Week 5:
Preparation: Chap 9: Valuing
stocks.
Total payout model: allows to ignore the firm’s choice between dividends and
share repurchases.
Discounted free cash flow model: focuses on the cash flows to all of the firm’s
investors, both debt and equity holders, allowing to avoid estimating the impact
of the firm’s borrowing decisions on earnings.
Dividend-Discount model: assumed that any cash paid out by the firm to
shareholders takes the form of a dividend.
In recent years, dividend payouts have been partially replaced by share
repurchases – the excess of cash is used to buy stocks back. 2 consequences for
the model: less cash available to pay dividends, decrease of share count and
thus increase of earnings and dividends on a per-share basis.
P0 = PV (Future Dividends per Share)
Other strategy: Total payout model, valuing all of the firm’s equity rather than a
single share.
Total Payout Model: P0 = PV (Future Dividends and Repurchases)/ Shares
Outstanding0
We discount total dividends and share purchases and use the growth rate of total
earnings (rather than earnings per share) when forecasting the growth of the
firm’s total payouts.
Discounted Free Cash Flow Model determine the total value of the firm to all
investors equity and debt holders).
Enterprise Value = Market Value of Equity + Debt – Cash
Free Cash Flow = Unlevered Net Income EBIT x (1 – T_c) + Depreciation – Capital
Expenditures – Increases in Net Working Capital
With Net Investment = Capital Expenditures – Depreciation.
Discounted Free Cash Flow Model: V0 = PV (Future Free Cash Flow of Firm)
P0 = (V0 + Cash0 – Debt0) / Shares Outstanding0
Weighted Average Cost Of Capital (WACC) or rWACC: average cost of capital the
firm must pay to all of its investors, both debt and equity holders.
If no debt: rWACC = rE
V0 = FCF1 / (1 + rWACC ) + FCF2 / (1 + rWACC )2 + … + (FCFN + VN) / (1 + rWACC )N
VN = FCFN+1 / (rWACC – gFCF) = (1 + gFCF) / (rWACC – gFCF) x FCFN
PV: the amount we would need to invest elsewhere in the market to replicate the
cash flows with the same risk.
, Method of comparables (comps): rather than value the cash flows directly, value
of the firm based on the value of other comparable firms or investments we
expect will generate very similar cash flow in the future.
Adjusting can be done with:
- Valuation multiple: a ratio of the value to some measure of the firm’s
scale.
- Price earning ratio: Share Price ÷ Earnings per Share.
Forward P/E = P0/ EPS1 = (Div1/ EPS1)/ (rE – g) = Dividend Payout Rate/ (rE –
g)
Trailing earnings: earnings over the prior 12 months.
- Enterprise Value Multiples: V0/ EBITDA1 = (FCF1/EBITDA1)/ (rWACC – gFCF)
- Other multiples.
But they have limits and they are not perfectly accurate.
Alternative method: DCF, make explicit the future performance the firm must
achieve in order to justify its current value.
Should not use a single one but combine them.
Chap 10: Capital Markets and the Pricing of Risk
≠ securities have ≠ initial prices, pay ≠ cash flows, and sell for ≠ future
amounts.
Comparable by expressing them in terms of their return: indicates the
percentage increase in the value of an investment per dollar initially invested in
the security.
Probability distribution to the likelihood of ≠ returns to occur.
Expected (Mean) Return = E[R] = ∑RpR x R
It is the return we would earn on average if we could repeat the investment
many times.
Variance and Standard Deviation of the Return Distribution: Var (R) = E[(R–
E(R])2] =∑RpR x (R–E(R))2
SD(R) = √Var (R)
SD of a return in finance is its volatility.
Realized Return is the return that actually occurs over a particular time period.
Rt+1 = (Divt+1 + Pt+1)/ Pt – 1 = Divt+1/ Pt + (Pt+1 – Pt) / Pt = Dividend Yield + Capital
Gain Rate
Returns of a single security: assuming all the dividends are reinvested
immediately and used to purchase additional shares of the same stock or
security.
1 + Rannual = (1 + RQ1)(1 + RQ2)…(1 + RQN)
Empirical distribution: when the probability distribution is plotted using empirical
data.
The Average Annual Return of an investment during some historical period is
simply the average of the realized returns for each year.
T
Average Annual Return of a Security: R = 1/T ∑ Rt
t =1
T
2
Variance Estimate Using Realized Returns: Var(R) = 1/ (T – 1)∑ (R¿¿ t−R) ¿
t =1
Preparation: Chap 9: Valuing
stocks.
