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Unformatted text preview: Chapter 7 (Cont’d)
Investment
Decision Rules Focusing Question As at HKT 2009/02/20 Spring 2009 2 Focusing Question
Peter bought 10,000 shares of Thiz Technology
and made a 74% return in one day.
John bought 10,000 shares of HKRH and made
a 16.8% return in one day.
Who is the more successful investor and why? Spring 2009 3 Outline
Decision
Rules Mutually
Exclusive
Projects Standalone
Projects NPV vs.
IRR Delayed
Investments Spring 2009 Pay Back Multiple
IRRs Differences
in Scales Projects w/
Resource
Constraints Timing
of CF Profitability
Index Differences
in Lives 4 Learning Objectives
1. Compute the crossover point or incremental IRR for
mutually exclusive projects with differences in
scales and timing of cash flows. 2. Compute Equivalent Annual Annuity (Equivalent
Annual Cost EAC) for mutually exclusive projects
with different lives. 3. Compare NPV and IRR in selecting mutually
exclusive projects, and tell why NPV always gives
the correct decision. 4. Compute profitability index and use it to select
projects under resource constraints. Spring 2009 5 Mutually Exclusive Projects
When you must choose only one project among several
possible projects, the choice is mutually exclusive.
Problem:
Consider the following two mutually exclusive projects
with same initial investment (projects of identical scale): Initial Investment
Cash FlowYear 13
Cost of Capital
Spring 2009 Girlfriend’s
Business
$10,000
$6,000
12% 2computer
Internet Cafe
$10,000
$5,000
12%
6 Projects of Identical Scale
Solution:
Girlfriend’s Business $10,000 $6,000 $6,000 $6,000 NPV = $4,411; IRR = 36.3%
Internet Cafe $10,000 $5,000 $5,000 $5,000 NPV = $2,009; IRR = 23.4%
Both the NPV rule and the IRR rule indicate the girlfriend’s business
is the better alternative.
Spring 2009 7 NPV Profiles of Projects w/ Identical Scale Spring 2009 8 Projects with Differences in Scale
What if there are 10 computers in the internet cafe? i.e.,
the internet café investment is 5 times larger?
The NPV would be 5 times larger at $2009*5 = $10,046,
but the IRR remains the same at 23.4%.
The girlfriend’s business has an IRR of 36.3%, but its
NPV is only $4,411.
Our decision: Use NPV rule
The 10computer internet café makes more money.
It has a higher NPV. Spring 2009 9 Return Vs Dollar Impact on Value
The IRR is a measure of the average return, but NPV is
a measure of the total dollar impact on value.
When a project’s size is doubled, its NPV will double.
This is not the case with IRR. Thus, the IRR rule cannot
be used to compare projects of different scales. Spring 2009 10 NPV Profiles of Projects w/ Different Scale
The NPV of
the 10computer
internet cafe
is larger than
the NPV of
the girlfriend’s
business for
cost of capital
lower than
20%. Spring 2009 11 Crossover Point (Incremental IRR)
Problem:
How to Compute the crossover point?
Solution:
Plan:
The crossover point is the discount rate that makes the
NPV of the two investments equal, i.e., NPV of internet
cafe equal NPV of his girlfriend’s business
At the crossover point, the difference of the NPVs
between internet café and his girlfriend’s business is 0.
The difference of the NPVs of two alternatives is the
incremental impact of choosing one project over another.
Spring 2009 12 Crossover Point for
Mutually Exclusive Projects
Execute:
Find the rate which sets the difference in CF equal to 0
Year Internet Cafe Girlfriend’s business Difference in CF 0 50,000 10,000 40,000 1 25,000 6,000 19,000 2 25,000 6,000 19,000 3 25,000 6,000 19,000 Given:
Solve for: 3 40,000 19,000 0 20.04 Excel Formula: =RATE(NPER, PMT, PV,FV) =
RATE(3,19000,40000,0)
Spring 2009 13 Crossover Point for
Mutually Exclusive Projects
Evaluate:
The crossover point is the discount rate at which one
would be indifferent between the two investment
opportunities because the incremental value of
choosing the internet café over girlfriend’s business
would be zero.
Decision Rules:
If cost of capital < crossover point, then you should
choose the Internet Cafe.
If cost of capital > the crossover point, then you should
choose the girlfriend’s business.
Since cost of capital < 20.04%, take the internet café.
Spring 2009 14 NPV Profiles of Projects w/ Different Scale
The NPV of
the 10computer
internet cafe
is larger than
the NPV of
the girlfriend’s
business for
cost of capital
lower than
20%. Spring 2009 15 Quick Quiz
Initial Investment
NPV
IRR
Cost of Capital Project A
$1,000
$600
50%
12% Project B
$10,000
$1,900
20%
12% 1. Which of the mutually exclusive projects will you prefer?
A. Project A
B. Project B
C. Neither
D. Both
Spring 2009 16 Outline
Decision
Rules Mutually
Exclusive
Projects Standalone
Projects NPV vs.
IRR Delayed
Investments Spring 2009 Pay Back Multiple
IRRs Differences
in Scales Projects w/
Resource
Constraints Timing
of CF Profitability
Index Differences
in Lives 17 Timing of Cash Flows
Assume you are offered a maintenance contract on the
internet café’s computers which would change the cash
flows each year as follows:
Year Internet Café
w/ contract 0 50,000 50,000 1 25,000 30,000 2 25,000 23,000 3 25,000 20,968 NPV $10,046 $10,046 IRR
Spring 2009 Internet Café
w/o contract 23.4% 24.2%
18 Timing of Cash Flows
The IRR with maintenance contract (24.2%) is larger
than the IRR without maintenance contract (23.4%).
