Transcript No Slide Title

8- 1
Chapter 8
Net Present Value and Other Investment
Criteria
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 2
Topics Covered
 Net Present Value
 Other Investment Criteria
 Mutually Exclusive Projects
 Capital Rationing
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 3
Net Present Value
Net Present Value - Present value of cash
flows minus initial investments.
Opportunity Cost of Capital - Expected rate
of return given up by investing in a project
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 4
Net Present Value
Example
Q: Suppose we can invest $50 today & receive $60
later today. What is our increase in value?
A: Profit = - $50 + $60
= $10
$10
$50
McGraw Hill/Irwin
Added Value
Initial Investment
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 5
Net Present Value
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
This is the definition of NPV
McGraw Hill/Irwin
$50
Added Value
Initial Investment
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 6
Valuing an Office Building
Step 1: Forecast cash flows
Cost of building = C0 = 350,000
Sale price in Year 1 = C1 = 400,000
Step 2: Estimate opportunity cost of capital
If equally risky investments in the capital market
offer a return of 7%, then
Cost of capital = r = 7%
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 7
Valuing an Office Building
Step 3: Discount future cash flows
PV 
C1
(1r )

400 , 000
(1.07 )
 373,832
Step 4: Go ahead if PV of payoff exceeds investment
NPV  350,000 373,832
 23,832
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 8
Risk and Present Value
 Higher risk projects require a higher
rate of return
 Higher required rates of return cause
lower PVs
P V of C1  $400,000at 7%
400,000
PV 
 373,832
1  .07
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 9
Risk and Present Value
P V of C1  $400,000at 12%
400,000
PV 
 357,143
1  .12
P V of C1  $400,000at 7%
400,000
PV 
 373,832
1  .07
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 10
Net Present Value
NPV = PV - required investment
Ct
NPV  C0 
t
(1  r )
C1
C2
Ct
NPV  C0 

...
1
2
t
(1  r ) (1  r )
(1  r )
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 11
Net Present Value
Terminology
C = Cash Flow
t = time period of the investment
r = “opportunity cost of capital”
 The Cash Flow could be positive or negative at any
time period.
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 12
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.
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 13
Net Present Value
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?
Assume a 7% opportunity cost of capital
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 14
Net Present Value
$466,000
Example - continued
$450,000
Present Value
0
$16,000
$16,000
1
2
$16,000
3
14,953
13,975
380,395
$409,323
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 15
Net Present Value
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?
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 16
Net Present Value
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?
16,000 16,000 466,000
NPV  350,000 


1
2
3
(1.07 )
(1.07 )
(1.07 )
NPV  $59,323
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 17
Payback Method
Payback Period - Time until cash flows recover the
initial investment of the project.
 The payback rule specifies that a project be accepted
if its payback period is less than the specified cutoff
period. The following example will demonstrate the
absurdity of this statement.
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 18
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.
Project C0
A
B
C
C1
Cash Flows
C2
C3
-2,000 +1,000 +1,000 +10,000
-2,000 +1,000 +1,000
0
-2,000
0
+2,000
0
McGraw Hill/Irwin
Payback NPV@10%
2
2
2
+ 7,249
- 264
- 347
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 19
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.
C1 - investment
Rate of Return =
investment
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 20
Internal Rate of Return
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?
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 21
Internal Rate of Return
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?
16,000
16,000
466,000
0  350,000 


1
2
(1  IRR )
(1  IRR )
(1  IRR ) 3
IRR = 12.96%
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 22
Internal Rate of Return
Calculating IRR by using a spreadsheet
Year
0
1
2
3
McGraw Hill/Irwin
Cash Flow
(350,000.00)
16,000.00
16,000.00
466,000.00
Formula
IRR = 12.96% =IRR(B4:B7)
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 23
Internal Rate of Return
200
150
NPV (,000s)
100
IRR=12.96%
50
0
-50
0
5
10
15
20
25
30
35
-100
-150
-200
Discount rate (%)
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 24
Internal Rate of Return
The rate of return rule will give the same answer as the
NPV rule as long as the NPV of a project declines
smoothly as discount rate increases.
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 25
Internal Rate of Return
Example
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?
Project
Initial Proposal
Revised Proposal
McGraw Hill/Irwin
C0
-350
-350
C1
400
16
C2
C3
16
466
IRR
14.29%
12.96%
NPV@7%
$
24,000
$
59,000
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 26
Internal Rate of Return
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?
16
16
466
NPV  350 


