Project Investment Analysis
Project Investment Analysis
Project Investment Analysis
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Example
Q: Suppose we can invest $50 today & receive $60
later today. What is our increase in value?
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Example
Suppose we can invest $50 today and receive $60
in one year. What is our increase in value given a
10% expected return?
60
Profit = -50 + $4.55
1.10
$4.55 Added Value
$50 Initial Investment
This is the definition of NPV
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Ct
NPV C0
(1 r ) t
C1 C2 Ct
NPV C0 ...
(1 r ) 1
(1 r ) 2
(1 r ) t
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Terminology
C = Cash Flow
t = time period of the investment
r = “opportunity cost of capital”
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Example
You have the opportunity to
purchase an office building. You
have a tenant lined up that will
generate $16,000 per year in cash
flows for three years. At the end
of three years you anticipate
selling the building for $450,000.
How much would you be willing
to pay for the building?
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Present Value 0 1 2 3
14,953
13,975
380,395
$409,323
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Example - continued
If the building is being
offered for sale at a price
of $350,000, would you
buy the building and what
is the added value
generated by your
purchase and management
of the building?
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Example - continued
If the building is being offered for sale at a price of
$350,000, would you buy the building and what is the
added value generated by your purchase and management
of the building?
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Payback Method
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Payback Method
Example
The three project below are available. The company accepts
all projects with a 2 year or less payback period. Show how
this decision will impact our decision.
Cash Flows
Project C0 C1 C2 C3 Payback NPV@10%
A -2000 +1000 +1000 +10000 2 + 7,249
B -2000 +1000 +1000 0 2 - 264
C -2000 0 +2000 0 2 - 347
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C1 - investment
Rate of Return =
investment
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Example
You can purchase a building for $350,000. The
investment will generate $16,000 in cash flows
(i.e. rent) during the first three years. At the end
of three years you will sell the building for
$450,000. What is the IRR on this investment?
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Example
You can purchase a building for $350,000. The investment will
generate $16,000 in cash flows (i.e. rent) during the first three years.
At the end of three years you will sell the building for $450,000. What
is the IRR on this investment?
IRR = 12.96%
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200
150
100 IRR=12.96%
NPV (,000s)
50
0
0 5 10 15 20 25 30 35
-50
-100
-150
-200
Discount rate (%)
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16 16 466
NPV 350 0
(1 IRR ) (1 IRR )
1 2
(1 IRR ) 3
12.96%
400
NPV 350 0
(1 IRR )1
14.29%
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Example
You have two proposals to choice between. The initial proposal (H)
has a cash flow that is different than the revised proposal (I). Using
IRR, which do you prefer?
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Project Interactions
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Example
Select one of the two following projects,
based on highest NPV.
System C0 C1 C2 C3 NPV
Faster 800 350 350 350 118.5
Slower 700 300 300 300 87.3
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Investment Timing
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Capital Rationing
Capital Rationing - Limit set on the amount of
funds available for investment.
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Profitability Index
Profitability
Project PV Investment NPV Index
L 4 3 1 1/3 = .33
M 6 5 1 1/5 = .20
N 10 7 3 3/7 = .43
O 8 6 2 2/6 = .33
P 5 4 1 1/4 = .25
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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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500 500
Apparent NPV = 2
$41.32
1.10 (1.10)
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1500 500
Cash NPV = -2000 1
2
$223.14
(1.10) (1.10)
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IMPORTANT
Ask yourself this question
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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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Financing Decisions
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Sensitivity Analysis
Example
Given the expected cash flow
forecasts listed on the next
slide, determine the NPV of
the project given changes in
the cash flow components
using an 8% cost of capital.
Assume that all variables
remain constant, except the
one you are changing.
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Sensitivity Analysis
Example – continued (,000s)
Year 0 Years 1 - 12
Investment - 5,400
Sales 16,000
Variable Costs 13,000
Fixed Costs 2,000
Depreciati on 450
Pretax profit 550
.Taxes @ 40% 220
Profit after tax 330
Operating cash flow 780
Net Cash Flow - 5,400 780
NPV= $478
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Sensitivity Analysis
Example - continued
Possible Outcomes
Range
Variable Pessimisti c Expected Optimistic
Investment(000s) 6,200 5,400 5,000
Sales(000s ) 14,000 16,000 18,000
Var Cost (% of sales) 83% 81.25% 80%
Fixed Costs(000s ) 2,100 2,000 1,900
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Sensitivity Analysis
Example - continued
NPV Calculations for Pessimistic Investment Scenario
Year 0 Years 1 - 12
Investment - 6,200
Sales 16,000
Variable Costs 13,000
Fixed Costs 2,000
Depreciati on 450
Pretax profit 550
.Taxes @ 40% 220
Profit after tax 330
Operating cash flow 780
Net Cash Flow - 6,200 780
NPV= ($121)
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Sensitivity Analysis
Example - continued
NPV Possibilities
NPV (000s )
Variable Pessimistic Expected Optimistic
Investment(000s) - 121 478 778
Sales(000s ) - 1,218 478 2,174
Var Cost (% of sales) - 788 478 1,382
Fixed Costs(000s ) 26 478 930
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Scenario Analysis
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Decision Trees
Success
Test (Invest Pursue project
$200,000) NPV=$2million
Failure
Stop project
NPV=0
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Real Options
1. Invest
2. Don’t Invest
3. Delay the Investment
4. Flexible Investment