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Asw
ath Dam
odaran158
Measuring Investm
ent Returns
Stern School of Business
Asw
ath Dam
odaran159
First P
rinciples
Invest in projects that yield a return greater than the minim
umacceptable hurdle rate.•
The hurdle rate should be higher for riskier projects and reflect the
financing mix used - ow
ners’ funds (equity) or borrowed m
oney (debt)
•R
eturns on projects should be measured based on cash flow
sgenerated and the tim
ing of these cash flows; they should also
consider both positive and negative side effects of these projects.
Choose a financing m
ix that minim
izes the hurdle rate and matches the
assets being financed.
If there are not enough investments that earn the hurdle rate, return the
cash to stockholders.•
The form
of returns - dividends and stock buybacks - will depend upon
the stockholders’ characteristics.
Asw
ath Dam
odaran160
Measures of return: earnings versus cash flow
s
Principles Governing A
ccounting Earnings M
easurement
•A
ccrual Accounting: Show
revenues when products and services are sold
or provided, not when they are paid for. Show
expenses associated with
these revenues rather than cash expenses.
•O
perating versus Capital E
xpenditures: Only expenses associated w
ithcreating revenues in the current period should be treated as operatingexpenses. E
xpenses that create benefits over several periods are written
off over multiple periods (as depreciation or am
ortization)
To get from
accounting earnings to cash flows:
•you have to add back non-cash expenses (like depreciation)
•you have to subtract out cash outflow
s which are not expensed (such as
capital expenditures)
•you have to m
ake accrual revenues and expenses into cash revenues andexpenses (by considering changes in w
orking capital).
Asw
ath Dam
odaran161
Measuring R
eturns Right: T
he Basic P
rinciples
Use cash flow
s rather than earnings. You cannot spend earnings.
Use “increm
ental” cash flows relating to the investm
ent decision, i.e.,cashflow
s that occur as a consequence of the decision, rather than totalcash flow
s.
Use “tim
e weighted” returns, i.e., value cash flow
s that occur earlierm
ore than cash flows that occur later.
The R
eturn Mantra: “T
ime-w
eighted, Incremental C
ash FlowR
eturn”
Asw
ath Dam
odaran162
Earnings versus C
ash Flow
s: A D
isney Them
eP
ark
The them
e parks to be built near Bangkok, m
odeled on Euro D
isney inParis, w
ill include a “Magic K
ingdom” to be constructed, beginning
imm
ediately, and becoming operational at the beginning of the second
year, and a second theme park m
odeled on Epcot C
enter at Orlando to
be constructed in the second and third year and becoming operational
at the beginning of the fifth year.
The earnings and cash flow
s are estimated in nom
inal U.S. D
ollars.
Asw
ath Dam
odaran163
Key A
ssumptions on S
tart Up and C
onstruction
Disney has already spent $ 500 m
illion researching the location andgetting the needed licenses for the park.
The cost of constructing M
agic Kingdom
will be $ 3 billion, w
ith $ 2billion invested up front, and $ 1 billion at the end of year 1.
The cost of constructing E
pcot will be $ 1.5 billion, w
ith $ 1 billionbeing spent in year 2 and $ 0.5 billion in year 3.
Asw
ath Dam
odaran164
Key R
evenue Assum
ptions
Revenue estim
ates for the parks and resort properties (in millions)
Year
Magic K
ingdomE
pcotR
esort Hotels
Total R
evenues
1$0
$0 $0
$0
2$1,000
$0 $200
$1,200
3$1,400
$0 $250
$1,650
4$1,700
$0 $300
$2,000
5$2,000
$500 $375
$2,875
6$2,200
$550 $688
$3,438
7$2,420
$605 $756
$3,781
8$2,662
$666 $832
$4,159
9$2,928
$732 $915
$4,575
10 on G
rows at the inflation rate forever: 3%
Asw
ath Dam
odaran165
Key E
xpense Assum
ptions
The operating expenses are assum
ed to be 60% of the revenues at the
parks, and 75% of revenues at the resort properties.
Disney w
ill also allocate the following portion of its general and
administrative expenses to the them
e parks. It is worth noting that a
recent analysis of these expenses found that only one-third of theseexpenses are variable (and a function of total revenue) and that tw
o-thirds are fixed. (in m
illions)
Year
G&
A C
ostsY
earG
& A
Costs
1$0
6$ 293
2$200
7$ 322
3$220
8$354
4$242
9$390
5$266
10 onG
row at inflation rate of 3%
Asw
ath Dam
odaran166
Depreciation and C
apital Maintenance
Year
Depreciation
Capital E
xpenditure
1$0
$0
2$375
$150
3$378
$206
4$369
$250
5$319
$359
6$302
$344
7$305
$303
8$305
$312
9$305
$343
10 $315
$315
After
Offsetting: D
epreciation = C
apital Maintenance
Asw
ath Dam
odaran167
Other A
ssumptions
Disney w
ill have to maintain net w
orking capital (primarily consisting
of inventory at the theme parks and the resort properties, netted against
accounts payable) of 5% of revenues, w
ith the investments in w
orkingcapital being m
ade at the end of each year.
The incom
e from the investm
ent will be taxed at a m
arginal tax rate of36%
.
