Transcript The Tools of Corporate Finance Present Value Financial Statement Analysis Fundamentals of Valuation Aswath Damodaran.

The Tools of Corporate Finance
Present Value
Financial Statement Analysis
Fundamentals of Valuation
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Present Value
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Intuition Behind Present Value

There are three reasons why a dollar tomorrow is worth less than a
dollar today
•
Individuals prefer present consumption to future consumption. To
induce people to give up present consumption you have to offer them
more in the future.
•
When there is monetary inflation, the value of currency decreases over
time. The greater the inflation, the greater the difference in value between
a dollar today and a dollar tomorrow.
•
If there is any uncertainty (risk) associated with the cash flow in the
future, the less that cash flow will be valued.

Other things remaining equal, the value of cash flows in future time
periods will decrease as
• the preference for current consumption increases.
• expected inflation increases.
• the uncertainty in the cash flow increases.
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Discounting and Compounding
• The mechanism for factoring in these elements is the discount rate.
• Discount Rate: The discount rate is a rate at which present and future
cash flows are traded off. It incorporates (1) Preference for current consumption (Greater ....Higher Discount Rate)
(2) expected inflation (Higher inflation
....
Higher Discount Rate)
(3) the uncertainty in the future cash flows (Higher Risk....Higher Discount Rate)
• A higher discount rate will lead to a lower value for cash flows in the
future.
• The discount rate is also an opportunity cost, since it captures the returns
that an individual would have made on the next best opportunity.
 Discounting future cash flows converts them into cash flows in present
value dollars. Just a discounting converts future cash flows into present
cash flows,
 Compounding converts present cash flows into future cash flows.
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Present Value Principle 1

Cash flows at different points in time cannot be compared and
aggregated. All cash flows have to be brought to the same point in
time, before comparisons and aggregations are made.
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Time Lines
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Cash Flow Types and Discounting Mechanics

There are five types of cash flows 




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simple cash flows,
annuities,
growing annuities
perpetuities and
growing perpetuities
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I.Simple Cash Flows
A simple cash flow is a single cash flow in a specified future time
period.
Cash Flow:
CFt
_______________________________________________|
Time Period:
t
 The present value of this cash flow isPV of Simple Cash Flow = CFt / (1+r)t
 The future value of a cash flow is FV of Simple Cash Flow = CF0 (1+ r)t

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Application: The power of compounding Stocks, Bonds and Bills


Between 1926 and 1998, Ibbotson Associates found that stocks on the
average made about 11% a year, while government bonds on average
made about 5% a year.
If your holding period is one year,the difference in end-of-period
values is small:
• Value of $ 100 invested in stocks in one year = $ 111
• Value of $ 100 invested in bonds in one year = $ 105
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Holding Period and Value
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Concept Check








Most pension plans allow individuals to decide where their pensions
funds will be invested - stocks, bonds or money market accounts.
Where would you choose to invest your pension funds?
Predominantly or all equity
Predominantly or all bonds and money market accounts
A Mix of Bonds and Stocks
Will your allocation change as you get older?
Yes
No
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The Frequency of Compounding

The frequency of compounding affects the future and present values of
cash flows. The stated interest rate can deviate significantly from the
true interest rate –
• For instance, a 10% annual interest rate, if there is semiannual
compounding, works out toEffective Interest Rate = 1.052 - 1 = .10125 or 10.25%
Frequency
Annual
Semi-Annual
Monthly
Daily
Continuous
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Rate
10%
10%
10%
10%
10%
t
1
2
12
365
Formula
r
(1+r/2)2-1
(1+r/12)12-1
(1+r/365)365-1
expr-1
Effective Annual Rate
10.00%
10.25%
10.47%
10.5156%
10.5171%
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II. Annuities

An annuity is a constant cash flow that occurs at regular intervals for a
fixed period of time. Defining A to be the annuity,
0
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A
|
1
A
|
2
A
|
3
A
|
4
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Present Value of an Annuity

The present value of an annuity can be calculated by taking each cash
flow and discounting it back to the present, and adding up the present
values. Alternatively, there is a short cut that can be used in the
calculation [A = Annuity; r = Discount Rate; n = Number of years]
1 

1n

(1+ r) 
PV of an Annuity = PV(A,r,n) = A

r



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Example: PV of an Annuity

The present value of an annuity of $1,000 at the end of each year for
the next five years, assuming a discount rate of 10% is 1 

