FIN 468: Intermediate
Corporate Finance
Topic 3–Capital Budgeting
Larry Schrenk, Instructor
1 (of 22)
Topics

Review of Decision Rules

Incremental Cash Flow Analysis

Model to Value the Net Cash Flows

Investments of Unequal Lives
Decision Rules
Decision Rules





Payback Period
Discounted Payback Period
Net Present Value (NPV)
Internal Rate of Return (IRR)
Modified Internal Rate of Return (MIRR)
Criteria for Decision Rules






Recognize the time value of money
Incorporate all relevant free cash flows
Minimize arbitrary assumptions
Minimize need for uncertain data
Minimize excessive calculation complexity
Minimize problems
Data

For simplicity, we shall use the following cash
flows for many of our examples (r = 10%):
0
-1,000
1
300
2
200
3
400
4
700
Payback Period

EXAMPLE:
0
-1,000

2
200
3
400
4
700
3 Year Payback Period Calculation


1
300
300 + 200 + 400 = 900 < 1,000
Result: $900.00 < $1,000.00 Bad Project
Discounted Payback Period

EXAMPLE (r = 10%):
0
-1,000

1
300
2
200
3
400
4
700
3 Year Discounted Payback Period Calculation:
300.00 200.00 400.00


 $738.54  $1,000.00
2
3
1.1 1.1
1.1

Result: $738.54 < $1,000.00 Bad Project
Net Present Value (NPV)

EXAMPLE (r = 10%):
0
-1,000

1
300
2
200
3
400
4
700
NPV Calculation:
300.00 200.00 400.00 700.00
1,000 



 $216.65  0
2
3
4
1.1 1.1
1.1
1.1

Result: $216.65 > 0 Good Project
Internal Rate of Return (IRR)

EXAMPLE (r = 10%):
0
-1,000

1
300
2
200
3
400
4
700
IRR Calculation:
300.00
200.00
400.00
700.00
1,000 



0
2
3
4
1  IRR  1  IRR  1  IRR  1  IRR 
iff IRR = 18.1%
18.1% > 10%

Result: 18.1% > 10% Good Project
Modified Internal Rate of Return

EXAMPLE (r = 10%):
0
-1,000


1
300
2
200
3
400
4
700
Find the MIRR that makes the present value of all
cash outflows equal to the present value of the
terminal value.
$1,781.30
MIRR s.t 1,000 
(1  MIRR )4
 MIRR  15.53%
Result: 15.53% > 10% Good Project
Summary of the Five Rules

Ineffective Rules:



Payback Period: Payback period cash flow >
investment
Discounted Payback Period: Discounted
payback period cash flow > investment
Effective Rules



NPV: NPV > 0
IRR: IRR > r
MIRR: MIRR > r
Some Additional Issues
Some Additional Issues



Comparing NPV, IRR, PI and MIRR
Using Decision Rules to Compare or Select
among Projects
Sign Changes in the Cash Flows and
Multiple IRR’s
Capital Budgeting
15 (of 22)
Topics

Two General Principles

Factors in Cash Flow Analysis








Fixed versus Variable Costs
Depreciation
Working Capital
Taxes
Interest Payments and Financing Costs
Sunk Costs
Opportunity Costs
Externalities
Two General Principles

Principle One: Use Increments.


The Incremental Approach to Cash Flow
Analysis
Principle Two: Use Real Cash Flows.

Real versus Accounting Cash Flows
The Incremental Approach

The Incremental Approach to Cash Flow
Analysis

Incremental: How real cash flows change

Alternate: Averages
Comparison Example

New Project Costs
Cost
Before
Furniture $10,000
Software
$9,000
Insurance $4,000
After
$12,000
$9,000
$6,000
Average
Increment
Comparison Example

Average Approach
Cost
Before
Furniture $10,000
Software
$9,000
Insurance $4,000
After
$12,000
$9,000
$6,000
Average
$4,000
$3,000
$2,000
Increment
Comparison Example

Incremental Approach

Cost
change in costs, i.e., the increment, associated with the new
project:
Before
Furniture $10,000
Software
$9,000
Insurance $4,000
After
$12,000
$9,000
$6,000
Average
$4,000
$3,000
$2,000
Increment
$2,000
$0
$2,000
Comparison Example

Conclusion: Use the increment
Cost
Before
Furniture $10,000
Software
$9,000
Insurance $4,000
After
$12,000
$9,000
$6,000
Average
$4,000
$3,000
$2,000
Increment
$2,000
$0
$2,000
Real versus Accounting Values

Real: Actual transfers of value at this time;
Market values


Money, assets, etc.
Accrual Accounting

May not be market values


Goodwill, depreciation
May not be current

‘accrued’, ‘payable’
NOTE: Possible ambiguity…
Real versus Accounting
Real versus Nominal
Real versus Accounting Example

Payment of $6,000 for insurance over the next
three years.
Accounting
Real
Real versus Accounting Example

Accrual Accounting Cash Flow


‘Matching’
Profit
Accounting
$2,000
$2,000
$2,000
Real
Real versus Accounting Example

Real Cash Flow
Accounting
Real
$2,000
$6,000
$2,000
$0
$2,000
$0
Real versus Accounting Cash Flows

A Complication

Non-real cash flow has an effect on a real cash
flow.