Asw
ath Dam
odaran168
Earnings on P
roject
01
23
45
67
89
10
Revenues
Magic K
ingdom1
,00
0$
1,4
00
$ 1
,70
0$
2,0
00
$ 2
,20
0$
2,4
20
$ 2
,66
2$
2,9
28
$ 3
,01
6$
Second T
heme P
ark5
00
$ 5
50
$ 6
05
$ 6
66
$ 7
32
$ 7
54
$ R
eso
rt & P
rop
ertie
s2
00
$ 2
50
$ 3
00
$ 3
75
$ 6
88
$ 7
56
$ 8
32
$ 9
15
$ 9
43
$ T
ota
l1
,20
0$
1,6
50
$ 2
,00
0$
2,8
75
$ 3
,43
8$
3,7
81
$ 4
,15
9$
4,5
75
$ 4
,71
3$
Operating E
xpensesM
agic Kingdom
60
0$
84
0$
1,0
20
$ 1
,20
0$
1,3
20
$ 1
,45
2$
1,5
97
$ 1
,75
7$
1,8
10
$ S
econd Them
e Park
-$
-$
-$
30
0$
33
0$
36
3$
39
9$
43
9$
45
2$
Re
sort &
Pro
pe
rty1
50
$ 1
88
$ 2
25
$ 2
81
$ 5
16
$ 5
67
$ 6
24
$ 6
86
$ 7
07
$ T
ota
l7
50
$ 1
,02
8$
1,2
45
$ 1
,78
1$
2,1
66
$ 2
,38
2$
2,6
20
$ 2
,88
2$
2,9
69
$
Other E
xpensesD
ep
recia
tion
& A
mo
rtizatio
n3
75
$ 3
78
$ 3
69
$ 3
19
$ 3
02
$ 3
05
$ 3
05
$ 3
05
$ 3
15
$ A
llocated G&
A C
osts2
00
$ 2
20
$ 2
42
$ 2
66
$ 2
93
$ 3
22
$ 3
54
$ 3
90
$ 4
01
$
Operating Incom
e(1
25
)$
25
$ 1
44
$ 5
09
$ 6
77
$ 7
72
$ 8
80
$ 9
98
$ 1
,02
8$
Taxes
(45
)$
9$
52
$ 1
83
$ 2
44
$ 2
78
$ 3
17
$ 3
59
$ 3
70
$ O
perating Income after T
axes(8
0)
$ 1
6$
92
$ 3
26
$ 4
33
$ 4
94
$ 5
63
$ 6
39
$ 6
58
$
Asw
ath Dam
odaran169
And the A
ccounting View
of Return
YearEBIT(1-t)
Beg BVDeprecn
Cap ExEnd BV
Avge BvROC
0$0
$2,500$2,500
1$0
$2,500$0
$1,000$3,500
$3,0002
($80)$3,500
$375$1,150
$4,275$3,888
-2.06%3
$16$4,275
$378$706
$4,604$4,439
0.36%4
$92$4,604
$369$250
$4,484$4,544
2.02%5
$326$4,484
$319$359
$4,525$4,505
7.23%6
$433$4,525
$302$344
$4,567$4,546
9.53%7
$494$4,567
$305$303
$4,564$4,566
10.82%8
$563$4,564
$305$312
$4,572$4,568
12.33%9
$639$4,572
$305$343
$4,609$4,590
13.91%10
$658$4,609
$315$315
$4,609$4,609
14.27%Average
7.60%
Asw
ath Dam
odaran170
Would lead use to conclude that...
Do not invest in this park. T
he return on capital of 7.60% is low
erthan the cost of capital for them
e parks of 12.32%; T
his would
suggest that the project should not be taken.
Given that w
e have computed the average over an arbitrary period of
10 years, while the them
e park itself would have a life greater than 10
years, would you feel com
fortable with this conclusion?
Yes
No
Asw
ath Dam
odaran171
From
Project to F
irm R
eturn on Capital: D
isneyin 1997
Just as a comparison of project return on capital to the cost of capital
yields a measure of w
hether the project is acceptable, a comparison
can be made at the firm
level, to judge whether the existing projects of
the firm are adding or destroying value.
Disney, in 1996, had earnings before interest and taxes of $5,559
million, had a book value of equity of $11,368 m
illion and a bookvalue of debt of $7,663 m
illion. With a tax rate of 36%
, we get
Return on C
apital = 5559 (1-.36) / (11,368+
7,663) = 18.69%
Cost of C
apital for Disney=
12.22%
Excess R
eturn = 18.69%
- 12.22% =
6.47%
This can be converted into a dollar figure by m
ultiplying by the capitalinvested, in w
hich case it is called economic value added
EV
A =
(.1869-.1222) (11,368+7,663) =
$1,232 million
Asw
ath Dam
odaran172
A
pplication Test: A
ssessing Investment
Quality
For the most recent period for w
hich you have data, compute the after-
tax return on capital earned by your firm, w
here after-tax return oncapital is com
puted to be
After-tax R
OC
= E
BIT
(1-tax rate)/ (BV
of debt + B
V of E
quity)previous yearFor the m
ost recent period for which you have data, com
pute thereturn spread earned by your firm
:
Return Spread =
After-tax R
OC
- Cost of C
apital
For the most recent period, com
pute the EV
A earned by your firm
EV
A =
Return Spread * ((B
V of debt +
BV
of Equity)previous year
Asw
ath Dam
odaran173
The cash flow
view of this project..
•0
12
39
10Operating Income after Taxes
(80)$
16$
639$
658$
+ Depreciation & Amortization-
$ -
$ 375
$ 378
$ 305
$ 315
$ - Capital Expenditures
2,500$
1,000$
1,150$
706$
343$
315$
- Change in Working Capital-
$ -
$ 60
$ 23
$ 21
$ 7
$ Cash Flow on Project
(2,500)$
(1,000)$
(915)$
(335)$
580$
651$
To get from
income to cash flow
, we
added back all non-cash charges such as depreciation
subtracted out the capital expenditures
subtracted out the change in non-cash working capital
Asw
ath Dam
odaran174
The D
epreciation Tax B
enefit
While depreciation reduces taxable incom
e and taxes, it does notreduce the cash flow
s.
The benefit of depreciation is therefore the tax benefit. In general, the
tax benefit from depreciation can be w
ritten as:
Tax B
enefit = D
epreciation * Tax R
ate
For example, in year 2, the tax benefit from
depreciation to Disney
from this project can be w
ritten as:
Tax B
enefit in year 2 = $ 375 m
illion (.36) = $ 135 m
illion
Proposition 1: T
he tax benefit from depreciation and other non-cash
charges is greater, the higher your tax rate.
Proposition 2: N
on-cash charges that are not tax deductible (such asam
ortization of goodwill) and thus provide no tax benefits have no
effect on cash flows.
Asw
ath Dam
odaran175
Depreciation M
ethods
Broadly categorizing, depreciation m
ethods can be classified asstraight line or accelerated m
ethods. In straight line depreciation, thecapital expense is spread evenly over tim
e, In accelerated depreciation,the capital expense is depreciated m
ore in earlier years and less in lateryears. A
ssume that you m
ade a large investment this year, and that you
are choosing between straight line and accelerated depreciation
methods. W
hich will result in higher net incom
e this year?
Straight Line D
epreciation
Accelerated D
epreciation
Which w
ill result in higher cash flows this year?
Straight Line D
epreciation
Accelerated D
epreciation
Asw
ath Dam
odaran176
The C
apital Expenditures E
ffect
Capital expenditures are not treated as accounting expenses but they
do cause cash outflows.
Capital expenditures can generally be categorized into tw
o groups•
New
(or Grow
th) capital expenditures are capital expenditures designed tocreate new
assets and future growth
•M
aintenance capital expenditures refer to capital expenditures designed tokeep existing assets.
Both initial and m
aintenance capital expenditures reduce cash flows
The need for m
aintenance capital expenditures will increase w
ith thelife of the project. In other w
ords, a 25-year project will require m
orem
aintenance capital expenditures than a 2-year asset.
Asw
ath Dam
odaran177
To cap ex or not to cap ex
Assum
e that you run your own softw
are business, and that you have anexpense this year of $ 100 m
illion from producing and distribution
promotional C
Ds in softw
are magazines. Y
our accountant tells youthat you can expense this item
or capitalize and depreciate. Which w
illhave a m
ore positive effect on income?