1 5

(1.10) 
PV of $1000 each year for next 5 years
= $1000
 $3,791
 .10




The notation that will be used in the rest of these lecture notes for the
present value of an annuity will be PV(A,r,n).
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Annuity, given Present Value

The reverse of this problem, is when the present value is known and
the annuity is to be estimated - A(PV,r,n).

r

Annuity given Present Value= A(PV,r,n) = PV
1
1 (1+ r)n

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



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Computing Monthly Payment on a Mortgage

Suppose you borrow $200,000 to buy a house on a 30-year mortgage
with monthly payments. The annual percentage rate on the loan is 8%.
The monthly payments on this loan, with the payments occurring at the
end of each month, can be calculated using this equation:
• Monthly interest rate on loan = APR/ 12 = 0.08/12 = 0.0067


0.0067 

Mont hly Paym ent on Mortgage
= $200,0 00
 $1473.11
1
1 
360
(1.0067) 

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Future Value of an Annuity

The future value of an end-of-the-period annuity can also be calculated
as follows(1 + r)n - 1 
FV of an Annuity = FV(A,r,n) = A 

r


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An Example

Thus, the future value of $1,000 at the end of each year for the next
five years, at the end of the fifth year is (assuming a 10% discount
rate) -
(1.10) - 1 
FV of $1,0 00 each year for next 5 years
= $1000
= $6,1 05

 .10

5

The notation that will be used for the future value of an annuity will be
FV(A,r,n).
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Annuity, given Future Value

if you are given the future value and you are looking for an annuity A(FV,r,n) in terms of notation 
r

Annuity given Future Value= A(FV,r,n) = FV 
n
(1+ r) - 1 

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Application : Saving for College Tuition

Assume that you want to send your newborn child to a private college
(when he gets to be 18 years old). The tuition costs are $ 16000/year
now and that these costs are expected to rise 5% a year for the next 18
years. Assume that you can invest, after taxes, at 8%.
• Expected tuition cost/year 18 years from now = 16000*(1.05)18 = $38,506
• PV of four years of tuition costs at $38,506/year = $38,506 * PV(A ,8%,4
years)= $127,537

If you need to set aside a lump sum now, the amount you would need
to set aside would be • Amount one needs to set apart now = $127,357/(1.08)18 = $31,916

If set aside as an annuity each year, starting one year from now • If set apart as an annuity = $127,537 * A(FV,8%,18 years) = $3,405
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Application : How much is an MBA worth?

Assume that you were earning $40,000/year before entering program
and that tuition costs are $16000/year. Expected salary is $ 54,000/year
after graduation. You can invest money at 8%.
For simplicity, assume that the first payment of $16,000 has to be made at the
start of the program and the second payment one year later.
• PV Of Cost Of MBA = $16,000+16,000/1.08 + 40000 * PV(A,8%,2
years) = $102,145

Assume that you will work 30 years after graduation, and that the
salary differential ($14000 = $54000-$40000) will continue through
this period.
• PV of Benefits Before Taxes = $14,000 * PV(A,8%,30 years) = $157,609
• This has to be discounted back two years - $157,609/1.082 = $135,124
• The present value of getting an MBA is = $135,124 - $102,145 = $32,979
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Some Follow-up Questions
1. How much would your salary increment have to be for you to break
even on your MBA?
2. Keeping the increment constant, how many years would you have to
work to break even?
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Application: Savings from Refinancing Your
Mortgage

Assume that you have a thirty-year mortgage for $200,000 that carries
an interest rate of 9.00%. The mortgage was taken three years ago.
Since then, assume that interest rates have come down to 7.50%, and
that you are thinking of refinancing. The cost of refinancing is
expected to be 2.50% of the loan. (This cost includes the points on the
loan.) Assume also that you can invest your funds at 6%.
Monthly payment based upon 9% mortgage rate (0.75% monthly rate)
= $200,000 * A(PV,0.75%,360 months)
= $1,609
Monthly payment based upon 7.50% mortgage rate (0.625% monthly rate)
= $200,000 * A(PV,0.625%,360 months)
= $1,398

Monthly Savings from refinancing = $1,609 - $1,398 = $211
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Refinancing: The Trade Off
If you plan to remain in this house indefinitely,
Present Value of Savings (at 6% annually; 0.5% a month)
= $211 * PV(A,0.5%,324 months)
= $33,815

