Some Complications in
Capital Budgeting Analysis
1
Learning Objectives
1. Illustrate the approach to deciding among
mutually exclusive projects with unequal lives.
2. Explain the importance of risk analysis in the
capital budgeting decision-making process.
3. Understand the use of sensitivity and scenario
analysis as well as simulation analysis to
investigate the determinants of project cash
flows.
4. Use break-even analysis to evaluate project risk.
5. Explain the types of real options.
2
Independent Versus Mutually
Exclusive Investment Projects
 An independent investment project is one
that stands alone and can be undertaken
without influencing the acceptance or
rejection of any other project.
 A mutually exclusive project prevents
another project from being accepted.
3
Evaluating Mutually Exclusive
Investment Opportunities
 There are times when a firm must choose the
best project or set of projects from the set of
positive NPV investment opportunities. These
are considered mutually exclusive
opportunities as the firm cannot undertake all
positive NPV projects.
4
Evaluating Mutually Exclusive
Investment Opportunities (cont.)
 Following are two situations where firm is
faced with mutually exclusive projects:
1.Substitutes – Where firm is trying to pick
between alternatives that perform the same
function. For example, a new machinery for
the new project. While there might be many
good machines, the firm needs only one.
5
Evaluating Mutually Exclusive
Investment Opportunities (cont.)
2. Firm Constraints – Firm may face constraints
such as limited managerial time or limited
financial capital that may limit its ability to
invest in all the positive NPV opportunities.
6
Choosing Between Mutually
Exclusive Investments
1. If mutually exclusive investments have equal
lives, we will calculate the NPVs and choose
the one with the higher NPV.
2. If mutually exclusive investments do not
have equal lives, we must calculate the
Equivalent Annual Cost (EAC), the cost per
year. We will then select the one that has a
lower EAC.
7
Choosing Between Mutually
Exclusive Investments (cont.)
 Computation of EAC requires two steps:
1. Compute NPV
2. Compute EAC as:
8
Checkpoint 11.2 - Calculating the Equivalent
Annual Cost (EAC)
Suppose your bottling plant is in need of a new bottle capper. You
are considering two different capping machines that will perform
equally well, but have different expected lives. The more expensive
one costs $30,000 to buy, requires the payment of $3,000 per year
for maintenance and operation expenses, and will last for 5 years.
The cheaper model costs only $22,000, requires operating and
maintenance costs of $4,000 per year, and lasts for only 3 years.
Regardless of which machine you select, you intend to replace it at
the end of its life with an identical machine with identical costs and
operating performance characteristics. Because there is not a
market for used cappers, there will be no salvage value associated
with either machine. Let’s also assume that the discount rate on
both of these machines is 8 percent.
9
Checkpoint 11.2
10
Checkpoint 11.2
11
Checkpoint 11.2
12
Checkpoint 11.2 (a): Check Yourself
OEC Ltd. is currently evaluating two different options to
control the emissions from their coal-burning electric
generation facility. A filtration system will cost $12 million
to install, $700,000 per year to operate and must be
replaced every five years. The alternative is to install a
precipitation system that scrubs the air coming from the
facility. The precipitation system, which will cost $20
million to install and $200,000 per year to operate, has a
useful life of eight years. OEC has an opportunity cost of
capital of 10 percent. Determine whether OEC should
purchase the filtration system or the precipitation system.
13
Checkpoint 11.2 (b) Check Yourself
 Lester Peabody decides to install a fuel storage
system for his farm that will save him an
estimated $6.50/gallon on his fuel cost. He
uses an estimated 20,000 gallons/year on his
farm. Initial cost of the system is $750,000 and
the annual maintenance is a uniform amount
of $25,000. After a period of 10 years the
estimated salvage is $30,000. If money is worth
12%, is it a wise investment?
14
Checkpoint 11.2 (c): Check Yourself
 What is the EAC for a machine that costs
$50,000, requires payment of $6,000 per year
for maintenance and operation expense, and
lasts for 6 years? You may assume that the
discount rate is 9% and there will be no
salvage value associated with the machine. In
addition, you intend to replace this machine at
the end of its life with an identical machine
with identical costs.
