Chapter 12

Cash Flow Estimation and

Risk Analysis

 Pearson Prentice Hall

 Capital Budgeting
 The process of planning for purchases
of long-term assets.
 Capital Budgeting Steps
1) Evaluate Cash Flows
Look at all incremental cash flows
occurring as a result of the project.
 Initial outlay
 Differential Cash Flows over the life
of the project (also referred to as
annual cash flows).
 Terminal Cash Flows
 Capital Budgeting Steps
1) Evaluate Cash Flows

Initial Terminal
outlay Cash flow

0 1 2 3 4 5 6 ... n

Annual Cash Flows

 Capital Budgeting Steps

2) Evaluate the Risk of the Project

 We’ll get to this in the next chapter.
 For now, we’ll assume that the risk of the
project is the same as the risk of the
overall firm.
 If we do this, we can use the firm’s cost of
capital as the discount rate for capital
investment projects.
 Capital Budgeting Steps

3) Accept or Reject the Project

Capital Budgeting: The process of planning
for purchases of long-term assets.

For example: Our firm must decide whether

to purchase a new plastic molding machine
for $127,000. How do we decide?
 Will the machine be profitable?
 Will our firm earn a high rate of return on
the investment?
 The relevant project information follows:
 The cost of the new machine is $127,000.
 Installation will cost $20,000.
 $4,000 in net working capital will be needed at
the time of installation.
 The project will increase revenues by $85,000 per
year, but operating costs will increase by 35% of
the revenue increase.
 Simplified straight line depreciation is used.
 Class life is 5 years, and the firm is planning to
keep the project for 5 years.
 Selling price at the end of year 5 will be $50,000.
 14% cost of capital; 34% marginal tax rate.
 Step 1: Evaluate Cash Flows
a) Initial Outlay: What is the cash flow at
“time 0?”

Purchase price of the asset

+ shipping and installation costs
Depreciable asset
+ Investment in working capital
- After-tax proceeds from sale of old asset
Net Initial Outlay
 Step 1: Evaluate Cash Flows
 a) Initial Outlay: What is the cash flow at
“time 0?”

127,000 Purchase price of asset

+ 20,000 Shipping and installation
147,000 Depreciable asset
+ 4,000 Net working capital
+ 0 Proceeds from sale of old asset
$151,000 Net initial outlay
 Step 1: Evaluate Cash Flows
b) Annual Cash Flows: What
incremental cash flows occur over the
life of the project?
 For Each Year, Calculate:
Incremental revenue
- Incremental costs
- Depreciation on project
Incremental earnings before taxes
- Tax on incremental EBT
Incremental earnings after taxes
+ Depreciation reversal
Annual Cash Flow
 For Years 1 - 5:
Incremental revenue
- Incremental costs
- Depreciation on project
Incremental earnings before taxes
- Tax on incremental EBT
Incremental earnings after taxes
+ Depreciation reversal
Annual Cash Flow
 For Years 1 - 5:
85,000 Incremental Revenue
(29,750) Incremental Costs (35% x 85,000)
(29,400) Incremental depreciation (147,000/5)
25,850 Incremental EBT
(8,789) Tax on incremental EBT (34%)
17,061 Incremental EAT
29,400 Depreciation reversal
46,461 Annual Cash Flow
 Step 1: Evaluate Cash Flows

c) Terminal Cash Flow: What is the cash

flow at the end of the project’s life?

Selling price
-/+ Tax effects of capital gain/loss
+ Recapture of net working capital
Terminal Cash Flow
 Step 1: Evaluate Cash Flows

c) Terminal Cash Flow: What is the cash

flow at the end of the project’s life?

50,000 Selling price

-/+ Tax effects of capital gain/loss
+ Recapture of net working capital
Terminal Cash Flow
 Tax Effects of Sale of Asset:
 Selling price = $50,000.
 Book value = depreciable asset - total
amount depreciated.
 Book value = $147,000 - $147,000
= $0.
 Capital gain = SV - BV
= 50,000 - 0 = $50,000.
 Tax payment = 50,000 x .34 = ($17,000).
 Step 1: Evaluate Cash Flows

c) Terminal Cash Flow: What is the cash

flow at the end of the project’s life?