•
•
The savings will last for 27 years - the remaining life of the existing mortgage.
You will need to make payments for three additional years as a consequence of the
refinancing Present Value of Additional Mortgage payments - years 28,29 and 30
= $1,398 * PV(A,0.5%,36 months)/1.0627
= $9,532



Refinancing Cost = 2.5% of $200,000 = $5,000
Total Refinancing Cost = $9,532 + $5,000 = $14,532
Net Effect = $ 33,815 - $ 14,532 = $ 19,283: Refinance
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Follow-up Questions
1. How many years would you have to live in this house for you break
even on this refinancing?
2. We've ignored taxes in this analysis. How would it impact your
decision?
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Valuing a Straight Bond

You are trying to value a straight bond with a fifteen year maturity and
a 10.75% coupon rate. The current interest rate on bonds of this risk
level is 8.5%.
PV of cash flows on bond = 107.50* PV(A,8.5%,15 years) + 1000/1.08515 =
$ 1186.85

If interest rates rise to 10%,
PV of cash flows on bond = 107.50* PV(A,10%,15 years)+ 1000/1.1015 =
$1,057.05
Percentage change in price = -10.94%

If interest rate fall to 7%,
PV of cash flows on bond = 107.50* PV(A,7%,15 years)+ 1000/1.0715 =
$1,341.55
Percentage change in price = +13.03%

This asymmetric response to interest rate changes is called convexity.
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Contrasting Short Term and Long Term Bonds
Price Changes as a function of Bond Maturities
20.00%
% Change in Price
15.00%
10.00%
% Change if rate drops
to 7%
5.00%
0.00%
% Change if rate
increases to 10%
-5.00%
-10.00%
-15.00%
1
5
15
30
Bond Maturity
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Bond Pricing Proposition 1

The longer the maturity of a bond, the more sensitive it is to changes in
interest rates.
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Contrasting Low-coupon and High-coupon
Bonds
Bond Price Changes as a function of Coupon Rates
25.00%
20.00%
% Price Change
15.00%
10.00%
% Change if rate
drops to 7%
5.00%
0.00%
% Change if rate
increases to 10%
-5.00%
-10.00%
-15.00%
-20.00%
0%
5%
10.75%
12%
Coupon Rate
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Bond Pricing Proposition 2

The lower the coupon rate on the bond, the more sensitive it is to
changes in interest rates.
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III. Growing Annuity

A growing annuity is a cash flow growing at a constant rate for a
specified period of time. If A is the current cash flow, and g is the
expected growth rate, the time line for a growing annuity looks as
follows –
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Present Value of a Growing Annuity

The present value of a growing annuity can be estimated in all cases,
but one - where the growth rate is equal to the discount rate, using the
following model:

(1+ g) n 
1 
n

(1+ r) 
PV of an Annuity= P V(A,r ,g,n) = A(1+ g) 

(r
g)







In that specific case, the present value is equal to the nominal sums of
the annuities over the period, without the growth effect.
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The Value of a Gold Mine

Consider the example of a gold mine, where you have the rights to the
mine for the next 20 years, over which period you plan to extract 5,000
ounces of gold every year. The price per ounce is $300 currently, but it
is expected to increase 3% a year. The appropriate discount rate is
10%. The present value of the gold that will be extracted from this
mine can be estimated as follows –

(1.03) 
1 
(1.10)20 
PV of extract ed gold= $300* 5000* (1.03)
 $16,145,980
 .10- .03 




20
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PV of Extracted Gold as a Function of
Expected Growth Rate
Present Value of Extracted Gold as a function of Grow th Rate
$50,000,000
$45,000,000
$40,000,000
Present Value of Extracted Gold
$35,000,000
$30,000,000
$25,000,000
$20,000,000
$15,000,000
$10,000,000
$5,000,000
15%
14%
13%
12%
11%
10%
9%
8%
7%
6%
5%
4%
3%
2%
1%
0%
$-
Growth Rate in Gold Prices
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Concept Check

If both the growth rate and the discount rate go up by 1%, will the
present value of the gold to be extracted from this mine increase or
decrease?
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IV. Perpetuity

A perpetuity is a constant cash flow at regular intervals forever. The
present value of a perpetuity isPV of Perpetuity=
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A
r
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Valuing a Console Bond

A console bond is a bond that has no maturity and pays a fixed
coupon. Assume that you have a 6% coupon console bond. The value
of this bond, if the interest rate is 9%, is as follows Value of Console Bond = $60 / .09 = $667
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V. Growing Perpetuities