Total payout model: allows to ignore the firm’s choice between dividends and
share repurchases.
Discounted free cash flow model: focuses on the cash flows to all of the firm’s
investors, both debt and equity holders, allowing to avoid estimating the impact
of the firm’s borrowing decisions on earnings.
Dividend-Discount model: assumed that any cash paid out by the firm to
shareholders takes the form of a dividend.
In recent years, dividend payouts have been partially replaced by share
repurchases – the excess of cash is used to buy stocks back. 2 consequences for
the model: less cash available to pay dividends, decrease of share count and
thus increase of earnings and dividends on a per-share basis.
P0 = PV (Future Dividends per Share)
Other strategy: Total payout model, valuing all of the firm’s equity rather than a
single share.
Total Payout Model: P0 = PV (Future Dividends and Repurchases)/ Shares
Outstanding0
We discount total dividends and share purchases and use the growth rate of total
earnings (rather than earnings per share) when forecasting the growth of the
firm’s total payouts.
Discounted Free Cash Flow Model determine the total value of the firm to all
investors equity and debt holders).
Enterprise Value = Market Value of Equity + Debt – Cash
Free Cash Flow = Unlevered Net Income EBIT x (1 – T_c) + Depreciation – Capital
Expenditures – Increases in Net Working Capital
With Net Investment = Capital Expenditures – Depreciation.
Discounted Free Cash Flow Model: V0 = PV (Future Free Cash Flow of Firm)
P0 = (V0 + Cash0 – Debt0) / Shares Outstanding0
Weighted Average Cost Of Capital (WACC) or rWACC: average cost of capital the
firm must pay to all of its investors, both debt and equity holders.
If no debt: rWACC = rE
V0 = FCF1 / (1 + rWACC ) + FCF2 / (1 + rWACC )2 + … + (FCFN + VN) / (1 + rWACC )N
VN = FCFN+1 / (rWACC – gFCF) = (1 + gFCF) / (rWACC – gFCF) x FCFN
PV: the amount we would need to invest elsewhere in the market to replicate the
cash flows with the same risk.
, Method of comparables (comps): rather than value the cash flows directly, value
of the firm based on the value of other comparable firms or investments we
expect will generate very similar cash flow in the future.
Adjusting can be done with:
- Valuation multiple: a ratio of the value to some measure of the firm’s
scale.
- Price earning ratio: Share Price ÷ Earnings per Share.
Forward P/E = P0/ EPS1 = (Div1/ EPS1)/ (rE – g) = Dividend Payout Rate/ (rE –
g)
Trailing earnings: earnings over the prior 12 months.
- Enterprise Value Multiples: V0/ EBITDA1 = (FCF1/EBITDA1)/ (rWACC – gFCF)
- Other multiples.
But they have limits and they are not perfectly accurate.
Alternative method: DCF, make explicit the future performance the firm must
achieve in order to justify its current value.
Should not use a single one but combine them.
Chap 10: Capital Markets and the Pricing of Risk
≠ securities have ≠ initial prices, pay ≠ cash flows, and sell for ≠ future
amounts.
Comparable by expressing them in terms of their return: indicates the
percentage increase in the value of an investment per dollar initially invested in
the security.
Probability distribution to the likelihood of ≠ returns to occur.
Expected (Mean) Return = E[R] = ∑RpR x R
It is the return we would earn on average if we could repeat the investment
many times.
Variance and Standard Deviation of the Return Distribution: Var (R) = E[(R–
E(R])2] =∑RpR x (R–E(R))2
SD(R) = √Var (R)
SD of a return in finance is its volatility.
Realized Return is the return that actually occurs over a particular time period.
Rt+1 = (Divt+1 + Pt+1)/ Pt – 1 = Divt+1/ Pt + (Pt+1 – Pt) / Pt = Dividend Yield + Capital
Gain Rate
Returns of a single security: assuming all the dividends are reinvested
immediately and used to purchase additional shares of the same stock or
security.
1 + Rannual = (1 + RQ1)(1 + RQ2)…(1 + RQN)
Empirical distribution: when the probability distribution is plotted using empirical
data.
The Average Annual Return of an investment during some historical period is
simply the average of the realized returns for each year.
T
Average Annual Return of a Security: R = 1/T ∑ Rt
t =1
T
2
Variance Estimate Using Realized Returns: Var(R) = 1/ (T – 1)∑ (R¿¿ t−R) ¿
t =1
