# Equity Valuation Finance

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```					               Chapter 5: Fundamentals of Valuation

Damodaran: Corporate FInance                          33
Discounted Cashflow Valuation: Basis for
Approach

t = n CF
Value =          t
t
t =1 (1 + r)

• The value of any asset is equal to the discounted value of its (expected)
cash flows
• Consider this for equity and bonds
• Issues of importance: appropriate discount rate, adjust cash flows for
uncertainty

• Self-work: In Practice 5.1 through 5.5; spreadsheet: bondval.xls

Damodaran: Corporate FInance                                                                  34
Uncertainty, Cash Flows and Cost

   Default Risk: credit rating agencies, default risk and default spreads
   Cash flows to Equity: cash flows generated by the asset after all
(including operating) expenses and taxes, and also after payments due
on the debt.
   Cash flow to Firm: a broader definition of cash flow generated by the
asset before debt payments but after operating expenses and taxes.
Relevant for both the equity investor and the lender.
   Expected Cash Flows: multiply cash flows by probability
   Cost of Capital= (cost of equity)×(equity %) + (cost of debt)×(debt%)
• Cost of Debt = default risk-adjusted interest rate
• Cost of Equity = equity (rather than default) risk-adjusted discount
(rather than interest) rate

Damodaran: Corporate FInance                                                             35
Equity Valuation

Damodaran: Corporate FInance                      36
Models of Equity Valuation

   Dividend-Discount Model: discounted sum of expected dividends
   Gordon Growth Model: dividends grow at a constant rate.
• Value of Equity = E(Div next period)/(ke – gn)
• gn < growth rate of the economy (for stability reasons)
– Implies that gn < discount rate (why??)
• Terminal Price method: if dividends growing quickly
– 1st stage: allow dividends to grow at a fast/unstable rate (say g = 10%) for N
years and calculate PV using formula for growing annuity
– 2nd stage: calculate terminal price by using stable growth rate after Nth year
using formula for growing perpetuity so that:
Terminal Price = E(DivN+1)/(ke – gn)
– Value of Equity = [DivN+1*PV(A, ke, g, N)] + [(Terminal Price)/(1 + ke)N]
   Selt test: In Practice 5.6 and 5.7

Damodaran: Corporate FInance                                                                            37
Free Cash Flow to Equity (FCFE)

   Problems of using only dividends to valuate equity
• Only works when dividends are actually handed out
• Depends on reinvestment needs of the company
   FCFE = Net Income – Reinvestment needs
– (Debt Repaid – New Debt Issued)
   Value of Equity = E(FCFEt)/(ke – gn)
• Terminal price methods from Gordon’s model can also be employed in
case the short-run growth rate is ‘unstably’ high

   Self test: In Practise 5.8

Damodaran: Corporate FInance                                                           38
Firm Valuation

Damodaran: Corporate FInance                    39
Free Cash Flow to Firm (FCFF)

   Consider cash flows to equity holders, bond holders and banks
   FCFF = After-tax Operating Income – Reinvestment needs
(before all debt servicing)
   Different from FCFE:
• FCFE: net income after interest and taxes
• FCFE: after net debt cash flows; FCF: before net debt cash flows
• FCFE: uses ke; FCFF uses kc
   Value of firm = E(FCFFt)/(kc – gn)
• Can use Terminal Value (just like Terminal Price) method

   Self test: In Practice 5.8 and 5.9

Damodaran: Corporate FInance                                                         40
Valuing Equity in a Finite Life Asset: Home
Dept

   Assume that you are trying to value the Home Depot’s equity
investment in a new store.
   Assume that the cash flows from the store after debt payments and
reinvestment needs are expected will be \$ 850,000 a year, growing at
5% a year for the next 12 years.
   In addition, assume that the salvage value of the store, after repaying
remaining debt will be \$ 1 million.
   Finally, assume that the cost of equity is 9.78%.

 (1.05) 
12
 -
850,000 (1.05)
1            
12 
 (1.0978)      1,000,000
Value of Equity in Store =                                +        12
= \$8,053,999
(.0978-.05)              (1.0978)

Damodaran: Corporate FInance                                                                    41
Valuing a Finite-Life Asset: Home Depot

   Consider the Home Depot's investment in a proposed store. The store
is assumed to have a finite life of 12 years and is expected to have cash
flows before debt payments and after reinvestment needs of \$ 1
million, growing at 5% a year for the next 12 years.
   The store is also expected to have a value of \$ 2.5 million at the end of
the 12th year (called the salvage value).
   The Home Depot's cost of capital is 9.51%.