A growing perpetuity is a cash flow that is expected to grow at a
constant rate forever. The present value of a growing perpetuity is PV of Growing Perpetuity
=
CF1
(r - g)
where
• CF1 is the expected cash flow next year,
• g is the constant growth rate and
• r is the discount rate.
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Valuing a Stock with Growing Dividends

Southwestern Bell paid dividends per share of $2.73 in 1992. Its
earnings and dividends have grown at 6% a year between 1988 and
1992, and are expected to grow at the same rate in the long term. The
rate of return required by investors on stocks of equivalent risk is
12.23%.
Current Dividends per share = $2.73
Expected Growth Rate in Earnings and Dividends = 6%
Discount Rate = 12.23%
Value of Stock = $2.73 *1.06 / (.1223 -.06) = $46.45
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Financial Statement Analysis
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Questions we would like answered…
Assets
Liabilities
W hat are the assets in place?
How valuable are these assets?Assets in P lace
How risky are these assets?
Debt
W hat is the value of the debt?
How risky is the debt?
W hat are the growth assets? Growth Assets
How valuable are these assets?
Equity
W hat is the value of the equity?
How risky is the equity?
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Basic Financial Statements



The balance sheet, which summarizes what a firm owns and owes at a
point in time.
The income statement, which reports on how much a firm earned in
the period of analysis
The statement of cash flows, which reports on cash inflows and
outflows to the firm during the period of analysis
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The Balance Sheet
Figure 4.1: The Balance Sheet
Assets
Long Lived Real Assets
Short-lived Assets
Investments in securities &
assets of other firms
Liabilities
Fixed Assets
Current
Short-term liabilities of the firm
Liabilties
Current Assets
Debt
Financial Investments Other
Liabilities
Assets which are not physical,Intangible Assets
like patents & trademarks
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Equity
Debt obligations of firm
Other long-term obligations
Equity investment in firm
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A Financial Balance Sheet
Assets
Existing Investments
Assets in P lace
Generate cashflows today
Includes long lived (fixed) and
short-lived(working
capital) assets
Expected Value that will be Growth Assets
created by future investments
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Liabilities
Debt
Equity
Fixed Claim on cash flows
Little or No role in management
Fixed M aturity
Tax Deductible
Residual Claim on cash flows
Significant Role in management
Perpetual Lives
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The Income Statement
Figure 4.2: Income Statement
Gross revenues from sale
of products or services
Revenues
Expenses associates wit h
generating revenues
- Operating Expenses
Operating income for the
period
= Operating Income
Expenses associated wit h
- Financial Expenses
borrowing and other financing
T axes due on taxable income - T axes
Earnings to Common &
P referred Equit y for
Current P eriod
= Net Income before extraordinary it ems
P rofit s and Losses not
associated wit h operations
- (+) Extraordinary Losses (Prof its)
P rofit s or losses associated
wit h changes in accounting
rules
- Income Changes Associated wit h Accounting Changes
Dividends paid to preferred
stockholders
- P referred Dividends
= Net Income to Common Stockholders
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Modifications to Income Statement

There are a few expenses that consistently are miscategorized in
financial statements.In particular,
• Operating leases are considered as operating expenses by accountants but
they are really financial expenses
• R &D expenses are considered as operating expenses by accountants but
they are really capital expenses.

The degree of discretion granted to firms on revenue recognition and
extraordinary items is used to manage earnings and provide misleading
pictures of profitability.
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Dealing with Operating Lease Expenses



Debt Value of Operating Leases = PV of Operating Lease Expenses at
the pre-tax cost of debt
This now creates an asset - the value of which is equal to the debt
value of operating leases. This asset now has to be depreciated over
time.
Finally, the operating earnings has to be adjusted to reflect these
changes:
• Adjusted Operating Earnings = Operating Earnings + Operating Lease
Expense - Depreciation on the leased asset
• If we assume that depreciation = principal payment on the debt value of
operating leases, we can use a short cut:
Adjusted Operating Earnings = Operating Earnings + Debt value of
Operating leases * Cost of debt
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Operating Leases at Boeing and The Home
Depot in 1998
Boeing
Year
Operating Lease Expense
Present Value at
Operating
Present Value
5.5%
Lease Expense
at 5.8%
1
$
205
$
194.31
$
294
$
277.88
2
$
167
$
150.04
$
291
$
259.97
3
$
120
$
102.19
$
264
$
222.92
4
$
86
$
69.42
$
245
$
195.53
5
$
61
$
46.67
$
236
$
178.03
-
$
270
$
1,513.37
$
2,647.70
Yr 6 -15
$
PV of O perating Lease Expenses
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Home Depot
-
$
$
562.64
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Imputed Interest Expenses on Operating
Leases
PV of O perating Leases
Interest rate on Debt
Imputed interest expense on P V of operating leases
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Boeing
$ 562.64
5.50%
$ 30.95
The Home Depot
$ 2647.70
5.80%
$ 153.57
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The Effects of Capitalizing Operating Leases