0
1
2
3
(1  IRR ) (1  IRR )
(1  IRR )
 12.96%
400
NPV  350 
0
1
(1  IRR )
 14.29%
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 27
Internal Rate of Return
NPV $, 1,000s
50
40
Revised proposal
30
IRR= 12.96%
20
10
IRR= 14.29%
Initial proposal
0
-10
IRR= 12.26%
-20
8
10
12
14
16
Discount rate, %
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 28
Internal Rate of Return
Pitfall 1 - Lending or Borrowing?
 With some cash the NPV of the project increases as the discount
rate increases
 This is contrary to the normal relationship between PV and
discount rates.
Pitfall 2 - Multiple Rates of Return
 Certain cash flows can generate NPV=0 at two different discount
rates.
Pitfall 3 - Mutually Exclusive Projects
 IRR sometimes ignores the magnitude of the project.
 The following two projects illustrate that problem.
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 29
Internal Rate of Return
Example
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?
Project
Initial Proposal
Revised Proposal
McGraw Hill/Irwin
C0
-350
-350
C1
400
16
C2
C3
16
466
IRR
14.29%
12.96%
NPV@7%
$
24,000
$
59,000
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 30
Project Interactions
When you need to choose between mutually
exclusive projects, the decision rule is simple.
Calculate the NPV of each project, and, from
those options that have a positive NPV,
choose the one whose NPV is highest.
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 31
Mutually Exclusive Projects
Example
Select one of the two following projects,
based on highest NPV.
System
Faster
Slower
C0
 800
 700
C1
350
300
C2
350
300
C3
NPV
350  118.5
300  87.3
assume 7% discount rate
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 32
i) Investment Timing
Sometimes you have the ability to defer an
investment and select a time that is more ideal
at which to make the investment decision. A
common example involves a tree farm. You
may defer the harvesting of trees. By doing
so, you defer the receipt of the cash flow, yet
increase the cash flow.
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 33
i) Investment Timing
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?
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 34
i) Investment Timing
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
0
1
2
3
4
5
50
45
40
36
33
31
70
70
70
70
70
70
20
25
30
34
37
39
McGraw Hill/Irwin
NPV Today
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 35
ii) Long-lived vs short-lived equipment
Equivalent Annual Cost - The cash flow per period
with the same present value as the cost of buying
and operating a machine.
present value of cash flows
Equivalentannualannuity=
annuityfactor
Rule for comparing assets with different lives: Select the
machine that has the lowest equivalent annuity for cost.
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 36
Equivalent Annual Annuity
Example
Given the following costs of operating two machines
and a 6% cost of capital, select the lower cost
machine using equivalent annual annuity method.
Mach. 0
F
-15
G
-10
McGraw Hill/Irwin
Year
1
2
-4
-4
-6
-6
3
-4
PV@6%
-25.69
-21.00
E.A.A.
- 9.61
-11.45
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 37
iii) Replacing an old machine
Example (Replacing an old machine)
You are operating an old machine that will last 2 more
years. It costs $12,000 per year to operate. You can
replace it now with a new machine that costs $25,000 but
is much more effecient ($8,000 per year in operating
costs) and will last for 5 years. Should you replace now?
(r=6%).
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 38
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.
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 39
Profitability Index
NPV
Profitabil ity Index 
Initial Investment
Profitability Index
Ratio of net present value to initial investment.
Pitfalls of PI: The PI is sometimes used to rank projects even
when there’s no soft or hard capital rationing. In this case,
small projects may be favored over larger projects with higher
NPVs
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 40
Profitability Index
The company has total resources of $20 million and face the following
projects. Which projects should be chosen?
Project
J
K
L
M
N
McGraw Hill/Irwin
PV
4
6
10
8
5
Investment
3
5
7
6
4
NPV
1
1
3
2
1
Profitability
Index
1/3 = .33
1/5 = .20
3/7 = .43
2/6 = .33
1/4 = .25
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
8- 41
Capital Budgeting Techniques
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved