THE TIME VALUE OF MONEY
Aswath Damodaran
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.
2
Discounting and Compounding

The mechanism for factoring in these elements is the 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) 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.
3
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.
That point of time can be today (present value) or a
point in time in the future (future value).
4
Time lines for cash flows


The best way to visualize cash flows is on a time line,
where you list out how much you get and when.
In a time line, today is specified as “time 0” and each
year is shown as a period.
Figure 3.1: A Time Line for Cash Flows: $ 100 in Cash Flows Received
at the End of Each of Next 4 years
Cash Flows
0
$ 100
$ 100
$ 100
1
2
3
$ 100
4
Year
5
Cash Flow Types and Discounting Mechanics

There are five types of cash flows 





simple cash flows,
annuities,
growing annuities
perpetuities and
growing perpetuities
Most assets represent combinations of these cash
flows. Thus, a conventional bond is a combination of
an annuity (coupons) and a simple cash flow (face
value at maturity). A stock may be a combination of
a growing annuity and a growing perpetuity.
6
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 is
PV 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

7
Application: The power of compounding Stocks, Bonds and Bills


Between 1926 and 2013, stocks on the average
made about 9.55% a year, while government bonds
on average made about 4.93% a year and T.Bills
earned 3.53% 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 = $ 109.55
 Value of $ 100 invested in bonds in one year = $ 104.93
 Value of $100 invested in T.Bills for one year= $103.53

8
Holding Period and Value
4500
4000
Future value of $100 investment
3500
3000
2500
Stocks ($)
2000
Treasury Bonds ($)
Treasury Bills ($)
1500
1000
500
0
1
5
10
20
30
40
Holding period (in years)
9
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?
a.
b.
c.

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?
a.
b.
Yes
No
10
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
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%
11
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, the time line looks as follows:
0
A
|
1
A
|
2
A
|
3
A
|
4
12
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 ù
é1 n
ê
(1 + r) ú
PV of an Annuity = PV(A,r, n) = A
ê
r
ú
ë
û
13
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 ù
é1 5
ê
(1.10) ú
PV of $1000 each year for next 5 years = $1000
= $3, 791
ê
.10
ú
ë
û

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).
14
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).
é
r
ê
Annuity given Present Value = A(PV, r,n) = PV
1
ê1 (1 + r)n
ë

ù
ú
ú
û
This, for instance, is the equation you would use to
determine your monthly payments on a home
mortgage.
15
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
é
ù
0.0067
ê
ú
Monthly Payment on Mortgage = $200, 000
= $1473.11
1
ê1 ú
(1.0067) 360 û
ë
16
Future Value of an Annuity

The future value of an end-of-the-period annuity can
also be calculated as followsé (1 + r)n - 1 ù
FV of an Annuity = FV(A,r,n) = A ê
úû
r
ë

This is the equation you would use to determine
how much money you will accumulate at a future
point in time if you set aside a constant amount each
period.
17
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) é(1.10) - 1 ù
FV of $1, 000 each year for next 5 years = $1000
= $6,105
êë
úû
.10
5

The notation that will be used for the future value of
an annuity will be FV(A,r,n).
18
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 é
r
ù
Annuity given Future Value = A(FV,r,n) = FV ê
n
ë (1+ r) - 1 úû
19
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%.



If you need to set aside a lump sum now, the amount you would
need to set aside would be 

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
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
20
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
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?
21
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
22
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
23
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?
24
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.
25
Bond Pricing Proposition 1
The longer the maturity of a bond, the more
sensitive it is to changes in interest rates.
Price Changes as a function of Bond Maturities
20.00%
15.00%
% Change in Price

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
26
Bond Pricing Proposition 2
The lower the coupon rate on the bond, the more
sensitive it is to changes in interest rates.
Bond Price Changes as a function of Coupon Rates
25.00%
20.00%
15.00%
% Price Change

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
27
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 –
28
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:
nù
é
(1+g)
ê1 ú
n
ê
(1+r) ú
PV of an Annuity = PV(A, r, g,n) = A(1 +g) ê
ú
ê (r - g) ú
êë
úû

In that specific case, the present value is equal to the
nominal sums of the annuities over the period, without
the growth effect.
29
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 –
é
(1.03) ù
1 20
ê
(1.10) ú
PV of extracted gold = $300 * 5000 * (1.03)
= $16,145,980
ê .10 - .03 ú
êë
úû
20
30
PV of Extracted Gold as a Function of Expected
Growth Rate
31
IV. Perpetuity

A perpetuity is a constant cash flow at regular
intervals forever. The present value of a perpetuity
isPV of Perpetuity =

A
r
Forever may be a tough concept for human beings to
grasp, but it makes the mathematics much simpler.
32
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
33
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 CF1
PV of Growing Perpetuity =
(r - g)
where
CF1 is the expected cash flow next year,
 g is the constant growth rate and
 r is the discount rate.