Debt : will increase, leading to an increase in debt ratios used in the
cost of capital and levered beta calculation
Operating income: will increase, since operating leases will now be
before the imputed interest on the operating lease expense
Net income: will be unaffected since it is after both operating and
financial expenses anyway
Return on Capital will generally decrease since the increase in
operating income will be proportionately lower than the increase in
book capital invested
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R&D Expenses: Operating or Capital Expenses


Accounting standards require us to consider R&D as an operating
expense even though it is designed to generate future growth. It is
more logical to treat it as capital expenditures.
To capitalize R&D,
• Specify an amortizable life for R&D (2 - 10 years)
• Collect past R&D expenses for as long as the amortizable life
• Sum up the unamortized R&D over the period. (Thus, if the amortizable
life is 5 years, the research asset can be obtained by adding up 1/5th of the
R&D expense from five years ago, 2/5th of the R&D expense from four
years ago...:
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Capitalizing R&D Expenses: Boeing
Year
R&D
1 989
1 990
1 991
1 992
1 993
1 994
1 995
1 996
1 997
1 998
Capita lized Value
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Value
$ 754
$ 827
$ 1,417
Unamo rt ized
Por t ion
0 .1 0
0 .2 0
0 .3 0
$ 1,846
$ 1,661
$ 1,704
$ 1,300
0 .4 0
0 .5 0
0 .6 0
0 .7 0
$ 738
$ 831
$ 1,022
$ 910
$ 1,633
0 .8 0
$ 1,924
0 .9 0
$ 1,895
1 .0 0
of R& D Expenses =
$ 75
$ 165
$ 425
$ 1,306
$ 1,732
$ 1,895
$ 9,100
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Boeing’s Corrected Operating Income
Operating Income
+ Research and Development Expenses
- Amortization of Research Asset
+ Imputed Interest Expense on Operating
Leases
= Adjusted Operating Income
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Boeing
$1,720
$1,895
$1,382
$
31
$2,264
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The Effect of Capitalizing R&D




Operating Income will generally increase, though it depends upon
whether R&D is growing or not. If it is flat, there will be no effect
since the amortization will offset the R&D added back. The faster
R&D is growing the more operating income will be affected.
Net income will increase proportionately, depending again upon how
fast R&D is growing
Book value of equity (and capital) will increase by the capitalized
Research asset
Capital expenditures will increase by the amount of R&D;
Depreciation will increase by the amortization of the research asset;
For all firms, the net cap ex will increase by the same amount as the
after-tax operating income.
Aswath Damodaran
55
The Statement of Cash Flows
Figure 4.3: Statem ent of Cash Flows
Net cash flow from operat ions,
aft er t axes and int erest expenses
Cash Flows From Operations
Includes divest it ure and acquisit ion
of real assets (capit al expenditures)
+ Cash Flows From Investing
and disposal and purchase of
financial asset s. Also includes
acquisitions of ot her firms.
Net cash flow from t he issue and
+ Cash Flows from Financing
repurchase of equity, from t he
issue and repayment of debt and aft er
dividend payment s
= Net Change in Cash Balance
Aswath Damodaran
56
The Financial perspective on cash flows

In financial analysis, we are much more concerned about
• Cash flows to the firm or operating cash flows, which are before cash
flows to debt and equity)
• Cash flows to equity, which are after cash flows to debt but prior to cash
flows to equity
Aswath Damodaran
57
Fundamentals of Valuation
Aswath Damodaran
58
Discounted Cashflow Valuation: Basis for
Approach
t = n CF
t
Value = 
t
t =1 (1+ r)
• where,
•
n = Life of the asset
•
CFt = Cashflow in period t
•
r = Discount rate reflecting the riskiness of the estimated cashflows
Aswath Damodaran
59
Two Measures of Cash Flows