15
Step 1: Picture the Problem
k=9%
Years
0
1
2
3
4
5
6
Cash flows
-$50
(in $, thousands)
-$6
-$6
-$6
-$6
-$6
-$6
EAC =?
16
Step 2: Decide on a Solution
Strategy
 Here we need to calculate the EAC, which will
tell us the annual cost for a machine that lasts
6 years.
 EAC can be computed using mathematical
formula or calculator.
17
Step 3: Solve
 Using Mathematical Formula
 It requires 2 steps:
 Computation of NPV
 Here the cash inflows are equal so we can use the
annuity equation to determine the PV of cash inflows.
 Computation of EAC
18
Step 3: Solve (cont.)
NPV = -$50,000 + PV of $6,000 each year
= -$50,000 + -$6,000 (PV of Annuity Factor)
= -$50,000 + -$6,000 {[1-(1/(1.09)6] ÷ (.06)}
= -$50,000 + -$6,000 {4.4859) = -$76,915
19
Step 3: Solve (cont.)
 EAC = NPV ÷ Annuity Factor
= -$76,915 ÷ 4.4859
= -$17,145.95
20
Step 4: Analyze
 Here EAC is equal to $17,145.86.
 EAC indicates the annual cost that is
adjusted for time value of money.
21
Tools for Analyzing the Risk of
Project Cash Flows
 It is reasonable to assume that the actual
cash flows an investment produces will
never equal the expected cash flows
used to estimate the investment’s NPV
as there are many possible cash flow
outcomes for any project.
22
Tools for Analyzing the Risk of
Project Cash Flows (cont.)
 Tools such as Sensitivity analysis,
Scenario analysis, and Simulation
analysis provide better understanding of
the uncertainty of future cash flows and,
consequently, the reliability of the NPV
estimate.
23
Key Concepts - Expected Values
and Value Drivers
 Expected Values
 The expected value of a future cash flow is
given by the probability weighted average
of all the possible cash flows that might
occur.
 The cash flows used to calculate a project’s
NPV are expected values.
24
Key Concepts - Expected Values
and Value Drivers (cont.)
 Example 13.1
 What is the expected cash value if there are
two possible cash flows, $100 and $400 and the
probabilities of these cash flows are 25% and
75%.
 Expected cash value = .25 ( 100) + .75 (400)
= $325
25
Value Drivers
 Value drivers are the basic determinants of an
investment’s cash flows and consequently its
performance.
 Value drivers may consist of determinants of
project revenues (e.g., market share, market
size, and price) and costs (e.g., variable and
cash fixed costs)
26
Value Drivers (cont.)
 Identification of value drivers allow the
financial manager to:
 Allocate more time and money toward refining
their forecasts of these key variables.
 Monitor the key value drivers regularly so that
prompt corrective action can be taken in the
event that the project is not proceeding as
expected.
27
Sensitivity Analysis
 Sensitivity analysis occurs when a financial
manager evaluates the effect of each value
driver on the investment’s NPV.
 It helps identify the variable that has the most
impact on NPV.
28
Checkpoint 13.2 - Project Risk Analysis: Sensitivity Analysis
Crainium, Inc. is considering an investment in a new plasma cutting tool to be
used in cutting out steel silhouettes that will be sold through the firm’s catalog
sales operations. The silhouettes can be cut into any two-dimensional shape
such as a state, university mascot or logo, etc. The products are expected to sell
for an average price of $25 per unit, and the company analysts expect the firm
can sell 200,000 units per year at this price for a period of five years. Launching
this service will require the purchase of a $1.5 million plasma cutter and
materials handling system that has a residual or salvage value in five years of
$250,000. In addition, the firm expects to have to invest an additional $500,000
in working capital to support the new business. Other pertinent information
concerning the business venture is provided below:
29
Checkpoint 13.2
Crainium’s analysts have estimated the project’s expected or base-case cash
flows as well as the NPV and IRR to be the following:
Although the project is expected to have a $209,934 NPV and a 15.59% IRR
(which exceeds the project’s 10% discount rate), it is risky, so the firm’s
analysts want to explore the importance of uncertainty in the project cash
flows. Perform a sensitivity analysis on this proposed investment.