Expense it
Capitalize and D
epreciate it
Which w
ill have a more positive effect on cash flow
s?
Expense it
Capitalize and D
epreciate it
Asw
ath Dam
odaran178
The W
orking Capital E
ffect
Intuitively, money invested in inventory or in accounts receivable
cannot be used elsewhere. It, thus, represents a drain on cash flow
s
To the degree that som
e of these investments can be financed using
suppliers credit (accounts payable) the cash flow drain is reduced.
Investments in w
orking capital are thus cash outflows
•A
ny increase in working capital reduces cash flow
s in that year
•A
ny decrease in working capital increases cash flow
s in that year
To provide closure, w
orking capital investments need to be salvaged at
the end of the project life.
Proposition 1: T
he failure to consider working capital in a capital
budgeting project will overstate cash flow
s on that project and make it
look more attractive than it really is.
Proposition 2: O
ther things held equal, a reduction in working capital
requirements w
ill increase the cash flows on all projects for a firm
.
Asw
ath Dam
odaran179
The increm
ental cash flows on the project
01
23
910
Cash Flow on Project(2,500)
$ (1,000)
$ (915)
$ (335)
$ 580
$ 651
$ + Sunk Costs
500$
+ Non-incr. Alloc Cost (1-t)-
$ -
$ 85
$ 94
$ 166
$ 171
$ Incremental Cash Flow on Project
(2,000)$
(1,000)$
(830)$
(241)$
746$
822$
To get from
cash flow to increm
ental cash flows, w
e
Taken out of the sunk costs from
the initial investment
Added back the non-increm
ental allocated costs (in after-tax terms)
Asw
ath Dam
odaran180
Sunk C
osts
Any expenditure that has already been incurred, and cannot be
recovered (even if a project is rejected) is called a sunk cost
When analyzing a project, sunk costs should not be considered since
they are incremental
By this definition, m
arket testing expenses and R&
D expenses are
both likely to be sunk costs before the projects that are based uponthem
are analyzed. If sunk costs are not considered in project analysis,how
can a firm ensure that these costs are covered?
Asw
ath Dam
odaran181
Allocated C
osts
Firms allocate costs to individual projects from
a centralized pool(such as general and adm
inistrative expenses) based upon some
characteristic of the project (sales is a comm
on choice)
For large firms, these allocated costs can result in the rejection of
projects
To the degree that these costs are not increm
ental (and would exist
anyway), this m
akes the firm w
orse off.•
Thus, it is only the increm
ental component of allocated costs that should
show up in project analysis.
How
, looking at these pooled expenses, do we know
how m
uch of thecosts are fixed and how
much are variable?
Asw
ath Dam
odaran182
The Increm
ental Cash F
lows
01
23
45
67
89
10
Operating Incom
e after Taxes
(8
0)
$ 1
6$
92
$ 3
26
$
43
3$
49
4$
56
3$
6
39
$ 6
58
$ +
De
pre
ciatio
n &
Am
ortiza
tion
37
5$
37
8$
36
9$
31
9$
3
02
$ 3
05
$ 3
05
$
30
5$
31
5$
- Capital E
xpenditures2
,00
0$
1,0
00
$ 1
,15
0$
70
6$
25
0$
35
9$
3
44
$ 3
03
$ 3
12
$
34
3$
31
5$
- Change in W
orking Capital
60
$ 2
3$
18
$ 4
4$
28
$ 1
7$
19
$ 2
1$
7$
+ N
on
-incre
m. A
lloca
ted
Co
st(1-t)
85
$ 9
4$
10
3$
11
4$
1
25
$ 1
37
$ 1
51
$
16
6$
17
1$
Cashflow
to Firm
(2,0
00
)$
(1
,00
0)
$
(83
0)
$ (2
41
)$
29
7$
35
5$
4
88
$ 6
17
$ 6
88
$
74
6$
82
2$
Asw
ath Dam
odaran183
To T
ime-W
eighted Cash F
lows
Incremental cash flow
s in the earlier years are worth m
ore thanincrem
ental cash flows in later years.
In fact, cash flows across tim
e cannot be added up. They have to be
brought to the same point in tim
e before aggregation.
This process of m
oving cash flows through tim
e is•
discounting, when future cash flow
s are brought to the present
•com
pounding, when present cash flow
s are taken to the future
The discounting and com
pounding is done at a discount rate that will
reflect•
Expected inflation: H
igher Inflation -> H
igher Discount R
ates
•E
xpected real rate: Higher real rate ->
Higher D
iscount rate
•E
xpected uncertainty: Higher uncertainty ->
Higher D
iscount Rate
Asw
ath Dam
odaran184
Present V
alue Mechanics
Cash Flow
Type
Discounting Form
ulaC
ompounding Form
ula
1. Simple C
F C
Fn / (1+
r) n C
F0 (1+
r) n
2. Annuity
3. Grow
ing Annuity
4. PerpetuityA
/r
5. Grow
ing PerpetuityE
xpected Cashflow
next year/(r-g)
A
1 - 1
(1+
r)r
n
A
(1+
r) - 1
r n
A(1
+g)
1 - (1+
g)
(1+
r)r-g
nn
Asw
ath Dam
odaran185
Discounted cash flow
measures of return
Net P
resent Value (N
PV
): The net present value is the sum
of thepresent values of all cash flow
s from the project (including initial
investment).
NPV
= Sum
of the present values of all cash flows on the project, including
the initial investment, w
ith the cash flows being discounted at the
appropriate hurdle rate (cost of capital, if cash flow is cash flow
to thefirm
, and cost of equity, if cash flow is to equity investors)
•D
ecision Rule: A
ccept if NPV
> 0
Internal Rate of R
eturn (IRR
): The internal rate of return is the
discount rate that sets the net present value equal to zero. It is thepercentage rate of return, based upon increm
ental time-w
eighted cashflow
s.•
Decision R
ule: Accept if IR
R >
hurdle rate
Asw
ath Dam
odaran186
Closure on C
ash Flow
s
In a project with a finite and short life, you w
ould need to compute a
salvage value, which is the expected proceeds from
selling all of theinvestm
ent in the project at the end of the project life. It is usually setequal to book value of fixed assets and w
orking capitalIn a project w
ith an infinite or very long life, we com
pute cash flows
for a reasonable period, and then compute a term
inal value for thisproject, w
hich is the present value of all cash flows that occur after the
estimation period ends..
Assum
ing the project lasts forever, and that cash flows after year 9
grow 3%
(the inflation rate) forever, the present value at the end ofyear 9 of cash flow
s after that can be written as:
•T
erminal V
alue = C
F in year 10/(Cost of C
apital - Grow
th Rate)
= 822/(.1232-.03) =
$ 8,821 million
Note that this is the term
inal value in year 9; So cash flow in year 10 is used.
Asw
ath Dam
odaran187
Which yields a N
PV
of..
