Post on 24-Oct-2020
McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
Professor James J. Barkocy
Corporate Financial Management
“There are three kinds of
people: the ones that can
count and the ones that
can’t.”
Net Present Value
Opportunity Cost of Capital - Expected rate of return given up by investing in a project.
Net Present Value - Present value of cash
flows minus initial investments.
2
Net Present Value
Example
Suppose we can invest $350,000 today and receive $400,000 in one year. What is our increase in value given a 7% expected return?
This is NPV
Profit = -350,000 +400,000
1.07= $23,832
Initial Investment
Added Value
$350,000
$23,832
3
Net Present Value
NPV = PV - required investment
NPV CC
r
t
t=
0
1( )
NPV CC
r
C
r
C
r
t
t=
0
1
1
2
21 1 1( ) ( )...
( )
4
Net Present Value
Example
You have the opportunity to purchase an
office building. You have a tenant lined
up that will generate $25,000 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?
5
Net Present Value
Example - continued
0 1 2 3
$25,000$25,000$25,000
$450,000
$475,000
Present Value
23,364
21,836
387,741
$432,942
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FV=450,000
PMT= 25,000
N=3
I=7
Net Present Value
Example - continued
If the building is being offered for
sale at a price of $375,000, would you
buy the building and what is the
added value generated by your
purchase and management of the
building?
7
Net Present Value
Example - continued
If the building is being offered for sale at a price of $375,000, would
you buy the building and what is the added value generated by your
purchase and management of the building?
942,57$
)07.1(
000,475
)07.1(
000,25
)07.1(
000,25000,375
321
=
=
NPV
NPV
8
Net Present Value
Net Present Value Rule
Managers increase shareholders’ wealth by
accepting all projects that are worth more than they
cost.
Therefore, they should accept all projects with a
positive net present value.
9
Net Present ValueCalculating the NPV can be a laborious task. Fortunately,
financial calculators can perform this function easily.
HP-10B HP-12C
-375,000 CFj -375,000 g CF0
25,000 CFj 25,000 g CFj
25,000 CFj 25,000 g CFj
475,000 CFj 475,000 g CFj
7 i 7 i
NPV f NPV Both produce
NPV=57,941.95
10
The Net Present Value Rule
Net Present Value (NPV) =
Total PV of future CF’s - Initial Investment
Estimating NPV: 1. Estimate future cash flows: how much? and when?
2. Estimate discount rate
3. Estimate initial costs
Minimum Acceptance Criteria: Accept if NPV > 0
Ranking Criteria: Choose the highest NPV
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Example:
You may purchase a computer anytime within the next five years. While the computer will save your company money, the cost of computers continues to decline. If your cost of capital is 10% and given the data listed below, when should you purchase the computer?
Year Cost PV Savings NPV at Purchase NPV Today
0 50 70 20 20.0
1 45 70 25 22.7
2 40 70 30 24.8
3 36 70 34 Date to purchase 25.5
4 33 70 37 25.3
5 31 70 39 24.2
Investment Timing
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Equivalent Annual Annuity (Cost)
Equivalent Annual Annuity (Cost) - The payment per
period with the same present value as the cash flows.
Calculate the NPV of both projects.
Use NPV as your present value and find the
appropriate annuity payment.
13
Equivalent Annual Cost
Example
Given the following costs of operating two machines and a
10% cost of capital, select the lower cost machine using
equivalent annual cost method.
Year Annual
0 1 2 3 4 (N)PV@10% Cost
A -500 -120 -120 -120 -798.42 -321.05
B -600 -100 -100 -100 -100 -961.99 -289.28
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Replacement Chain Method
NPV @10%= $-2,187.59
NPV @10%= $-1,971.08
0 1 2 3 4 5 6 7 8 9 10 11 12
-500 -120 -120 -120
-500 -120 -120 -120
-500 -120 -120 -120
-500 -120 -120 -120
-500 -120 -120 -620 -120 -120 -620 -120 -120 -620 -120 -120 -120
0 1 2 3 4 5 6 7 8 9 10 11 12
-600 -100 -100 -100 -100
-600 -100 -100 -100 -100
-600 -100 -100 -100 -100
-600 -100 -100 -100 -700 -100 -100 -100 -700 -100 -100 -100 -100
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Other Investment Criteria
Internal Rate of Return (IRR) - Discount rate at which NPV = 0.