30
Checkpoint 13.2
31
Checkpoint 13.2
32
Checkpoint 13.2: Check Yourself
• After a careful cost analysis of the costs for
making the silhouettes, Cranium’s management
has determined that it will be possible to reduce
the variable cost per unit down to $18 per unit by
purchasing an additional option for the equipment
that will raise its initial cost to $1.8 million (the
residual or salvage value for this configuration is
estimated to be $300,000). All other information
remains the same as before. For this new
machinery configuration, analyze the sensitivity of
the project NPV to the same percent changes
analyzed above.
33
Step 1: Picture the Problem
 To evaluate the sensitivity of the
project’s NPV and IRR to uncertainty
surrounding the project’s value drivers,
we need to analyze the effects of the
changes in the value drivers (unit sales,
price per unit, variable cost per unit, and
annual fixed operating cost other than
depreciation).
34
Step 1: Picture the Problem (cont.)
 We consider the following changes:
 Unit sales (-10%)
 Price per unit (-10%)
 Variable cost per unit (+10%)
 Cash fixed costs per year (+10%)
35
Step 2: Decide on a Solution
Strategy
 The objective of this analysis is to explore
the effects of the prescribed changes in
the value drivers on the project’s NPV.
 We will need to estimate the base-case
NPV based on given information and
then compute the NPV based on
assumed changes to the value drivers.
36
Step 3: Solve
 Following are the projected cash flows for years 0-5:
Year-0
Revenues
Years 1-4
Year-5
5,000,000
5,000,000
$(3,600,000.00)
$(3,600,000.00)
Less: Depreciation Expense
$(300,000.00)
$(300,000.00)
Less: Cash Fixed Cost
$(400,000.00)
$(400,000.00)
Net Operating Income
$700,000.00
$700,000.00
$(210,000.00)
$(210,000.00)
Net operating profit after tax
$490,000.00
$490,000.00
Plus: Depreciation Expense
$300,000.00
$300,000.00
Less: Variable Cost
Les: Taxes
Less: CAPEX
Less: Change in Working Capital
Free Cash Flow
$(1,800,000.00)
$300,000.00
$(500,000.00)
$500,000.00
$(2,300,000.00)
$790,000.00
$1,590,000.00
37
Step 3: Solve (cont.)
 Given the free cash flows for years 0-5, we can
compute the NPV and IRR on excel, which
gives us the following results:
Year
Free Cash Flow
0
$(2,300,000.00)
1
$790,000.00
2
$790,000.00
3
$790,000.00
4
$790,000.00
5
$1,590,000.00
NPV
$1,001,714.68
IRR
26.65%
38
Step 3: Solve (cont.)
 What if sales drop by 10%?
Year-0
Years 1-4
Revenues
Year-5
4,500,000
4,500,000
$(3,240,000.00)
$(3,240,000.00)
Less: Depreciation Expense
$(300,000.00)
$(300,000.00)
Less: Cash Fixed Cost
$(400,000.00)
$(400,000.00)
Net Operating Income
$560,000.00
$560,000.00
$(168,000.00)
$(168,000.00)
Net operating profit after tax
$392,000.00
$392,000.00
Plus: Depreciation Expense
$300,000.00
$300,000.00
Less: Variable Cost
Les: Taxes
Less: CAPEX
Less: Change in Working Capital
Free Cash Flow
$(1,800,000.00)
$300,000.00
$(500,000.00)
$500,000.00
$(2,300,000.00)
$692,000.00
NPV
$648,446.62
IRR
21.59%
$1,492,000.00
39
Step 3: Solve (cont.)
 What if variable costs increase by 10%?
Year-0
Years 1-4
Revenues
Year-5
5,000,000
5,000,000
$(3,960,000.00)
$(3,960,000.00)
Less: Depreciation Expense
$(300,000.00)
$(300,000.00)
Less: Cash Fixed Cost
$(400,000.00)
$(400,000.00)
Net Operating Income
$340,000.00
$340,000.00
$(102,000.00)
$(102,000.00)
Net operating profit after tax
$238,000.00
$238,000.00
Plus: Depreciation Expense
$300,000.00
$300,000.00
Less: Variable Cost
Les: Taxes
Less: CAPEX
Less: Change in Working Capital
Free Cash Flow
$(1,800,000.00)
$300,000.00
$(500,000.00)
$500,000.00
$(2,300,000.00)
$538,000.00
NPV
$220,414.70
IRR
15.19%
$1,338,000.00
40
Step 3: Solve (cont.)