Cash flows to Equity: Thesea are the cash flows generated by the
asset after all expenses and taxes, and also after payments due on the
debt. This cash flow, which is after debt payments, operating expenses
and taxes, is called the cash flow to equity investors.
Cash flow to Firm: There is also a broader definition of cash flow that
we can use, where we look at not just the equity investor in the asset,
but at the total cash flows generated by the asset for both the equity
investor and the lender. This cash flow, which is before debt payments
but after operating expenses and taxes, is called the cash flow to the
firm
Aswath Damodaran
60
Two Measures of Discount Rates


Cost of Equity: This is the rate of return required by equity investors
on an investment. It will incorporate a premium for equity risk -the
greater the risk, the greater the premium.
Cost of capital: This is a composite cost of all of the capital invested
in an asset or business. It will be a weighted average of the cost of
equity and the after-tax cost of borrowing.
Aswath Damodaran
61
Equity Valuation
Figure 5.5: Equity Valuation
Assets
Cash flows considered are
cashflows from assets,
after debt payments and
after making reinvestments
needed for future growth
Liabilities
Assets in P lace
Growth Assets
Debt
Equity
Discount rate reflects only the
cost of raising equity financing
P resent value is value of just the equity claims on the firm
Aswath Damodaran
62
Valuing Equity in a Finite Life Asset




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 - (1.0978)12 



1,000,000
Value of Equit y in St ore=
+
= $8,053,999
(.0978-.05)
(1.0978)12
Aswath Damodaran
63
Firm Valuation
Figure 5.6: Firm Valuation
Assets
Cash flows considered are
cashflows from assets,
prior to any debt payments
but after firm has
reinvested to create growth
assets
Liabilities
Assets in P lace
Growth Assets
Debt
Equity
Discount rate reflects the cost
of raising both debt and equity
financing, in proportion to their
use
P resent value is value of the entire firm, and reflects the value of
all claims on the firm.
Aswath Damodaran
64
Valuing a Finite-Life Asset



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%.
Aswath Damodaran
65
Expected Cash Flows and present value
Year
Expecte d Cash Flows
Value at End
1
$
1,050 ,0 00
$
958 ,8 17
2
$
1,102 ,5 0 0
$
919 ,3 29
3
$
1,157 ,6 25
$
881 ,4 68
4
$
1,215 ,5 06
$
845 ,1 66
5
$
1,276 ,2 82
$
810 ,3 59
6
$
1,340 ,0 96
$
776 ,9 86
7
$
1,407 ,1 00
$
744 ,9 87
8
$
1,477 ,4 55
$
714 ,3 06
9
$
1,551 ,3 28
$
684 ,8 88
10
$
1,628 ,8 95
$
656 ,6 82
11
$
1,710 ,3 39
$
629 ,6 38
12
$
1,795 ,8 56
$
1 ,4 44 ,1 24
$
2,500 ,0 00
Value of St ore =
Aswath Damodaran
PV at 9 .5 1%
$ 10 ,0 66 ,7 49
66
Valuation with Infinite Life
DISCOUNTED CASHFLOW VALUATION
Expecte d Gr ow th
Firm: Grow th in
Operating Earnings
Equity: Grow th in
Net Income/EPS
Cas h flow s
Firm: Pre-debt cash
f low
Equity: After debt
cash flow s
Firm is in stable grow th:
Grow s at constant rate
f orever
Terminal Value
Value
Firm: V alue of Firm
CF 1
CF 2
CF 3
CF 4
CF 5
CF n
.........
Forever
Equity: Value of Equity
Le ngth of Pe r iod of High Gr ow th
Dis count Rate
Firm:Cost of Capital
Equity: Cost of Equity
Aswath Damodaran
67
Valuing the Home Depot’s Equity

Assume that we expect the free cash flows to equity at th 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.
Aswath Damodaran
68
Estimating cash flows to equity: The Home
Depot
Year
Net Income
Reinvestment Needs
Net Debt
Issued
FCFE
PV of FCFE
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 =
Aswath Damodaran
$6,833
69
Terminal Value and Value of Equity today

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

Aswath Damodaran
70
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%.
Aswath Damodaran
71
Expected Cash Flows and Firm Value

Terminal Value = $ 1710 (1.05)/(.0917-.05) = $ 43,049 million
Year
Cash Flow
Terminal Value
1
$978
$895
2
$1,124
$943
3
$1,293
$994
4
$1,487
$1,047
5
$1,710
Value of Boeing as a firm =
Aswath Damodaran
$43,049
Present Value
$28,864
$32,743
72