Ye
ar
Incre
me
nta
l CF
Te
rmin
al V
alu
eP
V a
t 12
.32
%0
(2,0
00
)$
(2
,00
0)
$
1(1
,00
0)
$
(89
0)
$
2(8
30
)$
(6
58
)$
3
(24
1)
$
(17
0)
$
42
97
$
18
7$
5
35
5$
1
98
$
64
88
$
24
3$
7
61
7$
2
73
$
86
88
$
27
2$
9
74
6$
8
,82
1$
3
,36
3$
N
et P
rese
nt V
alu
e o
f Pro
ject =
81
8$
Asw
ath Dam
odaran188
Which m
akes the argument that..
The project should be accepted
. The positive net present value
suggests that the project will add value to the firm
, and earn a return inexcess of the cost of capital.
By taking the project, D
isney will increase its value as a firm
by $818m
illion.
Asw
ath Dam
odaran189
The IR
R of this project
NP
V P
rofile
for T
he
me
Pa
rk
($3
,00
0)
($2
,00
0)
($1
,00
0)
$0
$1
,00
0
$2
,00
0
$3
,00
0
$4
,00
0
$5
,00
0
$6
,00
0
$7
,00
0
$8
,00
0
0 %
2 %
4 %
6 %
8 %
1 0 %
1 2 %
1 4 %
1 6 %
1 8 %
2 0 %
2 2 %
2 4 %
2 6 %
2 8 %
3 0 %
3 2 %
3 4 %
3 6 %
3 8 %
4 0 %
Dis
co
un
t R
ate
NPV
Asw
ath Dam
odaran190
The IR
R suggests..
The project is a good one. U
sing time-w
eighted, incremental cash
flows, this project provides a return of 15.32%
. This is greater than the
cost of capital of 12.32%.
The IR
R and the N
PV w
ill yield similar results m
ost of the time,
though there are differences between the tw
o approaches that may
cause project rankings to vary depending upon the approach used.
Asw
ath Dam
odaran191
Case 1: IR
R versus N
PV
Consider a project w
ith the following cash flow
s:
Year
Cash F
low
0-1000
1800
21000
31300
4-2200
Asw
ath Dam
odaran192
Project’s N
PV
Profile
($100.00)
($80.00)
($60.00)
($40.00)
($20.00)
$0.00
$20.00
$40.00
$60.00
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
22%
24%
26%
28%
30%
32%
34%
36%
38%
40%
42%
44%
46%
48%
50%
Discount R
ate
NPV
Asw
ath Dam
odaran193
What do w
e do now?
This project has tw
o internal rates of return. The first is 6.60%
,w
hereas the second is 36.55%.
Why are there tw
o internal rates of return on this project?
If your cost of capital is 12.32%, w
ould you accept or reject thisproject?
I would reject the project
I would accept this project
Explain.
Asw
ath Dam
odaran194
Case 2: N
PV
versus IRR
Cash Flow
Investment
$ 350,000
$ 1,000,000
Project A
Cash Flow
Investment
Project B
NPV
= $467,937
IRR
= 33.66%
$ 450,000$ 600,000
$ 750,000
NPV
= $1,358,664
IRR
=20.88%
$ 10,000,000
$ 3,000,000$ 3,500,000
$ 4,500,000$ 5,500,000
Asw
ath Dam
odaran195
Which one w
ould you pick?
Assum
e that you can pick only one of these two projects. Y
our choicew
ill clearly vary depending upon whether you look at N
PV or IR
R.
You have enough m
oney currently on hand to take either. Which one
would you pick?
Project A. It gives m
e the bigger bang for the buck and more m
arginfor error.
Project B. It creates m
ore dollar value in my business.
If you pick A, w
hat would your biggest concern be?
If you pick B, w
hat would your biggest concern be?
Asw
ath Dam
odaran196
Capital R
ationing, Uncertainty and C
hoosing aR
ule
If a business has limited access to capital, has a stream
of surplus valueprojects and faces m
ore uncertainty in its project cash flows, it is m
uchm
ore likely to use IRR
as its decision rule.
Small, high-grow
th companies and private businesses are m
uch more
likely to use IRR
.
If a business has substantial funds on hand, access to capital, limited
surplus value projects, and more certainty on its project cash flow
s, itis m
uch more likely to use N
PV as its decision rule.
As firm
s go public and grow, they are m
uch more likely to gain from
using NPV
.
Asw
ath Dam
odaran197
An A
lternative to IRR
with C
apital Rationing
The problem
with the N
PV rule, w
hen there is capital rationing, is thatit is a dollar value. It m
easures success in absolute terms.
The N
PV can be converted into a relative m
easure by dividing by theinitial investm
ent. This is called the profitability index.
•Profitability Index (PI) =
NPV
/Initial Investment
In the example described, the PI of the tw
o projects would have been:
•PI of Project A
= $467,937/1,000,000 =
46.79%
•PI of Project B
= $1,358,664/10,000,000 =
13.59%
Project A w
ould have scored higher.
Asw
ath Dam
odaran198
Case 3: N
PV
versus IRR
Cash Flow
Investment
$ 5,000,000
$ 10,000,000
Project A
Cash Flow
Investment
Project B
NPV
= $1,191,712
IRR
=21.41%
$ 4,000,000$ 3,200,000
$ 3,000,000
NPV
= $1,358,664
IRR
=20.88%
$ 10,000,000
$ 3,000,000$ 3,500,000
$ 4,500,000$ 5,500,000
Asw
ath Dam
odaran199
Why the difference?
These projects are of the sam
e scale. Both the N
PV and IR
R use tim
e-w
eighted cash flows. Y
et, the rankings are different. Why?
Which one w
ould you pick?
Project A. It gives m
e the bigger bang for the buck and more m
arginfor error.
Project B. It creates m
ore dollar value in my business.
Asw
ath Dam
odaran200
NP
V, IR
R and the R
einvestment R
ateA
ssumption
The N
PV rule assum
es that intermediate cash flow
s on the project getreinvested at the hurdle rate (w
hich is based upon what projects of
comparable risk should earn).
The IR
R rule assum
es that intermediate cash flow
s on the project getreinvested at the IR
R. Im
plicit is the assumption that the firm
has aninfinite stream
of projects yielding similar IR
Rs.
Conclusion: W
hen the IRR
is high (the project is creating significantsurplus value) and the project life is long, the IR
R w
ill overstate thetrue return on the project.
Asw
ath Dam
odaran201
Solution to R
einvestment R
ate Problem
Cash Flow
Investment
$ 300$ 400
$ 500$ 600
<$ 1000>
$300(1.15) 3
$400(1.15) 2 $500(1.15)$600$575
$529
$456
Term
inal Value =
$2160
Internal Rate of R
eturn = 24.89%
Modified Internal R
ate of Return =
21.23%
Asw
ath Dam
odaran202
Why N
PV
and IRR
may differ..
