is the formula for terminal value derived from 2 stage Gordon growth model?
Vn = ((D0 (1+gs)^n)* (1+gl)) / (r - gl)
Vn = terminal value
D0 = dividend now at time 0
gs = short term dividend growth rate
gl = long term dividend growth rate
r = discount rate
n = time
Vn = short term dividend total * long term dividend growth rate / r-gl
What is the formula for present value of stock for a company that doesn’t pay dividends until a later date?
V0 = D / (((1 + r)^n) * (r-g))
V0 = present value
D = dividend when they start paying dividends in the future
r = discount rate
n = years or time until they pay dividend
g = dividend growth rate
What is the difference in assumption from the 2 stages Gordon growth model and the h model?
- Gordon growth model: assumes high growth for a period then normal growth thereafter, which can result in very abrupt change in growth rate
- h model: overcomes abrupt change in growth rate by smoothing transition from short term growth rate to long term growth rate
What is the formula for h model?
V0 = (D0 (1+gl)) + ((D0*H) * (gs -gl)) / (r -gl)
V0 = present value
D0 = dividend now
gl = dividend growth rate long term
H = period of high growth divided by half
gs = dividend growth rate short term
r = discount rate
D0 * (1+ gl) = traditional Gordon growth model
(D0 * H) * (gs-gl) = additional value from higher growth during the transition period, assuming growth declines linearly over time from gs to gl.
What is formula of sustainable growth rate with retention ratio and ROE?
g = b * ROE
g = growth rate
b = retention rate
ROE = return on equity
What is the formula for ROE using DuPoint three way analysis?
ROE = net income/sales * sales/total assets * total assets/shareholders equity
net income/sales = retention rate
sales/total assets = asset turnover
total assets/shareholders equity = financial leverage
What is formula of sustainable growth rate using the PRAT method?
g = (net income - dividends /net income) * (net income/sales) * (sales/total assets) * (total assets/shareholders equity)
net income - dividends/ net income = profit margin (P)
net income/sales = retention rate (R)
sales/total assets = asset turnover (A)
total assets/shareholders equity = financial leverage (T)
What is residual income?
Company’s earnings in excess of the investors required return on common stock
What 2 rates does the Gordon growth model assume grow at a constant proportional rate/relationship?
The Gordon growth model assumes a constant, proportional relationship between earnings and dividends (i.e., fixed payout ratio). Thus, is the rate of capital appreciation as well as the dividend growth rate.
What is the actually (current) P/E ratio formula?
Actual P/E = P0/E0
P0 = current stock price
E0 = trailing annual earnings per share
How is the dividend payout ratio related to retention rate and what’s the formula?
dividend payout ratio is the percentage of a company’s profits that is paid out to shareholders, while the retention ratio is the percentage of profits that is kept by the company
Retention ratio = 1 - dividend payout ratio
Dividend payout ratio = dividends / net income
Retention ratio = retained earnings/ net income
What is forecasted EPS in 1 year given dividend payout ratio and dividend amount?
dividend in 1 year / 1-b
1-b = dividend payout ratio