Is the maintenance contract valuable?
Should we take the maintenance contract?
Sensitivity to timing of cash flows:
This is another problem with the IRR. It can be affected
by changing the timing of the cash flows, even when that
change in timing does not affect the NPV.
It is possible to alter the ranking of projects based on
IRR without changing their ranking in terms of NPV.
Hence you cannot use the IRR to choose between
mutually exclusive investments.
Spring 2009 19 Quick Quiz
Net present value Year 160 0 1 2 3 4 140
120 Project A: – $350 50 100 150 200 100 Project B: – $250 125 100 75 50 80
60
40 Crossover
Point 20
0
– 20
– 40
– 60
– 80 Discount rate – 100
0 Spring 2009 2% 6% 10% 14% 18% 22% 26% 20 Quick Quiz
2. If projects A and B are mutually exclusive, and the
cost of capital for your firm is 12%, which project
should you accept?
A. Project A
B. Project B
C. neither project A nor B because their IRR are
lower than your required rate of return
D. both projects A and B because their IRR are
higher than your cost of capital Spring 2009 21 Outline
Decision
Rules Mutually
Exclusive
Projects Standalone
Projects NPV vs.
IRR Delayed
Investments Spring 2009 Pay Back Multiple
IRRs Differences
in Scales Projects w/
Resource
Constraints Timing
of CF Profitability
Index Differences
in Lives 22 Projects with Different Lives
Solution:
Plan:
Benefits are the same. The objective is to minimize the
cost.
Put the choices in an equal footing: computing their
constant annual cost that is the same as the PV of one
lump sum at time zero.
Computing an Equivalent Annual Annuity (Equivalent
Annual Cost EAC) by
1. Computing its PV at the cost of capital.
2. Computing the equivalent nyear annuity with the
same PV as the cash flows of the project.
Spring 2009 24 Projects with Different Lives
Execute:
Given: 3 10 12.49 Solve for: 0 5.02 Excel Formula: =PMT(RATE,NPER, PV, FV) =
PMT(0.08,30,80000,0) Spring 2009 25 Projects with Different Lives
Evaluate:
By putting all the costs associated with purchasing and
maintaining these two servers into an equivalent annuity,
Server A appears to be a less expensive option to run for
three years on a per year basis.
Additional consideration before making decision:
Consider all available options and possible scenarios
beyond the existing conditions of these two proposed
servers:
Required life, either shorter or longer
Replacement cost, either higher or lower
Spring 2009 26 Outline
Decision
Rules Mutually
Exclusive
Projects Standalone
Projects NPV vs.
IRR Delayed
Investments Spring 2009 Pay Back Multiple
IRRs Differences
in Scales Projects w/
Resource
Constraints Timing
of CF Profitability
Index Differences
in Lives 27 Project Selection w/ Resource Constraints
Consider three possible projects that require warehouse
space. Profitability Index = Spring 2009 Value Created
NPV
=
Resource Consumed
Resource Consumed
28 Profitability Index
Profitability Index
Measures the “bang for your buck”
Value created in terms of NPV per unit of resource
consumed.
The profitability index can be used to identify the
optimal combination of projects to undertake.
Instead of selecting the project with the highest NPV
(Project A), select the projects with the highest PI
(Projects C and then Project B)
Result: Investments in Projects C and B with total NPV
of $150 mil
Spring 2009 29 PI Rule with Resource Constraint
Example 7.5 Spring 2009 30 PI Rule with Resource Constraint
Solution:
Plan:
Resource constraint: 190 employees at most
Goal: maximize the total NPV
Steps:
Use Engineering Headcount in the denominator for
profitability index for each project
Sort the projects based on their PI
Calculate the cumulative required EHC up to 190 Spring 2009 31 PI Rule with Resource Constraint
Execute: Spring 2009 32 PI Rule with Resource Constraint
Evaluate:
To maximize NPV within the constraint of 190 employees,
NetIt should choose the first four projects on the list.
No other combination will create more value without using
more engineers.
This ranking also shows us exactly the costs of the
engineering constraint – NetIt has to forgo three otherwise
valuable projects (C, D, and B) with a total NPV of $33.6
million.
Shortcomings of Profitability Index: In some situations
the profitability Index does not give an accurate answer.
With multiple resource constraints, the profitability index
can break down completely.
Spring 2009 33 Quick Quiz Spring 2009 34 Quick Quiz
3. Suppose NetIt has an additional small project with a
NPV of $100,000 that requires 3 engineers. This
project’s PI is 0.03 and so it is ranked the lowest.
Should this project be accepted?
A. Yes
B. No
C. Insufficient information Spring 2009 35 Outline
Decision
Rules Mutually
Exclusive
Projects Standalone
Projects NPV vs.
IRR Delayed
Investments Spring 2009 Pay Back Multiple
IRRs Differences
in Scales Projects w/
Resource
Constraints Timing
of CF Profitability
Index Differences
in Lives 36 ...
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This note was uploaded on 04/03/2010 for the course FINA FINA111 taught by Professor Lynnpi during the Spring '09 term at HKUST.
 Spring '09
 LynnPi

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