50,000 Selling price

(17,000) Tax on capital gain
4,000 Recapture of NWC
37,000 Terminal Cash Flow
 Project NPV:
 CF(0) = -151,000.
 CF(1 - 4) = 46,461.
 CF(5) = 46,461 + 37,000 = 83,461.
 Discount rate = 14%.
 NPV = PV of CF(1-5) – CF(0)
= 46,461[(1-(1.14)^-4)/.14] +
83,461x(1.14)^-5 – 151,000
 NPV = $27,721.
 We would accept the project.
 Capital Rationing

 Suppose that you have evaluated

five capital investment projects
for your company.
 Suppose that the VP of Finance
has given you a limited capital
budget.
 How do you decide which
projects to select?
 Capital Rationing

 You could rank the projects by IRR:

IRR
25% Our budget is limited
so we accept only
20% projects 1, 2, and 3.
15%
10%
5% 1 2 3 4 5

$X $
 Capital Rationing

 Ranking projects by IRR is not

always the best way to deal with a
limited capital budget.
 It’s better to pick the largest NPVs.
 Let’s try ranking projects by NPV.
Problems with Project Ranking

1) Mutually exclusive projects of unequal

size (the size disparity problem)
 The NPV decision may not agree with
IRR or PI.
 Solution: select the project with the
largest NPV.
 Size Disparity Example
Project A Project B
year cash flow year cash flow
0 (135,000) 0 (30,000)
1 60,000 1 15,000
2 60,000 2 15,000
3 60,000 3 15,000
required return = 12% required return = 12%
IRR = 15.89% IRR = 23.38%
NPV = $9,110 NPV = $6,027
PI = 1.07 PI = 1.20
 Problems with Project Ranking
2) The time disparity problem with mutually
exclusive projects.
 NPV and PI assume cash flows are
reinvested at the required rate of return for
the project.
 IRR assumes cash flows are reinvested at
the IRR.
 The NPV or PI decision may not agree with
the IRR.
 Solution: select the largest NPV.
 Time Disparity Example
Project A Project B
year cash flow year cash flow
0 (48,000) 0 (46,500)
1 1,200 1 36,500
2 2,400 2 24,000
3 39,000 3 2,400
4 42,000 4 2,400
required return = 12% required return = 12%
IRR = 18.10% IRR = 25.51%
NPV = $9,436 NPV = $8,455
PI = 1.20 PI = 1.18
 Mutually Exclusive Investments
with Unequal Lives

 Suppose our firm is planning to

expand and we have to select one of
two machines.
 They differ in terms of economic life
and capacity.
 How do we decide which machine to
select?
The after-tax cash flows are:
Year Machine 1 Machine 2
0 (45,000) (45,000)
1 20,000 12,000
2 20,000 12,000
3 20,000 12,000
4 12,000
5 12,000
6 12,000
Assume a required return of 14%.
 Step 1: Calculate NPV
 NPV1 = $1,433
 NPV2 = $1,664

 So, does this mean #2 is better?

 No! The two NPVs can’t be
compared!
 Step 2: Equivalent Annual
Annuity (EAA) method

 If we assume that each project will be

replaced an infinite number of times in the
future, we can convert each NPV to an
annuity.
 The projects’ EAAs can be compared to
determine which is the best project!
 EAA: Simply annuitize the NPV over the
project’s life.
 EAA with your calculator:

 Simply “spread the NPV over the life of

the project”
 Machine 1: PV = 1433, N = 3, I = 14,
solve: PMT = 1433/((1-(1.14)^-3)/.14
PMT = 617.24.
 Machine 2: PV = 1664, N = 6, I = 14,
solve: PMT = 1664/((1-(1.14)^-6)/.14
PMT = 427.91.
 EAA1 = $617
 EAA2 = $428
 This tells us that:
 NPV1 = annuity of $617 per year.
 NPV2 = annuity of $428 per year.
 So, we’ve reduced a problem with
different time horizons to a couple of
annuities.
 Decision Rule: Select the highest EAA.
We would choose machine #1.
Three Measures of a Project’s Risk