A project can have only one N
PV, w
hereas it can have more than one
IRR
.
The N
PV is a dollar surplus value, w
hereas the IRR
is a percentagem
easure of return. The N
PV is therefore likely to be larger for “large
scale” projects, while the IR
R is higher for “sm
all-scale” projects.
The N
PV assum
es that intermediate cash flow
s get reinvested at the“hurdle rate”, w
hich is based upon what you can m
ake on investments
of comparable risk, w
hile the IRR
assumes that interm
ediate cashflow
s get reinvested at the “IRR
”.
Asw
ath Dam
odaran203
Case: N
PV
and Project Life
Project A
-$1500
$350$350
$350$350
$350
-$1000
$400$400
$400$400
$400
$350$350
$350$350
$350
Project B
NPV
of Project A =
$ 442
NPV
of Project B =
$ 478
Hurdle R
ate for Both Projects =
12%
Asw
ath Dam
odaran204
Choosing B
etween M
utually Exclusive P
rojects
The net present values of m
utually exclusive projects with different
lives cannot be compared, since there is a bias tow
ards longer-lifeprojects.
To do the com
parison, we have to
•replicate the projects till they have the sam
e life (or)
•convert the net present values into annuities
Asw
ath Dam
odaran205
Solution 1: P
roject Replication
Project A: R
eplicated
-$1500
$350$350
$350$350
$350$350
$350$350
$350$350
Project B
-$1000
$400$400
$400$400
$400$400
$400$400
$400$400
-$1000 (Replication)
NPV
of Project A replicated =
$ 693
NPV
of Project B=
$ 478
Asw
ath Dam
odaran206
Solution 2: E
quivalent Annuities
Equivalent A
nnuity for 5-year project=
$442 * PV(A
,12%,5 years)
= $ 122.62
Equivalent A
nnuity for 10-year project =
$478 * PV(A
,12%,10 years)
= $ 84.60
Asw
ath Dam
odaran207
What w
ould you choose as your investment
tool?
Given the advantages/disadvantages outlined for each of the different
decision rules, which one w
ould you choose to adopt?
Return on Investm
ent (RO
E, R
OC
)
Payback or Discounted Payback
Net Present V
alue
Internal Rate of R
eturn
Profitability Index
Asw
ath Dam
odaran208
What firm
s actually use ..
Decision R
ule%
of Firm
s using as primary decision rule in
19761986
IRR
53.6%49.0%
Accounting R
eturn25.0%
8.0%
NPV
9.8%21.0%
Payback Period8.9%
19.0%
Profitability Index2.7%
3.0%
Asw
ath Dam
odaran209
The D
isney Them
e Park: T
he Risks of
International Expansion
The cash flow
s on the Bangkok D
isney park will be in T
hai Baht.
This w
ill expose Disney to exchange rate risk. In addition, there are
political and economic risks to consider in an investm
ent in Thailand.
The discount rate of 12.32%
that we used is a cost of capital for U
.S.them
e parks. Would you use a higher rate for this project?
Yes
No
Asw
ath Dam
odaran210
Should there be a risk prem
ium for foreign
projects?
The exchange rate risk m
ay be diversifiable risk (and hence should notcom
mand a prem
ium) if
•the com
pany has projects is a large number of countries (or)
•the investors in the com
pany are globally diversified.
For Disney, this risk should not affect the cost of capital used.
The sam
e diversification argument can also be applied against political
risk, which w
ould mean that it too should not affect the discount rate.
It may, how
ever, affect the cash flows, by reducing the expected life or
cash flows on the project.
For Disney, this risk too is assum
ed to not affect the cost of capital
Asw
ath Dam
odaran211
Dom
estic versus international expansion
The analysis w
as done in dollars. Would the conclusions have been
any different if we had done the analysis in T
hai Baht?
Yes
No
Asw
ath Dam
odaran212
The ‘‘C
onsistency Rule” for C
ash Flow
s
The cash flow
s on a project and the discount rate used should bedefined in the sam
e terms.
•If cash flow
s are in dollars (baht), the discount rate has to be a dollar(baht) discount rate
•If the cash flow
s are nominal (real), the discount rate has to be nom
inal(real).
If consistency is maintained, the project conclusions should be
identical, no matter w
hat cash flows are used.
Asw
ath Dam
odaran213
Disney T
heme P
ark: Project A
nalysis in Baht
The inflation rates w
ere assumed to be 15%
in Thailand and 3%
in theU
nited States. The B
aht/dollar rate at the time of the analysis w
as 35B
T/dollar.
The expected exchange rate w
as derived assuming purchasing pow
erparity.E
xpected Exchange R
atet =
Exchange R
ate today * (1.15/1.03) t
The expected grow
th rate after year 9 is still expected to be theinflation rate, but it is the 15%
Thai inflation rate.
The cost of capital in B
aht was derived from
the cost of capital indollars and the differences in inflation rates:B
aht Cost of C
apital =( 1 +
$ Cost of C
apital)*(1.15/1.03) - 1
= (1.1232) (1.15/1.03) - 1 =
.2541 or 25.41%
Asw
ath Dam
odaran214
Disney T
heme P
ark: The B
aht NP
V
Year
$ Cash Flow
sE
xchange Rate
BT
Cash Flow
sT
erminal V
alueT
otal FCFF
PV of FC
FF0
(2,000.00)$
35.00($70,000 B
t)($70,000 B
t)(70,000 B
t)1
(890.31)$
39.08($39,078 B
t)($39,078 B
t)(31,161 B
t)2
(657.64)$
43.63($36,199 B
t)($36,199 B
t)(23,017 B
t)3
(170.35)$
48.71($11,759 B
t)($11,759 B
t)(5,962 B
t)4
186.63$
54.3916,155
Bt
16,155B
t6,532
Bt
5198.49
$ 60.73
21,548B
t21,548
Bt
6,947B
t6
243.21$
67.8033,109
Bt
33,109B
t8,512
Bt
7273.49
$ 75.70
46,692B
t46,692
Bt
9,572B
t8
271.69$
84.5258,169
Bt
58,169B
t9,509
Bt
9746.27
$ 94.37
70,423B
t832,421
Bt
902,843B
t117,694
Bt
NPV
28,626B
t
NPV
= 28,626 B
t/35 Bt =
$ 818 Million
NPV
is equal to NPV
in dollar terms
Asw
ath Dam
odaran215
Dealing w
ith Inflation
In our analysis, we used nom
inal dollars and Bt. W
ould the NPV
havebeen different if w
e had used real cash flows instead of nom
inal cashflow
s?
