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Chapter 7Fundamentals of Corporate FinanceThird Edition
Using
Discounted
Cash Flow
Analysis to
Make
Investment
Decisions
Brealey Myers Marcus
slides by Matthew Will
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Topics Covered
?Discounted Cash Flows,NetProfits
?Incremental Cash Flows
?Treatment of Inflation
?Separation of Investment & Financing
Decisions
?Example,Blooper Industries
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Cash Flow vs,Accounting Income
?Discount actual cash flows
?Using accounting income,rather than cash flow,
could lead to erroneous decisions.
Example
A project costs $2,000 and is expected to last 2
years,producing cash income of $1,500 and $500
respectively,The cost of the project can be
depreciated at $1,000 per year,Given a 10% required
return,compare the NPV using cash flow to the NPV
using accounting income.
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Y ea r 1 Y ea r 2
C ash I n co m e $ 1 5 0 0 $ 5 0 0
D ep rec i ati on - $1000 - $1000
A cc o u n t i n g I n co m e + 5 0 0 - 5 0 0
A cco u n t i n g N P V = 500
1, 1 0
? ? ?500
1 10
322
(, )
$41,
Cash Flow vs,Accounting Income
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T o d ay Y ear 1 Y ear 2
C ash I n co m e $ 1 5 0 0 $ 5 0 0
P ro j ect C o st - 2000
Free C ash Fl o w - 2000 + 1500 + 5 0 0
C a s h N P V = - 2000
1, 1 0
? ? ? ?1500
1 10
500
1 10
142 3
(, ) (, )
$223,
Cash Flow vs,Accounting Income
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Incremental Cash Flows
?Discount incremental cash flows
?Include All Indirect Effects
?Forget Sunk Costs
?Include Opportunity Costs
?Recognize the Investment in Working Capital
?Beware of Allocated Overhead Costs
Incremental
Cash Flow
cash flow
with project
cash flow
without project= -
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Incremental Cash Flows
IMPORTANT
Ask yourself this question
Would the cash flow still exist if the project
does not exist?
?If yes,do not include it in your analysis.
?If no,include it.
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Inflation
INFLATION RULE
?Be consistent in how you handle inflation!!
?Use nominal interest rates to discount
nominal cash flows.
?Use real interest rates to discount real cash
flows.
?You will get the same results,whether you
use nominal or real figures
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Inflation
Example
You own a lease that will cost you $8,000 next
year,increasing at 3% a year (the forecasted
inflation rate) for 3 additional years (4 years
total),If discount rates are 10% what is the
present value cost of the lease?
1 ? r e a l i n t e r e s t r a t e = 1 + n o m i n a l i n t e r e s t r a t e1 + i n f l a t i o n r a t e
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Inflation
Example - nominal figures
Yea r C a sh Flo w P V @ 1 0 %
1 8000
2 8 0 0 0 x 1,0 3 = 8240
8 0 0 0 x 1,0 3 = 8240
8 0 0 0 x 1,0 3 = 8 4 8 7,2 0
8000
1,1 0
2
3
?
?
?
?
7272 73
6809 92
3 6376 56
4 5970 78
429 99
8240
1 10
8487 20
1 10
8741 82
1 10
2
3
4
.
.
.
.
$26,.
.
.
.
.
.
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Inflation
Example - real figures
Y ea r C ash Fl o w P V @ 6,7 9 6 1 %
1 = 7 7 6 6,9 9
2 = 7 7 6 6,9 9
= 7 7 6 6,9 9
= 7 7 6 6,9 9
8000
1,0 3
7 7 6 6,9 9
1,0 6 8
8240
1,0 3
8 4 8 7,2 0
1,0 3
8 7 4 1,8 2
1,0 3
2
3
4
?
?
?
?
7272 73
6809 92
3 6376 56
4 5970 78
26 429 99
7766 99
1 068
7766 99
1 068
7766 99
1 068
2
3
4
.
.
.
.
.
.
.
.
.
.
= $,.
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Separation of Investment &
Financing Decisions
?When valuing a project,ignore how the
project is financed.
?Following the logic from incremental
analysis ask yourself the following
question,Is the project existence dependent
on the financing? If no,you must separate
financing and investment decisions.
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Blooper Industries
Y e a r 0 1 2 3 4 5 6
Ca p I n v e s t
WC
Ch a n g e i n WC
Re v e n u e s
E x p e n s e s
D e p r e c ia ti on
Pr e ta x Pr o f it
,T a x ( 3 5 % )
Pr o f it
10 000
1 500 4 075 4 279 4 493 4 717 3 039 0
1 500 2 575 204 214 225 1 678 3 039
15 000 15 750 16 538 17 364 18 233
10 000 10 500 11 025 11 576 12 155
2 000 2 000 2 000 2 000 2 000
3 000 3 250 3 513 3 788 4 078
1 050 1 137 1 230 1 326 1 427
1 950 2 113 2
,
,,,,,,
,,,,
,,,,,
,,,,,
,,,,,
,,,,,
,,,,,
,,
? ?
,,,283 2 462 2 651
(,000s)
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Blooper Industries
Cash Flow From Operations (,000s)
Re ve nue s
- Ex pe nse s
D e pr e c ia ti on
= P r of it be f or e ta x
.- Ta x @ 35 %
= N e t pr of it
+ D e pr e c ia ti on
= CF f r om op e r a tions
15 000
10 000
2 000
3 000
1 050
1 950
2 000
3 950
,
,
,
,
,
,
,
,
?
or $3,950,000
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Blooper Industries
Net Cash Flow (entire project) (,000s)
Y e a r 0 1 2 3 4 5 6
Ca p I nve st - 10,000
Cha ng e in WC - 1,500 - 2,575 - 204 - 214 - 225 1,678 3,039
CF f r om Op 3,950 4,113 4,283 4,462 4,651
N e t C a sh F low - 11,500 1,375 3,909 4,069 4,237 6,329 3,039
NPV @ 12% = $3,564,000