V & VI. Shareholder Value Analysis - DCF
Value Based on Discounted Cash Flows:
infinity

General Model: Intrinsic value/share0 =
t=1
CF t
(1+ k )t
nso
where:
o CFt is the total cash flow in period t;
o k is investors' required rate of return;
o nso is the number of shares outstanding.
Note: If cash flows are expected to be constant then:
CF
Intrinsic value/share0 = k
nso
And if cash flows are expected to grow at a constant rate (g) then:
CF 0(1  g )
(k  g )
Intrinsic value/share0 =
nso
Dividend Discount Model:
infinity
Intrinsic value/share =
 (1 + k
Div .t
t =1
t
e
)
nso
where:
o Divt is expected dividends in period t;
o ke is stockholders' required rate of return; and
o nso is the number of shares outstanding.
Cash Flow Discount Models:
Direct Cash Flow Discount Model:
infinity
Intrinsic value/share =

t=1
CF t
(1+ k e )t
nso
where: CFt is the total cash flow available
to stockholders in period t
ke is stockholders' required rate of
return; and
nso is the number of shares outstanding.
Note: If the stock pays dividends that equal cash flow available to shareholders
then using a dividend discount model (discounting all future dividends) is the
exact same as using the direct Direct Cash Flow Model. But if dividends are
less (greater) than cash flow available to shareholders, the dividend discount
model underestimates (overestimates) the value.
Understanding ‘growth’:
In constant growth DDM, the ‘g’ is expected constant rate of growth in
dividends
If a firm maintains a constant payout ratio, then (and only then),
growth in dividends = growth in earnings
Where does growth come from?
A firms (economic) earnings (and therefore dividends) can grow only if
firm reinvests a part of its earnings
Is all growth good?, i.e., lead to an increase in stock price?
No.
It is possible to show that:
g = ROE * b
where:
o ROE = return on equity i.e. rate earned on marginal investment by
firm
o b = plowback ratio, i.e. the fraction of earnings reinvested back
into firm
Note:
Earnings are defined as economic earnings – i.e., net of funds
(capital expenditures) needed to maintain current level of production
of firm, i.e., net of economic depreciation
Ex. Alpha and Gamma Cos. Stock both have required returns of 9%, Alpha has
investment opportunities which earn a 12% return and Gamma has investment
opportunities which earn a 7% return. Both firms expect earnings to be $2 per
share for the coming year and both expect to retain no earnings.
 Dividend = Earnings = $2
 g A  .12 * 0  0; gG  .07 * 0  0
 neither firm is expected to increase its dividend
VA  VG 
2
 $22.22
.09
Q: What if both firms begin to retain 70% of their earnings?
Div1 = 2*(1-.7) = $0.60
g A  .12 * .7  .084;
gG  .07 * .7  .049
Note: Beta’s earnings and dividends grow at a slower rate because
earning lower rate on investment
Q: Is the growth beneficial to the S/H?
VA 
.6
 100;
.09  .084
VG 
.6
 14.63
.09  .049
A: For Alpha (ROE > k), for Gamma (ROE < k)
Implication:
Indirect Discount Cash Flow Model:
Intrinsic value/sh = (Value of Assets - Value of Liabilities)/nso
Intrinsic value/sh = (Value of Operating Assets + Value of Non-Operating
Assets - Value of Liabilities)/nso
Intrinsic value/sh =
infinity
 (1+WACC )
CF t
t
+ MV(Non - Oper. Assets) - MV(Interest - Bearing Liab. )
t=1
nso
where:
o CFt is operating cash flow available to both bondholders and
stockholders in period t (defined earlier);
o MV is the market value;
o Non-operating assets are assets not necessary to operate in a
particular business;
o Interest-bearing liabilities are liabilities which explicitly pay interest
(notes payable, LT debt);
o WACC is investors' weighted average required rate of return;
o nso is the number of shares outstanding.
Estimation of Cash Flows under the direct and the indirect approach:
Estimation of Cash Flows
Free cash flow to equity (FCFE/Direct) v/s the Free cash flow to firm (FCFF/Indirect) approach:
FCFE (Direct Model):
Revenue
FCFF (Indirect Model):
Revenue
- Operating Exp.
- Operating Exp.
- Depr. Exp
- Depr. Exp.
Operating Profit
Operating Profit
+/- Non-Operating Rev (Exp.)
+/- Non-Operating Rev (Exp.)
= EBIT
= EBIT
- interest exp
- Taxes** (based on EBIT)
= EBT
= After-Tax EBIT
- Taxes* (based on EBT)
+ Depr. Exp.
= Net Income
- Change in W/C
+ Depr. Exp
- Change in LT Assets (Capital Exp., etc.)
- Change in W/Capital
= Free Cash Flow to Firm
(All investors: Bond and Stockholders)
- Change in LT Assets (Capital Exp., etc.)
