Ch 09
March 2, 2012
Ch. 9 NPV and other Investment Criteria
I. Net Present Value (NPV)
II. Payback Rule
III. Discounted Payback
(IV. Average Accounting Return: Do not cover)
V. Internal Rate of Return (IRR)
IV. Profitability Index (PI)
VII. Capital Budgeting Practice
Ch. 9 Investment Criteria
Capital Budgeting Decision = long-run investment decision (most important
- decides what business the firm is in)
There are several methods by which the fin. manager can evaluate the
different investment opportunities.
Assume CFs and discount rates are given. How we calculate those will be
covered in subsequent chapters.
You need to understand what they are how to calculated them and the
advantages and disadvantages.
I. Net Present Value
most important
based on the principle that fin. manager tries to create value for
stockholders: project is will be worth more than it costs.
NPV = Market value of investment - cost
Goal: positive NPV
NPV>0 => accept project NPV<0 => reject
market value is calculated by using the “discounted cash flow valuation”
NPV = - Investment + CF 1 /(1+r) 1 + CF 2 /(1+r) 2 + ....
NPV > 0 => accept project
NPV < 0 => reject project
Use your CF and NPV functions
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Example:
Calculate the NPV given the following information:
r=.15
0
1
2
-$100
$50
$40
3
$40
4
$15
NPV= -100 + 50/1.15 1 +40/1.15 2 +40/1.15 3 +15/1.15 4
NPV= $8.60
>0 => accept
Advantages:
Takes into consideration time value of money & risk
Uses CFs (not accounting income)
Always gives the right answer
Can be used for mutually exclusive (=dependent) projects
Disadvantages:
Harder to calculate than others????
II. The Payback Rule
Length of time it takes to get initial investment back.
Calculate your cumulative CFs until it becomes positive.
The fin. manager set a specific time after which the initial investment has to
be recovered.
If the payback period of a project < specified time => accept
Example:
Use same numbers:
0
1
2
3
CFs
-$100
$50
$40
$40
Cum. CFs
-50
-10
30
4
$15
investment = 100
- first CF
-50
50
-sec. CF
-40
10
third CF = 40
payback sometime between 2 nd and 3 rd year
10/40=.25 (what is left/ CF in next period)
=>2.25 years
==========
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Advantages:
-easy to calculate ( but we still need to come up with CFs)
-quick and can be used as a preliminary test
-tends to favor short-term projects (which are more liquid= bias towards
liquidity) benefit for small corporations who need more cash available
Disadvantages of Payback Rule:
- ignores time value of money
- ignores risk of investment
- cut-off point is chosen subjectively (arbitrary)
- ignores the CF after the cutoff-point (further in the future): bias against
long-term investments
- cannot be used for mutually exclusive projects
III. Disounted Payback Rule
length of time required for discounted cash flows to equal the initial costs
r=10%
0
1
2
3
4
CFs
-$100
$50
$40
$40
$15
Disc. CFs
-100
45.45
33.06
30.05
10.25
Cum. Disc CFs
-54.55
-21.49
8.56
2+ (21.49/30.05) years = 2.7151 years
Advantages & Disadvantages
considers time value of money, CFs
but harder to calculate than the discounted payback method
(NOTE: discounted payback always LONGER than regular payback
because discounted CFs are smaller, it takes longer to recover the costs).
not used very often (not easier than NPV, and a project could be rejected
with this rule even though it has a positive NPV)
uses arbitrary cutoff.
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(Do not cover: VI. Average Accounting Return
Worst of all methods:
Average accounting profit/average accounting value, specifically
Average net income/average book value
Average NI: add up income/ number of years
Average book value (assuming straight-line depreciation: start out with
cost, end up with 0: cost/2 = average book value
Average book value depends on depreciation method
Book value in each year = beg book value – depreciation
Add them up divide by # of years
Example:
Cost: 600,000, straight-line depreciation ($600,000/2) = $300,000
NI
Year 1
2
3
15000
18000
33000 =66,000
66,000/3=22,000
Avg. accounting return = 22,000/300,000 = 7.33%
If the avg. accounting return > target avg. accounting return => accept
Advantages:
Relatively easy to calculate, the numbers are readily available
Disadvantages:
Does not account for risk or time value of money
Used accounting not market value for investment
Gives different answer from NPV
Uses arbitrary benchmark
Also returns are not as good of an indicator of profitability than absolute
numbers: I would rather have 10% of 1000 than 100% of 1.)