Stand-Alone
Risk The risk an asset
would have if it were
a firm’s only asset
and if investors
owned only one
Corporate stock.
(Within-Firm)
Risk
Risk
considering the firm’s
diversification but not
stockholder
Considers both
Market Risk diversification
firm and
stockholder
diversification
 Incorporating Risk into
Capital Budgeting

Two Methods:
 Certainty Equivalent Approach
 Risk-Adjusted Discount Rate
 How can we adjust this model to
take risk into account?
n

S
FCFt
NPV = - IO
(1 + k) t
t=1
 Adjust the After-tax Cash Flows (ACFs),
or
 Adjust the discount rate (k).
Certainty Equivalent Approach
 Adjusts the risky after-tax cash flows
to certain cash flows.
 The idea:

Risky Certainty Certain

Cash X Equivalent = Cash
Flow Factor (a) Flow
 Certainty Equivalent Approach
Risky Certainty Certain
Cash X Equivalent = Cash
Flow Factor (a) Flow

Risky “safe”
$1000 .70 $700
 Certainty Equivalent Approach
Risky Certainty Certain
Cash X Equivalent = Cash
Flow Factor (a) Flow

Risky “safe”
$1000 .95 $950
 The greater the risk associated
with a particular cash flow,
the smaller the CE factor.
Certainty Equivalent Method

n
NPV = S
t=1
t ACFt
(1 + krf) t
- IO
 Certainty Equivalent Approach

 Steps:
1) Adjust all after-tax cash flows by
certainty equivalent factors to get
certain cash flows.

2) Discount the certain cash flows by

the risk-free rate of interest.
 Incorporating Risk into
Capital Budgeting

 Risk-Adjusted Discount Rate

 The discount rate (cost of capital)
appropriate for a given project,
given the riskiness of that project.
The greater the risk, the higher
the discount rate.
 How can we adjust this model
to take risk into account?

S
ACFt
NPV = - IO
(1 + k) t
t=1

 Adjust the discount rate (k).

 Risk-Adjusted Discount Rate

 Simply adjust the discount rate (k)

to reflect higher risk.
 Riskier projects will use higher
risk-adjusted discount rates.
 Calculate NPV using the new risk-
adjusted discount rate.
Risk-Adjusted Discount Rate

S
FCFt
NPV = t - IO
(1 + k*)
t=1
 Risk-Adjusted Discount Rates

 How do we determine the

appropriate risk-adjusted discount
rate (k*) to use?
 Many firms set up risk classes to
categorize different types of
projects.
 Risk Classes
Risk RADR
Class (k*) Project Type
1 12% Replace equipment,
Expand current business
2 14% Related new products
3 16% Unrelated new products
4 24% Research & Development
Other Approaches to Evaluating
Risk in Capital Budgeting
 Monte Carlo Simulation
 Scenario Analysis
 Sensitivity Analysis
 Monte Carlo Simulation
 A risk analysis technique in which probable future events are
simulated on a computer, generating estimated rates of return
and risk indexes.
 Step 1: Develop probability distribution for key factors
ex. units sold, sales price, variable cost per unit, fixed costs,
market share, and others
 Step 2: Randomly select values from these distributions
 Step 3: Combine these factors and determine an NPV.
 Step 4: Repeat this process perhaps 1,000 times, generating
1,000 NPVs.clear portrait of the results is obtained.
 Step 5: Compute the mean of 1,000 NPVs as measure of
expected probability and the standard deviation of the NPV as
a measure of risk.
 Scenario Analysis
 A risk analysis technique in which “bad” and
“good” sets of financial circumstances are
compared with a most likely situation.
 Example:
Outcome Internal Rate of Return
Best 30%
Most Likely 15%
Worst 0%
 Sensitivity Analysis
 Percentage change in NPV resulting from a given
percentage change in an input variable, other things
held constant.
 This is done by changing the value of one input
variable while holding the other input variables
constant.
 The distribution of possible NPVs that is generated is
compared with the distribution of possible returns
generated before the change was made to determine
the effect of the change.