 What if price per unit drops by 10%
Year-0
Years 1-4
Revenues
Year-5
4,500,000
4,500,000
$(3,600,000.00)
$(3,600,000.00)
Less: Depreciation Expense
$(300,000.00)
$(300,000.00)
Less: Cash Fixed Cost
$(400,000.00)
$(400,000.00)
Net Operating Income
$200,000.00
$200,000.00
Les: Taxes
$(60,000.00)
$(60,000.00)
Net operating profit after tax
$140,000.00
$140,000.00
Plus: Depreciation Expense
$300,000.00
$300,000.00
Less: Variable Cost
Less: CAPEX
Less: Change in Working Capital
Free Cash Flow
$(1,800,000.00)
$300,000.00
$(500,000.00)
$500,000.00
$(2,300,000.00)
$440,000.00
NPV
($259,956.99)
IRR
8.02%
$1,240,000.00
41
Step 3: Solve (cont.)
 What if fixed costs increase by 10%?
Year-0
Years 1-4
Revenues
Year-5
5,000,000
5,000,000
$(3,600,000.00)
$(3,600,000.00)
Less: Depreciation Expense
$(300,000.00)
$(300,000.00)
Less: Cash Fixed Cost
$(440,000.00)
$(440,000.00)
Net Operating Income
$660,000.00
$660,000.00
$(198,000.00)
$(198,000.00)
Net operating profit after tax
$462,000.00
$462,000.00
Plus: Depreciation Expense
$300,000.00
$300,000.00
Less: Variable Cost
Les: Taxes
Less: CAPEX
Less: Change in Working Capital
Free Cash Flow
$(1,800,000.00)
$300,000.00
$(500,000.00)
$500,000.00
$(2,300,000.00)
$762,000.00
NPV
$900,780.95
IRR
25.22%
$1,562,000.00
42
Step 3: Solve (cont.)
 The following table shows the impact on NPV
of changes in the value drivers.
Value Drivers
Expected NPV
Revised NPV
% Change
Unit Sales (-10%)
$1,001,714.68
$648,446.62
-35%
Price per unit (-10%)
$1,001,714.68
$(259,956.99)
-126%
Variable Cost (+10%)
$1,001,714.68
$220,414.70
-78%
Cash Fixed Cost (+10%)
$1,001,714.68
$900,780.95
-10%
43
Step 4: Analyze
 Here we observe that a 10% adverse
change in value drivers has a significant
impact on NPV. If the price per unit
drops by 10%, the project turns negative
with the value of NPV declining by 126%.
44
Step 4: Analyze (cont.)
 The results also show that NPV is most
sensitive to changes in the selling price
and variable cost. Thus management
must be doubly sure that the estimates
on these value drivers are accurate.
Furthermore, once the project is
implemented, these two value drivers
must be closely monitored.
45
Scenario Analysis
 Sensitivity analysis involves changing one
value driver at a time and analyzing its effect
on the investment NPV.
 Scenario analysis considers the effect of
multiple changes in value drivers on the NPV.
For example, the scenarios could be Expected
or base-case, Worst-case and Best-case.
46
Checkpoint 13.3 - Project Risk Analysis: Scenario Analysis
The analysts performing the risk analysis on the
plasma cutting tool being considered by
Crainium, Inc. (described in Checkpoint 13.2)
now want to evaluate the project risk using
scenario analysis. Specifically, they now want to
evaluate the project’s risk using scenario analysis
aimed at evaluating the project’s NPV under
worst- and best-case scenarios for the project’s
value drivers.
47
Checkpoint 13.3
48
Checkpoint 13.3
49
Checkpoint 13.3: Check Yourself
The deepening recession that characterized the
economy caused Cranium’s management to
reconsider the base-case scenario for the
project by lowering their unit sales estimates to
175,000 at revised price per unit of $24.50.