Rate of Return Rule - Invest in any project offering a rate of return that is higher than the opportunity cost of capital.
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Internal Rate of ReturnExample
You can purchase a building for $375,000. The investment
will generate $25,000 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?
321 )1(
000,475
)1(
000,25
)1(
000,25000,3750
IRRIRRIRR
=
IRR = 12.56%
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Internal Rate of ReturnCalculating the IRR can be a laborious task. Fortunately,
financial calculators can perform this function easily.
HP-10B HP-12C
-375,000 CFj -375,000 g CF0
25,000 CFj 25,000 g CFj
25,000 CFj 25,000 g CFj
475,000 CFj 475,000 g CFj
{IRR/YR} f IRR
Both produce
IRR=12.56
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-$60.00
-$40.00
-$20.00
$0.00
$20.00
$40.00
$60.00
$80.00
$100.00
$120.00
9% 19% 29% 39%
Discount rate
NP
V
NPV Payoff Profile
Discount Rate NPV
0% $100.00
4% $71.04
8% $47.32
12% $27.79
16% $11.65
20% -$1.74
24% -$12.88
28% -$22.17
32% -$29.93
36% -$36.43
40% -$41.86
If we graph NPV versus discount rate, we can see the
IRR as the x-axis intercept.
IRR = 19.44%
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The Internal Rate of Return (IRR) Rule
IRR: the discount that sets NPV to zero
Minimum Acceptance Criteria: Accept if the IRR exceeds the required return.
Ranking Criteria: Select alternative with the highest IRR
Disadvantages: Does not distinguish between investing and borrowing. IRR may not exist or there may be multiple IRR Problems with mutually exclusive investments
Reinvestment assumption: All future cash flows assumed reinvested at the IRR.
Advantages: Easy to understand and communicate
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Multiple IRRs
There are two IRRs for this project:
0 1 2 3
$200 $800
-$200 - $800
($120.00)
($100.00)
($80.00)
($60.00)
($40.00)
($20.00)
$0.00
$20.00
$40.00
$60.00
-50% 0% 50% 100% 150% 200%
NP
V
Discount rate
100% = IRR2
0% = IRR1
Which one
should we use?
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The Timing Problem
($4,000.00)
($3,000.00)
($2,000.00)
($1,000.00)
$0.00
$1,000.00
$2,000.00
$3,000.00
$4,000.00
$5,000.00
10% 20% 30% 40%
Discount rate
NP
V
Project A
Project B
10.55% = crossover rate
16.04% = IRRA12.94% = IRRB
The preferred project in this case depends on the discount rate…
…not the IRR. 22
Calculating the Crossover Rate
Compute the IRR for either project “A-B” or
“B-A”Year Project A Project B Project A-B Project B-A
0 ($10,000) ($10,000) $0 $0
1 $10,000 $1,000 $9,000 ($9,000)
2 $1,000 $1,000 $0 $0
3 $1,000 $12,000 ($11,000) $11,000
($3,000.00)
($2,000.00)
($1,000.00)
$0.00
$1,000.00
$2,000.00
$3,000.00
0% 5% 10% 15% 20%
Discount rate
NP
V A-B
B-A
10.55% = IRR
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Project C0 C1 C2 C3 IRR NPV@7%
Initial Proposal -350 400 14.29% 23,832$
Revised Proposal -375 25 25 475 12.56% 57,942$
Internal Rate of ReturnExample
You have two proposals to choice between. The initial
proposal has a cash flow that is different than the revised
proposal. Using IRR, which do you prefer?
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The Payback Period Rule
How long does it take the project to “pay back” its initial investment?
Payback Period = number of years to recover initial costs
Minimum Acceptance Criteria:
set by management
Ranking Criteria:
set by management
25
Payback Method
Example
The three projects below are available. The company accepts all
projects with a 2 year or less payback period. Show how this will
impact our investment decision.
Cash Flows
Prj. C0 C1 C2 C3 Payback NPV@10%
A -2000 +500 +1000 +10000 2+ +6,794
B -2000 +1000 +1000 0 2 - 264
C -2000 0 +2000 0 2 - 347
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Capital Rationing
Capital Rationing - Limit set on the amount of funds available for investment.
Soft Rationing - Limits on available funds imposed by management.
Hard Rationing - Limits on available funds imposed by the unavailability of funds in the capital market.
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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
Profitability Index
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