It would be m
uch lower, since real cash flow
s are lower than nom
inalcash flow
s
It would be m
uch higher
It should be unaffected
Asw
ath Dam
odaran216
Disney T
heme P
ark
The nom
inal cash flows in B
t are deflated first at the inflation rate:•
Real C
ash Flows
t = N
ominal C
ash Flowt /(1+
Inflation Rate) t
The real cost of capital is obtained by deflating the nom
inal discountrate at the inflation rate.•
Real C
ost of Capital =
(1+N
ominal C
ost of Capital)/(1+
Inflation Rate) - 1
•For the them
e park, this would be:
Real C
ost of Capital =
1.25411/1.15 -1 = 9.05%
Asw
ath Dam
odaran217
Disney T
heme P
ark: Real N
PV
Year
Nom
inal CF (B
t)R
eal CF
PV at
0(70,000 B
t)(70,000 B
t)(70,000 B
t)
1(39,078 B
t)(33,981 B
t)(31,161 B
t)
2(36,199 B
t)(27,371 B
t)(23,017 B
t)
3(11,759 B
t)(7,731 B
t)(5,962 B
t)
416,155 B
t9,237 B
t6,532 B
t
521,548 B
t10,713 B
t6,947 B
t
633,109 B
t14,314 B
t8,512 B
t
746,692 B
t17,553 B
t9,572 B
t
858,169 B
t19,015 B
t9,509 B
t
9902,843 B
t256,644 B
t117,694 B
t
NP
V of P
roject =28,626 B
t
Asw
ath Dam
odaran218
Equity A
nalysis: The P
arallels
The investm
ent analysis can be done entirely in equity terms, as w
ell.T
he returns, cashflows and hurdle rates w
ill all be defined from the
perspective of equity investors.
If using accounting returns,•
Return w
ill be Return on E
quity (RO
E) =
Net Incom
e/BV
of Equity
•R
OE
has to be greater than cost of equity
If using discounted cashflow m
odels,•
Cashflow
s will be cashflow
s after debt payments to equity investors
•H
urdle rate will be cost of equity
Asw
ath Dam
odaran219
A B
rief Exam
ple: A P
aper Plant for A
racruz -Investm
ent Assum
ptions
The plant is expected to have a capacity of 750,000 tons and w
ill have thefollow
ing characteristics:
It will require an initial investm
ent of 250 Million B
R. A
t the end ofthe fifth year, an additional investm
ent of 50 Million B
R w
ill beneeded to update the plant.
Aracruz plans to borrow
100 Million B
R, at a real interest rate of
5.5%, using a 10-year term
loan (where the loan w
ill be paid off inequal annual increm
ents).
The plant w
ill have a life of 10 years. During that period, the plant
(and the additional investment in year 5) w
ill be depreciated usingdouble declining balance depreciation, w
ith a life of 10 years.
Asw
ath Dam
odaran220
Operating A
ssumptions
The plant w
ill be partly in comm
ission in a couple of months, but w
illhave a capacity of only 650,000 tons in the first year, 700,000 tons inthe second year before getting to its full capacity of 750,000 tons in thethird year. T
he capacity utilization rate will be 90%
for the first 3years, and rise to 95%
after that. The investm
ent will be salvaged at
book value at the end of year 10.
The price per ton of linerboard is currently $400, and is expected to
keep pace with inflation for the life of the plant.
The variable cost of production, prim
arily labor and material, is
expected to be 55% of total revenues; there is a fixed cost of 50
Million B
R, w
hich will grow
at the inflation rate.
The w
orking capital requirements are estim
ated to be 15% of total
revenues, and the investments have to be m
ade at the beginning ofeach year. A
t the end of the tenth year, it is anticipated that the entirew
orking capital will be salvaged.
Asw
ath Dam
odaran221
The H
urdle Rate
The analysis is done in real, equity term
s. Thus, the hurdle rate has to
be a real cost of equity
The real cost of equity for A
racruz, based upon•
the beta estimate of 0.71,
•the real riskless rate of 5%
(using the real growth rate in B
razil as proxy)
•and the risk prem
ium for B
razil of 7.5% (based upon country rating
spread over U.S prem
ium of 5.5%
)
Real C
ost of Equity =
5% +
0.71 (7.5%) =
10.33%
Asw
ath Dam
odaran222
A R
OE
Analysis
Year
Net Incom
eD
epreciationC
ap ExpE
nding BV
: Assets
Debt
BV: EquityAvge BV
ROE0
0BR
250,000BR
250,000BR
100,000BR
150,000BR
1(1,289 BR
)50,000
BR0
BR200,000
BR92,233
BR107,767
BR128,883
BR-1.00%
27,371
BR40,000
BR0
BR160,000
BR84,039
BR75,961
BR91,864
BR8.02%
315,122
BR32,000
BR0
BR128,000
BR75,395
BR52,605
BR64,283
BR23.52%
421,526
BR25,600
BR0
BR102,400
BR66,275
BR36,125
BR44,365
BR48.52%
524,234
BR20,480
BR50,000
BR131,920
BR56,653
BR75,267
BR55,696
BR43.51%
621,864
BR26,384
BR0
BR105,536
BR46,502
BR59,034
BR67,151
BR32.56%
724,684
BR21,107
BR0
BR84,429
BR35,793
BR48,636
BR53,835
BR45.85%
827,036
BR16,886
BR0
BR67,543
BR24,495
BR43,048
BR45,842
BR58.98%
929,020
BR13,509
BR0
BR54,034
BR12,575
BR41,459
BR42,254
BR68.68%
10
30,715BR
10,807BR
0BR
43,228BR
(0 BR)
43,228BR
42,343BR
72.54%40.12%
Real R
OE
of 40.12% is greater than
Real C
ost of Equity of 10.33%
Asw
ath Dam
odaran223
From
Project R
OE
to Firm
RO
E
As w
ith the earlier analysis, where w
e used return on capital and costof capital to m
easure the overall quality of projects at Disney, w
e cancom
pute return on equity and cost of equity at Aracruz to pass
judgment on w
hether Aracruz is creating value to its equity investors
In 1996, Aracruz had net incom
e of 47 million B
R on book value of
equity of 2,115 million B
R, yielding a return on equity of:
RO
E =
47/2115 = 2.22%
(Real because book value is inflation adjusted)
Cost of E
quity = 10.33%
Excess R
eturn = 2.22%
- 10.33% =
-8.11%
This can be converted into a dollar value by m
ultiplying by the bookvalue of equity, to yield a equity econom
ic value addedE
quity EV
A =
(2.22% - 10.33%
) (2,115 Million) =
-171 Million B
R
Asw
ath Dam
odaran224
An Increm
ental CF
Analysis
Year
FCFE
PV
of FC
FE
(at 10.33%)
0(1
85
,10
0 B
R)
(18
5,1
00
BR
)1
38
,24
4BR
34
,66
3BR
23
6,4
77
BR2
9,9
66
BR3
36
,22
7BR
26
,97
4BR
43
8,0
06
BR2
5,6
49
BR5
(14,907 BR
)(9,119 B
R)
63
8,0
97
BR2
1,1
22
BR7
35
,08
2BR
17
,62
9BR
83
2,6
24
BR1
4,8
59
BR9
30
,60
9BR
12
,63
6BR
10
11
4,9
25
BR4
3,0
01
BRN
PV
32
,28
0BR
Asw
ath Dam
odaran225
The R
ole of Sensitivity A
nalysis
Our conclusions on a project are clearly conditioned on a large num
berof assum
ptions about revenues, costs and other variables over verylong tim
e periods.