Based on these projections, is the project still
viable? What if Longhorn followed a higher
price strategy of $35 per unit but only sold
100,000 units? What would you recommend
Longhorn do?
50
Step 1: Picture the Problem
 We are given the following revised estimates
for two scenarios:
Scenario 1
Unit Sales
Price per unit
Scenario 2
$175,000.00 $100,000.00
$24.50
$35
 Assume other relevant information is the
same as Checkpoint 13.2
51
Step 2: Decide on a Solution
Strategy
 Our objective is to determine the
sensitivity of NPV to the two scenarios.
 We can estimate the free cash flows as
before and then compute the NPVs for
the two scenarios and compare.
52
Step 3: Solve
 Scenario 1 cash flow and NPV/IRR estimates
Year-0
Years 1-4
Revenues
Year-5
$4,287,500.00
$4,287,500.00
$(3,500,000.00)
$(3,500,000.00)
Less: Depreciation Expense
$(250,000.00)
$(250,000.00)
Less: Cash Fixed Cost
$(400,000.00)
$(400,000.00)
Net Operating Income
$137,500.00
$137,500.00
Les: Taxes
$(41,250.00)
$(41,250.00)
Net operating profit after tax
$96,250.00
$96,250.00
Plus: Depreciation Expense
$250,000.00
$250,000.00
Less: Variable Cost
Less: CAPEX
Less: Change in Working Capital
Free Cash Flow
$(1,500,000.00)
$250,000.00
$(500,000.00)
$500,000.00
$(2,000,000.00)
$346,250.00
NPV
$326,276.10
IRR
6.29%
$1,096,250.00
53
Step 3: Solve (cont.)
 Scenario 2 cash flow and NPV/IRR estimates
Year-0
Years 1-4
Revenues
Year-5
$3,500,000.00
$3,500,000.00
$(2,000,000.00)
$(2,000,000.00)
Less: Depreciation Expense
$(250,000.00)
$(250,000.00)
Less: Cash Fixed Cost
$(400,000.00)
$(400,000.00)
Net Operating Income
$850,000.00
$850,000.00
$(255,000.00)
$(255,000.00)
Net operating profit after tax
$595,000.00
$595,000.00
Plus: Depreciation Expense
$250,000.00
$250,000.00
Less: Variable Cost
Les: Taxes
Less: CAPEX
Less: Change in Working Capital
Free Cash Flow
$(1,500,000.00)
$250,000.00
$(500,000.00)
$500,000.00
$(2,000,000.00)
$845,000.00
NPV
$1,471,606.03
IRR
36.10%
$1,595,000.00
54
Step 4: Analyze
 Examination of the two scenarios reveals
that this is a risky opportunity as there is
a wide divergence in the two NPV
estimates. The NPV could be as high as
$1,491,606 or as low as a negative
$326,276.
55
Simulation Analysis
 Scenario analysis provides the analyst with a
discrete number of estimates of project NPVs
for a limited number of cases or scenarios.
 Simulation analysis generates thousands of
estimates of NPV that are built upon
thousands of values for each of the
investment’s value drivers. These different
values arise out of each value driver’s
individual probability distribution.
56
Simulation Analysis (cont.)
 Simulation process involves the following steps:
1. Estimate the probability distributions for each of
the investment’s key value drivers.
2. Randomly select one value for each of the value
drivers from their respective probability
distributions.
3. Combine the values selected for each of the values
drivers to estimate project cash flows for each year
of the project’s life and calculate the project’s NPV.
57
Simulation Analysis (cont.)
4. Store or save the calculated value of the NPV
and repeat Steps 2 and 3. Computer
softwares can easily repeat steps 2 and 3
thousands of times.
5. Use the stored values of the project NPV to
construct a histogram or probability
distribution of NPV.
58
59
Break-Even Analysis
 Break-even analysis determines the minimum
level of output or sales that the firm must
achieve in order to avoid losing money i.e. to
break even.
 In most cases, break-even sales is defined as
the level of sales for which net operating
income equals zero.