34
Valuing a Stock with Growing Dividends
In twelve months leading into January 2014, Con Ed
paid dividends per share of $2.52.
 Its earnings and dividends had grown at 2% a year
between 2004 and 2013 and were expected to grow
at the same rate in the long run.
 The rate of return required by investors on stocks of
equivalent risk was 7.50%.
 With these inputs, we can value the stock using a
perpetual growth model:
Value of Stock = $2.52 (1.02)/(0.075  0.02) = $46.73

35
Value and Growth!
36
FINANCIAL STATEMENT ANALYSIS
Questions we would like answered…
Assets
Liabilities
What are the assets in place?
How valuable are these assets?
How risky are these assets?
Assets in Place
Debt
What is the value of the debt?
How risky is the debt?
What are the growth assets?
How valuable are these assets?
Growth Assets
Equity
What is the value of the equity?
How risky is the equity?
38
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
39
The Balance Sheet
Figure 4.1: The Balance Sheet
Assets
Liabilities
Fixed Assets
Current
Liabilties
Current Assets
Debt
Debt obligations of firm
Investments in securities &
assets of other firms
Financial Investments
Other
Liabilities
Other long-term obligations
Assets which are not physical,
like patents & trademarks
Intangible Assets
Equity
Equity investment in firm
Long Lived Real Assets
Short-lived Assets
Short-term liabilities of the firm
40
A Financial Balance Sheet
Assets
Existing Investments
Generate cashflows today
Includes long lived (fixed) and
short-lived(working
capital) assets
Expected Value that will be
created by future investments
Liabilities
Assets in Place
Debt
Growth Assets
Equity
Fixed Claim on cash flows
Little or No role in management
Fixed Maturity
Tax Deductible
Residual Claim on cash flows
Significant Role in management
Perpetual Lives
41
The Income Statement
42
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.
43
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

44
Operating Leases at Boeing and The Home
Depot in 1998
Boeing
Year
Home Depot
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
Yr 6 -15
$
PV of Operating Lease Expenses
-
$
$
562.64
$ 2,647.70
45
Imputed Interest Expenses on Operating Leases
PV of Operating Leases
Interest rate on Debt
Imputed interest expense on PV of operating leases
Boeing
$ 562.64
5.50%
$ 30.95
The Home Depot
$ 2647.70
5.80%
$ 153.57
46
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
47
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...: 48

Capitalizing R&D Expenses: Boeing
49
Boeing’s Corrected Operating Income
Operating Income
+ Research and Deve lopment Expenses
- Amortization of Research Asset
+ Imputed Interest Expense on Operating
Leases
= Adjusted Operating Income
Boeing
$1,720
$1,895
$1,382
$
31
$2,264
50
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 51
The Statement of Cash Flows
Figure 4.3: Statement of Cash Flows
Net cash flow from operations,
after taxes and interest expenses
Cash Flows From Operations
Includes divestiture and acquisition
of real assets (capital expenditures)
and disposal and purchase of
financial assets. Also includes
acquisitions of other firms.
+ Cash Flows From Investing
Net cash flow from the issue and
repurchase of equity, from the
issue and repayment of debt and after
dividend payments
+ Cash Flows from Financing
= Net Change in Cash Balance
52
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

53
FUNDAMENTALS OF VALUATION
Discounted Cashflow Valuation: Basis for
Approach
t = n CF
t
Value = å
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

55
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
56
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 aftertax cost of borrowing.
57
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 Place
Growth Assets
Debt
Equity
Discount rate reflects only the
cost of raising equity financing
Present value is value of just the equity claims on the firm
58
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
æ
store, after repaying
remaining
(1.05) ö÷debt will be $ 1
ç
850,000 (1.05) ç1 (1.0978) ÷ø
è
1,000,000
million.
Value of Equity in Store =
+
= $8,053,999
(.0978 -.05)
(1.0978)
Finally, assume that the cost of equity is 9.78%.
12
12
12

59
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 Place
Growth Assets
Debt
Equity
Discount rate reflects the cost
of raising both debt and equity
financing, in proportion to their
use
Present value is value of the entire firm, and reflects the value of
all claims on the firm.
60
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%.
61
Expected Cash Flows and present value
62
Valuation with Infinite Life
63
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 that64

Estimating cash flows to equity: The Home
Depot
Year
Net Income
Reinvestment Needs
1
$
1,856
$
1,392
Net Debt
Issued
$
(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 =
FCFE
PV of FCFE
$6,833
65
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.
66
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%.
67
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 =
$43,049
Present Value
$28,864
$32,743
68