To the degree that these assum
ptions are wrong, our conclusions can
also be wrong.
One w
ay to gain confidence in the conclusions is to check to see howsensitive the decision m
easure (NPV
, IRR
..) is to changes in keyassum
ptions.
Asw
ath Dam
odaran226
Viability of P
aper Plant: S
ensitivity to Price per
Ton
Ara
cru
z: N
PV
v
ers
us
P
rice
p
er
To
n
-60
,00
0
-40
,00
0
-20
,00
0 0
20
,00
0
40
,00
0
60
,00
0
80
,00
0
10
0,0
00
12
0,0
00
30
03
25
35
03
75
40
04
25
45
04
75
50
0
Pric
e
pe
r T
on
NPV
NP
V
Asw
ath Dam
odaran227
What does sensitivity analysis tell us?
Assum
e that the manager at A
racruz who has to decide on w
hether to takethis plant is very conservative. She looks at the sensitivity analysis anddecides not to take the project because the N
PV w
ould turn negative ifthe price drops below
$360 per ton. (Though the expected price per ton
is $400, there is a significant probability of the price dropping below$360.)Is this the right thing to do?
Yes
No
Explain.
Asw
ath Dam
odaran228
Side C
osts and Benefits
Most projects considered by any business create side costs and benefits
for that business.
The side costs include the costs created by the use of resources that the
business already owns (opportunity costs) and lost revenues for other
projects that the firm m
ay have.
The benefits that m
ay not be captured in the traditional capitalbudgeting analysis include project synergies (w
here cash flow benefits
may accrue to other projects) and options em
bedded in projects(including the options to delay, expand or abandon a project).
The returns on a project should incorporate these costs and benefits.
Asw
ath Dam
odaran229
Opportunity C
ost
An opportunity cost arises w
hen a project uses a resource that may
already have been paid for by the firm.
When a resource that is already ow
ned by a firm is being considered
for use in a project, this resource has to be priced on its next bestalternative use, w
hich may be
•a sale of the asset, in w
hich case the opportunity cost is the expectedproceeds from
the sale, net of any capital gains taxes
•renting or leasing the asset out, in w
hich case the opportunity cost is theexpected present value of the after-tax rental or lease revenues.
•use elsew
here in the business, in which case the opportunity cost is the
cost of replacing it.
Asw
ath Dam
odaran230
Case 1: O
pportunity Costs
Assum
e that Disney ow
ns land in Bangkok already. T
his land isundeveloped and w
as acquired several years ago for $ 5 million for a
hotel that was never built. It is anticipated, if this them
e park is built,that this land w
ill be used to build the offices for Disney B
angkok. The
land currently can be sold for $ 40 million, though that w
ould create acapital gain (w
hich will be taxed at 20%
). In assessing the theme park,
which of the follow
ing would you do:
Ignore the cost of the land, since Disney ow
ns its already
Use the book value of the land, w
hich is $ 5 million
Use the m
arket value of the land, which is $ 40 m
illion
Other:
Asw
ath Dam
odaran231
Case 2: E
xcess Capacity
In the Aracruz exam
ple, assume that the firm
will use its existing
distribution system to service the production out of the new
paperplant. T
he new plant m
anager argues that there is no cost associatedw
ith using this system, since it has been paid for already and cannot be
sold or leased to a competitor (and thus has no com
peting current use).D
o you agree?
Yes
No
Asw
ath Dam
odaran232
Estim
ating the Cost of E
xcess Capacity
Existing C
apacity = 100,000 units
Current U
sage = 50,000 (50%
of Capacity); 50%
Excess C
apacity;
New
Product will use 30%
of Capacity; Sales grow
th at 5% a year; C
M per
unit = $5/unit
Book V
alue = $1,000,000
Cost of a building new
capacity = $1,500,000;
Cost of C
apital = 12%
Current product sales grow
ing at 10% a year. C
M per unit =
$4/unit
Basic Fram
ework
•If I do not take this product, w
hen will I run out of capacity?
•If I take thisproject, w
hen will I run out of capacity
•W
hen I run out of capacity, what w
ill I do?–
cut back on production: cost is PV of after-tax cash flow
s from lost sales
–buy new
capacity: cost is difference in PVbetw
een earlier & later investm
ent
Asw
ath Dam
odaran233
Opportunity C
ost of Excess C
apacity
Year
Old
New
Old +
New
Lost A
TC
F PV
(AT
CF)
150.00%
30.00%80.00%
$0
255.00%
31.50%86.50%
$0
360.50%
33.08%93.58%
$0
466.55%
34.73%101.28%
$5,115 $ 3,251
573.21%
36.47%109.67%
$38,681 $ 21,949
680.53%
38.29%118.81%
$75,256 $ 38,127
788.58%
40.20%128.78%
$115,124 $ 52,076
897.44%
42.21%139.65%
$158,595 $ 64,054
9107.18%
44.32%151.50%
$ 206,000 $ 74,286
10117.90%
46.54%164.44%
$ 257,760 $ 82,992
PV(L
OST
SAL
ES)=
$ 336,734
PV (B
uilding Capacity In Y
ear 3 Instead Of Y
ear 8) = 1,500,000/1.12
3 -1,500,000/1.12
8 = $ 461,846
Opportunity C
ost of Excess C
apacity = $ 336,734
Asw
ath Dam
odaran234
Product and P
roject Cannibalization: A
Real
Cost?
Assum
e that in the Disney them
e park example, 20%
of the revenues atthe B
angkok Disney park are expected to com
e from people w
how
ould have gone to Disneyland in A
naheim, C
alifornia. In doing theanalysis of the park, w
ould you
Look at only increm
ental revenues (i.e. 80% of the total revenue)
Look at total revenues at the park
Choose an interm
ediate number
Would your answ
er be different if you were analyzing w
hether tointroduce a new
show on the D
isney cable channel on Saturdaym
ornings that is expected to attract 20% of its view
ers from A
BC
(which is also ow
ned by Disney)?
Yes
No
Asw
ath Dam
odaran235
Project S
ynergies
A project m
ay provide benefits for other projects within the firm
. Ifthis is the case, these benefits have to be valued and show
n in theinitial project analysis.