60
Accounting Break-Even Analysis
 Accounting break-even analysis involves
determining the level of sales necessary to
cover total fixed costs (both cash fixed costs
and depreciation).
 To compute the accounting break-even point,
we need to decompose the costs into two
components: fixed costs and variable costs.
61
Accounting Break-Even Analysis
(cont.)
 Fixed costs are costs that do not vary directly
with sales revenue. For example, insurance
premiums, administrative salaries.
 As the number of units sold increases, fixed
cost per unit decreases, as fixed costs are
spread over larger quantities of output.
 Fixed costs are also known as indirect costs.
62
Accounting Break-Even Analysis
(cont.)
 Variable costs are costs that vary directly with
the level of sales. Hence, they are also
referred to as direct costs. For example,
hourly wages, cost of materials used, sales
commission.
 Variable costs per unit remain the same
regardless of the level of output.
63
64
Accounting Break-Even Analysis
(cont.)
 The accounting break-even point is the
level of sales that is necessary to cover both
variable and total fixed costs, such that the
net operating income is equal to zero.
65
Checkpoint 13.4 - Project Risk Analysis: Accounting
Break-Even Analysis
The new plasma cutting tool that Crainium, Inc. is considering
investing in as described in Checkpoint 13.2 has the following value
driver estimates of fixed and variable costs:
Company analysts are evaluating the project’s risks and want to
estimate the accounting break-even for the project’s annual
revenues and expenses. What is the break-even level of units?
66
Checkpoint 13.4
67
Checkpoint 13.4
68
Checkpoint 13.4
69
Checkpoint 13.4
70
Calculating the Cash Break-Even
Point
 The cash break-even point computes the level
of sales where cash fixed costs (ignoring
depreciation) are covered and as a result, cash
flow is equal to zero.
71
NPV Break-Even Analysis
 The NPV break-even analysis identifies
the level of sales necessary to produce a
zero level of NPV.
 NPV break-even focuses on cash flows,
not accounting profits.
72
73
Operating Leverage and the
Volatility of Project Cash Flows
 The composition of fixed and variable
costs vary by firm. For example, a
manufacturing firm is likely to have a
higher fixed cost component compared
to service firm.
74
Operating Leverage and the Volatility of
Project Cash Flows (cont.)
 Most businesses may have some flexibility in
their cost structure and maybe able to alter
the composition of fixed and variable costs, at
least marginally.
 The mix of fixed and variable costs will impact
the breakeven output and also the operating
leverage.
75
Operating Leverage and the Volatility
of Project Cash Flows (cont.)
 Operating leverage results from the use of
fixed costs in the operations of the firm and
measures the sensitivity of changes in
operating income to changes in sales.
 Degree of operating leverage (DOL) measures
the firm’s operating leverage for a particular
level of sales.
76
Operating Leverage and the Volatility
of Project Cash Flows (cont.)
 DOL indicates by what percentage the NOI will
change for a given percentage change in sales.
77
78
Operating Leverage and the Volatility
of Project Cash Flows (cont.)
 We can make the following observations
about operating leverage:
 Operating leverage results from
substitution of fixed operating costs for
variable operating costs.
 The effect of operating leverage is to
increase the effect of changes in sales on
operating income.
79
Operating Leverage and the Volatility
of Project Cash Flows (cont.)

The degree of operating leverage is an
indication of the firm’s use of operating
leverage. The DOL is not a constant but
decreases as the level of sales increases
beyond the breakeven point.

Operating leverage is a double-edged sword,
magnifying both profits and losses.
80
Real Options in
Capital Budgeting
Copyright © 2011 Pearson Prentice Hall. All rights reserved.
“The Edsel is here to stay.”
That's what Ford Motor
Company chairman Henry
Ford II told Ford dealers in
1957.
"The aim was right, but the target moved"
Even for business leaders with vision, the future is difficult to predict!
"There is no reason why anyone would
want a computer in their home."
Thus intoned Digital Equipment Corp.
founder Kenneth Olsen in 1977.
82
83
Real Options in Capital Budgeting
 Opportunities to alter the project’s cash flow
stream after the project has begun are
referred to as real options. The most common
sources of flexibility or real options that can
add value to an investment opportunity
include:
1. Timing Option – the option to delay a
project until expected cash flows are more
favorable.