+ Change in Interest Bearing Liabilities
(addition or redemption of debt)
= Free Cash Flow to Equity
Notes:
* Taxes here are taxes on EBT, i.e., amount actually owed/paid: (EBT x T)
** Taxes here are computed on EBIT: (EBIT x T), not the actual taxes paid based on EBT
If firm has excess cash and marketable securities, (i.e., more than that required for working
capital/running the business), it is necessary to remove that from working capital calculation. Any income
from excess cash or marketable securities is considered as non-operating income.
Non-operating income is income from any asset that is not the core business of the firm.
If all or part of the Short Term Debt is permanent, and used to finance long term assets, it is necessary to
exclude that portion of ST Debt from working capital calculation; however, include that portion in WACC
calculation.
Use WACC to discount FCFF; Use cost of equity (levered Re) to discount FCFE
Summary: Discounted Cash Flow Models:
Valuation is a three-step process:
1. Estimate the appropriate future cash flows
o dividends
o cash flows to shareholders
o cash flows to all investors
2. Estimate the appropriate discount rate
o cost of equity capital for the dividend and direct model
o WACC for the indirect model
3. Calculate the present value of the estimated cash flows
o discount cash flows explicitly estimated
o discount all future cash flows or estimate the terminal value
A. How financial leverage affects discount rates and valuation:
To measure the effect a change in a firm’s capital structure will have on the cost
of equity capital we need to understand the relation between the concepts of
business and financial risk with beta or systematic risk.
According to the CAPM:
ke = RF + (Rm - RF)B
where:
o
o
o
o
ke is the required return of a stock;
RF is the risk-free rate of return;
Rm is the expected return of the stock market;
B is a measure of the stock's systematic risk, i.e. beta.
Note: Beta a measure of systematic risk and is a function of two types of risk:
business risk and financial risk. If a firm has no debt, then beta is only
determined by the level of business risk and would be referred to as an
unlevered beta or the asset beta BU.
Hamada suggested that we combine the business and financial risk concepts
with the CAPM:
ke = RF + business risk premium + financial risk premium
ke = RF + (Rm - RF)BU + (Rm - RF)BU(1-tc)D/E
where:
o D/E is the firm's debt to equity ratio measured in market value terms
o tc is the firm's marginal corp. tax rate
If we equate the ke from the CAPM with the ke from Hamada's equation and
solve for Beta we get:
ke from CAPM = ke from Hamada's equation
RF + (Rm - RF)B = RF + (Rm - RF)BU + (Rm - RF)BU(1-tc)D/E
solving for B we get:
B = BU[1 + (1 - tc) D/E]
rearranging terms:
BU = B / [1 + (1 - tc) D/E]
Note: The measure of systematic risk when investing in the equity (stock) of a
firm is a function of the firm's business risk (BU) and the firm's use of debt
financing (D/E ratio).
In practice:
Step 1: Unlever the firm’s current equity beta given the firm’s existing
capital structure to get an estimate of the firm’s asset beta.
Step 2: Given the firm’s asset beta, relever it using the future or expected
capital structure to get an estimate of the new equity beta.
Step 3: Plug the new equity beta into the CAPM to get an estimate of the
new cost of equity capital.
Notes:
EX 1. The ABC Corporation wants to determine the effect on the firm's
cost of equity capital if the firm issues additional debt to retire some of its
equity capital. Currently, the firm's D/E ratio is .25 and the stock’s beta
equals 1.2. Following the debt for equity swap the firm's D/E ratio will
equal .80. If we assume the market rate on 90-day T-Bills (RF) equals
6%/yr, the expected return on the market is 18%/yr and the firm's
corporate tax rate is 30%, what will the change in investors' required
return or the cost associated with equity financing equal?
Before issuing debt, the cost of or the required return on the firm's equity
capital:
ke = RF + (Rm - RF)B
ke = 6% + (18% - 6%)1.2 = 20.4%
After issuing debt, the cost of or the required return on the firm's equity
capital:
Unlever Beta:
BU = B/[1 + (1 - tc) D/E]
BU =1.2/[1+(1-.3).25] = 1.0213
Relever Beta:
B = BU[1 + (1 - tc) D/E]
B = 1.0213[1 + (1 - .3).8] = 1.5932
Cost of Equity:
ke = 6% + (18% - 6%)1.5932 = 25.12%
EX 2. The XYZ Corporation is considering issuing additional debt and is
interested in the effect this financing decision will have on its cost of equity
capital. Currently, the beta of this firm's stock is 0.88 and the debt to
equity ratio is 1.3. After they issue additional debt their debt to equity ratio
will equal 1.55. Assuming the risk-free rate is 5.2%, the expected return
on the market is 16%, and the firm has an expected marginal tax rate of
30%, what will the change in the cost of equity capital be due to the
additional debt? (Assume the capital being raised will be used to invest in
a project with the same business risk as all of the firm's other
investments).