Consider, for instance, a typical D
isney animated m
ovie. Assum
e thatit costs $ 50 m
illion to produce and promote. T
his movie, in addition
to theatrical revenues, also produces revenues from•
the sale of merchandise (stuffed toys, plastic figures, clothes ..)
•increased attendance at the them
e parks
•stage show
s (see “Beauty and the B
east” and the “Lion K
ing”)
•television series based upon the m
ovie
Asw
ath Dam
odaran236
Project O
ptions
One of the lim
itations of traditional investment analysis is that it is
static and does not do a good job of capturing the options embedded in
investment.
•T
he first of these options is the option to delay taking a project, when a
firm has exclusive rights to it, until a later date.
•T
he second of these options is taking one project may allow
us to takeadvantage of other opportunities (projects) in the future
•T
he last option that is embedded in projects is the option to abandon a
project, if the cash flows do not m
easure up.
These options all add value to projects and m
ay make a “bad” project
(from traditional analysis) into a good one.
Asw
ath Dam
odaran237
The O
ption to Delay
When a firm
has exclusive rights to a project or product for a specificperiod, it can delay taking this project or product until a later date.
A traditional investm
ent analysis just answers the question of w
hetherthe project is a “good” one if taken today.
Thus, the fact that a project does not pass m
uster today (because itsN
PV is negative, or its IR
R is less than its hurdle rate) does not m
eanthat the rights to this project are not valuable.
Asw
ath Dam
odaran238
Valuing the O
ption to Delay a P
roject
Present Value of E
xpected C
ash Flows on Product
PV of C
ash Flows
from Project
Initial Investment in
Project
Project has negativeN
PV in this section
Project's NPV
turns positive in this section
Asw
ath Dam
odaran239
Insights for Investment A
nalyses
Having the exclusive rights to a product or project is valuable, even if
the product or project is not viable today.
The value of these rights increases w
ith the volatility of the underlyingbusiness.
The cost of acquiring these rights (by buying them
or spending money
on development - R
&D
, for instance) has to be weighed off against
these benefits.
Asw
ath Dam
odaran240
The O
ption to Expand/T
ake Other P
rojects
Taking a project today m
ay allow a firm
to consider and take othervaluable projects in the future.
Thus, even though a project m
ay have a negative NPV
, it may be a
project worth taking if the option it provides the firm
(to take otherprojects in the future) provides a m
ore-than-compensating value.
These are the options that firm
s often call “strategic options” and useas a rationale for taking on “negative N
PV” or even “negative return”
projects.
Asw
ath Dam
odaran241
The O
ption to Expand
Present Value of E
xpected C
ash Flows on E
xpansion
PV of C
ash Flows
from E
xpansion
Additional Investm
ent to E
xpand
Firm w
ill not expand inthis section
Expansion becom
es attractive in this section
Asw
ath Dam
odaran242
An E
xample of an E
xpansion Option
Disney is considering investing $ 100 m
illion to create a Spanishversion of the D
isney channel to serve the growing M
exican market.
A financial analysis of the cash flow
s from this investm
ent suggeststhat the present value of the cash flow
s from this investm
ent to Disney
will be only $ 80 m
illion. Thus, by itself, the new
channel has anegative N
PV
of $ 20 million
.
If the market in M
exico turns out to be more lucrative than currently
anticipated, Disney could expand its reach to all of L
atin Am
ericaw
ith an additional investment of $ 150 m
illion any time over the
next 10 years. While the current expectation is that the cash flow
s fromhaving a D
isney channel in Latin A
merica is only $ 100 m
illion, thereis considerable uncertainty about both the potential for such an channeland the shape of the m
arket itself, leading to significant variance inthis estim
ate.
Asw
ath Dam
odaran243
Valuing the E
xpansion Option
Value of the U
nderlying Asset (S) =
PV of C
ash Flows from
Expansion to L
atin Am
erica, if done now =
$ 100 Million
Strike Price (K) =
Cost of E
xpansion into Latin A
merican =
$ 150M
illion
We estim
ate the variance in the estimate of the project value by using
the annualized variance in firm value of publicly traded entertainm
entfirm
s in the Latin A
merican m
arkets, which is approxim
ately 10%.
•V
ariance in Underlying A
sset’s Value =
0.10
Tim
e to expiration = Period for w
hich expansion option applies = 10
years
Call V
alue= $ 45.9 Million
Asw
ath Dam
odaran244
Considering the P
roject with E
xpansion Option
NPV
of Disney C
hannel in Mexico =
$ 80 Million - $ 100 M
illion = -
$ 20 Million
Value of O
ption to Expand =
$ 45.9 Million
NPV
of Project with option to expand
= - $ 20 m
illion + $ 45.9 m
illion
= $ 25.9 m
illion
Take the project
Asw
ath Dam
odaran245
The O
ption to Abandon
A firm
may som
etimes have the option to abandon a project, if the
cash flows do not m
easure up to expectations.
If abandoning the project allows the firm
to save itself from further
losses, this option can make a project m
ore valuable.
Present Value of E
xpected C
ash Flows on Project
PV of C
ash Flows
from Project
Cost of A
bandonment
Asw
ath Dam
odaran246
Valuing the O
ption to Abandon
Disney is considering taking a 25-year project w
hich•
requires an initial investment of $ 250 m
illion in an real estate partnershipto develop tim
e share properties with a South Florida real estate
developer,
•has a present value of expected cash flow
s is $ 254 million.
While the net present value of $ 4 m
illion is small, assum
e that Disney
has the option to abandon this project anytime by selling its share back
to the developer in the next 5 years for $ 150 million.
A sim
ulation of the cash flows on this tim
e share investment yields a
variance in the present value of the cash flows from
being in thepartnership is 0.09.
Asw
ath Dam
odaran247
Project w
ith Option to A
bandon
Value of the U
nderlying Asset (S) =
PV of C
ash Flows from
Project=
$ 254 million
Strike Price (K) =
Salvage Value from
Abandonm
ent = $ 150 m
illion
Variance in U
nderlying Asset’s V
alue = 0.09
Tim
e to expiration = L
ife of the Project =5 years
Dividend Y
ield = 1/L
ife of the Project = 1/25 =
0.04 (We are assum
ingthat the project’s present value w
ill drop by roughly 1/n each year intothe project)
Assum
e that the five-year riskless rate is 7%. T
he value of the putoption can be estim
ated as follows:
Asw
ath Dam
odaran248
Should D
isney take this project?
Call V
alue = 254 exp(-0.04)(5) (0.9105) -150 (exp(-0.07)(5) (0.7496)
= $ 110.12 m
illion
Put Value=
$ 110.12 - 254 exp(-0.04)(5) +150 (exp(-0.07)(5) =
$7.86 m
illion
The value of this abandonm
ent option has to be added on to the netpresent value of the project of $ 4 m
illion, yielding a total net presentvalue w
ith the abandonment option of $ 11.86 m
illion.