Damodaran: Corporate FInance                                                           42
Expected Cash Flows and present value:
Home Depot
Year       Expecte d Cash Flows      Value at End           PV at 9 .5 1%
1         \$     1,050 ,000                               \$     958 ,8 17
2         \$     1,102 ,50 0                              \$     919 ,3 29
3         \$     1,157 ,625                               \$     881 ,4 68
4         \$     1,215 ,506                               \$     845 ,1 66
5         \$     1,276 ,282                               \$     810 ,3 59
6         \$     1,340 ,096                               \$     776 ,9 86
7         \$     1,407 ,100                               \$     744 ,9 87
8         \$     1,477 ,455                               \$     714 ,3 06
9         \$     1,551 ,328                               \$     684 ,8 88
10           \$     1,628 ,895                               \$     656 ,6 82
11           \$     1,710 ,339                               \$     629 ,6 38
12           \$     1,795 ,856        \$    2,500 ,000        \$   1 ,4 44 ,1 24
Value of St ore =       \$ 10 ,0 66 ,7 49

Damodaran: Corporate FInance                                                                             43
Valuation with Infinite Life

DISCOUNTED CASHFLOW VALUATION

Expe cte d Growth
Cash flows                                Firm: Growth in
Firm: Pre-debt cash                       Operating Earnings
flow                                      Equity: Growth in
Equity: After debt                        Net Income/EPS             Firm is in stable growth:
cash flows                                                           Grows at con stant rate
forever

Terminal Value
CF1          CF2      CF3        CF4           CF5          CFn
Value                                                                               .........
Firm: Value of Firm                                                                                           Fore ver
Equity: Value of Equity
Le ngth of Pe riod of High Growth

Disc ount Rate
Firm:Cost of Capital

Equity: Cost of Equity

Damodaran: Corporate FInance                                                                                                           44
Valuing the Home Depot’s Equity

   Assume that we expect the free cash flows to equity at the Home
Depot to grow for the next 10 years at rates much higher than the
growth rate for the economy. To estimate the free cash flows to equity
for the next 10 years, we make the following assumptions:
• The net income of \$1,614 million will grow 15% a year each year for the
next 10 years.
• The firm will reinvest 75% of the net income back into new investments
each year, and its net debt issued each year will be 10% of the
reinvestment.
• To estimate the terminal price, we assume that net income will grow 6% a
year forever after year 10. Since lower growth will require less
reinvestment, we will assume that the reinvestment rate after year 10 will
be 40% of net income; net debt issued will remain 10% of reinvestment.

Damodaran: Corporate FInance                                                               45
Estimating cash flows to equity: The Home
Depot

Year   Net Income   Rei nvestment Needs   Net Debt        FCFE      PV of FCFE
Issued
1    \$    1,856      \$     1,392        \$   (139)   \$      603    \$       549
2    \$    2,135       \$     1,601       \$   (160)   \$      694    \$       576
3    \$   2,455        \$     1,841       \$   (184)   \$      798    \$       603
4    \$   2,823        \$     2,117       \$   (212)   \$      917    \$       632
5    \$   3,246       \$     2,435        \$   (243)   \$    1,055    \$       662
6    \$   3,733       \$     2,800        \$   (280)   \$     1,213   \$       693
7    \$   4,293       \$     3,220        \$   (322)   \$    1,395    \$       726
8    \$   4,937       \$     3,703        \$   (370)   \$    1,605    \$       761
9    \$   5,678       \$     4,258        \$   (426)   \$    1,845    \$       797
10    \$   6,530       \$     4,897        \$   (490)   \$    2,122    \$       835
Sum of PV of FCFE =                             \$6,833

Damodaran: Corporate FInance                                                                     46
Terminal Value and Value of Equity today:
Home Depot

   FCFE11 = Net Income11 – Reinvestment11 – Net Debt Paid (Issued)11
= \$6,530 (1.06) – \$6,530 (1.06) (0.40) – (-277) = \$ 4,430 million
   Terminal Price10 = FCFE11/(ke – g)
= \$ 4,430 / (.0978 - .06) = \$117,186 million
  The value per share today can be computed as the sum of the present
values of the free cash flows to equity during the next 10 years and the
present value of the terminal value at the end of the 10th year.
Value of the Stock today = \$ 6,833 million + \$ 117,186/(1.0978)10
= \$52,927 million

Damodaran: Corporate FInance                                                            47
Valuing Boeing as a firm

   Assume that you are valuing Boeing as a firm, and that Boeing has
cash flows before debt payments but after reinvestment needs and
taxes of \$ 850 million in the current year.
   Assume that these cash flows will grow at 15% a year for the next 5
years and at 5% thereafter.
   Boeing has a cost of capital of 9.17%.

Damodaran: Corporate FInance                                                         48
Expected Cash Flows and Firm Value: Boeing

   Terminal Value = \$ 1710 (1.05)/(.0917-.05) = \$ 43,049 million

Year             Cash Flow       Terminal Value    Present Value

1                 \$978                               \$895
2                \$1,124                              \$943
3                \$1,293                              \$994
4                \$1,487                             \$1,047
5                \$1,710               \$43,049      \$28,864
Value of Boeing as a firm =             \$32,743

Damodaran: Corporate FInance                                                            49
Market Value vs. ‘true’ value of the Asset

    Pricing Process: continuous vs. call markets
    Market deviates from ‘true’ value because of: (1) incorrect
information, (2) poor processing/analysis and (3) speculative
incentives and/or differential expectations
    Market Efficiency:
• Size and duration of deviations of actual/market value from ‘true’ value
• Speed with which markets react to relevant new information
• Do some investors in the market earn higher returns than others who are
exposed to the same amount of risk (e.g., Wall Street)

Damodaran: Corporate FInance                                                                  50

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