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Real Options in Capital Budgeting
(cont.)
2. Expansion options – the option to increase
the scale and scope of an investment in
response to realized demand; and
3. Contract, Shut-down, and Abandonment
option – the option to slow down
production, halt production temporarily, or
stop production permanently
(abandonment).
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Checkpoint 13.5 - Analyzing Real Options: Option to Expand
You are considering introducing a new drive-in restaurant called SmoothThru featuring high protein and vitamin-laced smoothies along with other
organic foods. The initial outlay on this new restaurant is $2.4 million and
the present value of the free cash flows (excluding the initial outlay) is $2
million, such that the project has a negative expected NPV of$400,000.
Looking closer, you find that there is a 50% chance that this new
restaurant will be well received and will produce annual cash flows of
$320,000 per year forever (a perpetuity), while there is a 50% chance of it
producing a cash flow of only $80,000 per year forever (a perpetuity) if it
isn’t received well. The required rate of return you use to discount the
project cash flows is 10%. However, if the new restaurant is successful,
you will be able to build 4 more of them and they will have costs and cash
flows similar to the successful restaurant’s cash flows. If your new
restaurant is not received favorably, you will not expand. Ignoring the fact
that there would be a time delay in building additional new restaurants if
the project is favorably received, determine the project’s NPV.
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Checkpoint 13.5
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Checkpoint 13.5
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Checkpoint 13.5 – Check Yourself
 If you thought there was a 40% chance
that this project would be favorably
received and 60% chance that the
project would be unfavorably received,
what would be the NPV of the project if
you were to introduce 10 additional
restaurants if it is well received?
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Step 1: Picture the Problem
P(favorable)
=.4
Build 1 smooth-Thru
at a cost of $2.4
million
P(Unfavorable)
=.6
Build 10 more
restaurants
NPV =10 x $800,000
Don’t build any
more restaurants
NPV = -$1,600,000
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Step 2: Decide on a Solution
Strategy
 We need to determine the NPV of
this project assuming we will build
10 restaurants if the project is
favorably received and will not build
any additional restaurants if it is not
favorably received.
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Step 3: Solve
 We are given the following information (per
Restaurant):
 Perpetual annual cash flow (if favorably
received) = $320,000
 Perpetual annual cash flow (if not favorably
received) = $80,000
 Probability of being favorably received = 40%
 Discount rate = 10%
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Step 3: Solve (cont.)
 We use the PV of perpetuity equation (given
by CF/i) to determine the present value of
cash flows.
 NPV (if favorably received)
 =($320,000 ÷.10) - $2,400,000 = $800,000
 NPV (if not favorably received)
 = ($80,000 ÷.10) - $2,400,000 = -$1,600,000
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Step 3: Solve (cont.)
 Assuming we will open 10 restaurants if
it is favorably received and only one if it
is unfavorably received, we can
determine the expected NPV as follows:
 Expected NPV
= 10 (.4)($800,000) + 1(.60)(-1,600,000)
= $2,240,000
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Step 4: Analyze
 Without the option to expand, this project
would have had a NPV of -$640,000.
 NPV = $800,000(.4) + (-$1,600,000)(.6)
= -$640,000
 However, by considering the option to
expand, the project has a positive NPV.
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Real Options Example#3:
OI Ltd. is considering a project that has an up-front cost of
$250,000. The project’s subsequent cash flows critically depend
on whether its products become the industry standard. There is a
50% chance that the products will become the industry standard,
in which case the project’s expected cash flows will be $110,000
at the end of each of the next five years. There is a 50% chance
that the products will not become the industry standard, in which
case the project’s expected cash flows will be $25,000 at the end
of each of the next five years. Assume that the cost of capital is 12
percent. Further, assume that one year from now OI will know if its
products will have become the industry standard. Also assume
that after receiving the cash flows at t = 1, the company has the
option to abandon the project. If it abandons the project it will
receive an additional $100,000 at t = 1, but will no longer receive
any cash flows after t = 1. Assume that the abandonment option
does not affect the cost of capital. What is the estimated value
of the abandonment option?
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