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V. Internal Rate of Return
Second best evaluation criteria; but not as good as NPV
closely related
IRR is the rate of return ( discount rate = r ) that makes the NVP equal to
zero.
OR: the rate that sets the PV of future CFs = cost
0 = - I + CF 1 /(1+IRR) + CF 2 /(1+IRR) 2 + ...
Decision rule: If IRR > than required return => accept.
Without financial calculator: trial-and-error!!!
Example:
Calculate the IRR for the following cash flows:
0
1
-100
50
28.61%
draw the NPV profile
2
70
3
40
=60 at r = 0
If required return is 20% => accept
Advantages:
Easy to communicate
Takes risk and time value into consideration
Uses CFs
Does not depend on a pre-determined rate
Disadvantages:
2 Problems with IRR:
1. If CFs are not conventional (conventional: initial investment - CFs + )
if CFs change signs => there are several IRRs and IRR rule does not lead to
right decision rule
2. When comparing two project: If projects are dependent or mutually
exclusive (taking one prevents us from taking the other)
Which investment has a higher NPV depends on the required rate of return
NPV and IRR can lead to conflicting results
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- Plot p. 280 example of NPV profiles for mutually exclusive investments
if required rate of return is < 11.1% NPV B > NPV A
if required rate of return is > 11.1% NPV B < NPV A
IRR of A = 24%
IRR of B = 21%
do not rank project on their IRRs
use NPV method & rank them on the size of their NPV
the 11.1 % is the crossover rate (discount rate which makes both project
NPVs equal.)
it is calculated as the IRR of the difference in cash flows between project.
Example:
Project A:
0
-300
1
200
2
170
= 70 at r = 0
1
250
2
230
= 80 at r = 0
2
60
= 10 at r= 0
IRR 15.66
Project B:
0
-400
IRR 13.27
Draw NPV profiles
Differential CFs:
Project B-A
0
-100
1
50
Crossover IRR 6.39%
At discount rates < 6.39% => B is better, at rates > 6.39% A is better
Note: MIRR covered in text, we will skip. You will have this in an advanced
FIN class. Different methods to calculate. You modify CF, by either
discounting and compounding at a given rate and then calculating the IRR.
This is then not really the IRR because we used an arbitrary interest rate
the modify the CFs and this defeats the purpose to the IRR.
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IV. Profitability Index (PI)
(PV of CFs)/(Initial Investment)
if > 1 PV of CFs > Initial Investment => project makes more than it costs =>
NPV > 0
If PI > 1 => accept
if PI < 1 => reject
0
1
2
3
-100
50
70
40
R=20%
PV of future CFs = use CF function with 0 CF0 = $113.43
Cost = 100
PI = 113.43/100 = 1.13
PI = 1.13 means that for each dollar invested $1.13 in value is created (NPV
of 13 cents results)
PI is NOT an absolute measure but a relative measure => and cannot be
used to compare two mutually exclusive investments.
Project 1: cost = $10, PV = $20
Project 2: cost = $300, PV = $450
=>
Project 1: NPV = $10 , PI = 2
Project 2: NPV = $150 , PI = 1.5
according to NPV: accept project 2; according to PI: accept project 1
Advantages:
Uses time value of money and considers risk
Uses CFs
Use to rank projects under capital rationing (it measures bang for your
bug)
Disadvantages:
Do not rank mutually exclusive investments, except under capital rationing
(when money is tight)
In Practice:
Multiple criterion are used
(NPV: keep in mind discount rate and CFs are only estimated)
IRR & NPV are most commonly used and are getting more & more popular.
Over 80% of time, the more educated the financial manager the more likely
to use NPV & IRR.
Criteria differ across industries: Cap rate for real estate investments
(NOI/Value of property), In film industry: script, cast, producer
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