Incorporate the effect, but not non-real cash flow itself.

Depreciation
Factors in Cash Flow
Analysis
Factors in Cash Flow Analysis







Depreciation
Working Capital
Taxes
Interest Payments and Financing Costs
Sunk Costs
Opportunity Costs
Externalities
Depreciation
Depreciation

Depreciation not real cash flow!

Effects on real cash flow, i.e., taxes


If a firm had no taxable income, then we could ignore
depreciation.
Incorporate


the tax effect of depreciation
not the depreciation itself.
Classes of Expenditures



Costs: ‘expensed’

In theory, the value is exhausted during that one period

E.g. Stationary, production materials, etc.
Deductible Investments: Over time.

In theory, the value is exhausted over multiple periods.

E.g. Factory equipment, computers, etc.
Non-Deductible Investments: Never

In theory, the value is never exhausted

E.g. Land
Depreciation

Different methods (‘schedules’) and over
different lengths of time.
MARCS Example
Schedule

1
2
3
4
20%
32%
19.2%
11.52% 11.52% 5.76%

Capital investment $1,000,000

Yearly depreciation is:
1
2
3
4
5
5
6
6
$200,000 $320,000 $192,000 $115,200 $115,200 $57,600
For More Depreciation Details…

If you actually want to know more…

To dip in your toe:
http://www.irs.gov/businesses/small/article/0,,id=137026,00.html

Not for the faint of heart: Publication 946 (2005),
How To Depreciate Property
http://www.irs.gov/publications/p946/index.html
Depreciation Calculation
1.
2.
3.
4.
Begin with gross income/EBDIT.
Subtract the depreciation to get taxable
income/EBIT.
Subtract the taxes based on this taxable
income to get net income.
Add depreciation back to net income to get
operating cash flow.
Depreciation Example▪
Gross Income/EBDIT
$200,000
Less: Depreciation
$50,000
Taxable Income/EBIT
$150,000
Less: Taxes
(tC = 35%)
$52,500
Net Income
$97,500
Plus: Depreciation
$50,000
Real Cash Flow
$147,500 ▪
Working Capital
Working Capital

Metaphorically, the grease that keeps the
machine of business going!

Production takes place over time.

Materials paid for long before product sold

Money must be available for suppliers, employees, etc.

This investment is ‘working capital’.
Working Capital


All working capital eventually returned

Working capital as a ‘loan’ to the project

But ‘cost’ to tying up value in working capital
Calculations

Increase in working capital → negative CF

Decrease in working capital → positive CF
Working Capital Example


Initial working capital required $10,000
Working capital must be10% of sales:
Period
0
1
2
3
4
Sales
$0
$130,000
$150,000
$90,000
$50,000
WC
$10,000
$13,000
$15,000
$9,000
$5,000
D WC
($10,000)
($3,000)
($2,000)
$6,000
$9,000*
* Remember that at the end of the project all remaining working
capital is recovered―$9,000 = $4,000 released plus $5,000
remaining.
Taxes, Interest Payments,
Sink Costs, etc.
Taxes

The corporate tax rate is tC.

Marginal Tax Rate

Negative Earnings Issue
Interest/Financing Payments

Not included in cash flows

Accounted for in the discount rate

‘Double counting’

Contrast income statement
Sunk Costs

Past expenditures



Irrelevant to project the.


No value to project
No value as salvage
Ignore sunk costs
Psychological Problem

Behavioral finance
Opportunity Costs

What you give up

Technically: next most valuable use for the
asset




The value from selling or renting,
The value for another project,
Nothing,
Etc.
Opportunity Costs

Using Unoccupied Factory Space

Could be rented out for $10,000/year.


Otherwise unused.


Opportunity cost = $10,000/year.
Opportunity cost = $0/year.
Include all opportunity costs.
Externalities

Project not independent of the firm.

Externalities




Possible interactions with other parts of firm
Positive: Synergies
Negative: Cannibalization
Incremental principle

Externality costs must be applied to the new project,
Steps in Estimating Cash Flows▪







Get input parameters.
Determine investment.
Determine operating cash flow.
Determine working capital needs.
Incorporate after tax salvage value
Find annual, net project cash flows.
Apply decision criteria. ▪
Example: Data

Production

Units/year
1
50,000

100,000
3
4
5
80,000
60,000
20,000
Costs



2
Fixed = $50,000 (real)
Variable = $150.00/unit (nominal)
Revenue


Initial Price = $300.00/unit (nominal)
Increase in Price = 2%/year
Example: Data

Capital Spending



Opportunity Cost



Investment = $20,000,000 (nominal)
Set Up Costs = $500,000 (nominal, non-depreciable)
Factory Capacity = $5,000,000 (nominal)
Project Feasibility Study = $2,000,000 (nominal)
Salvage Value = $2,000,000 (nominal)
Example: Data



Nominal Discount Rate = 15%
Inflation Rate = 5%
Working Capital



Initial = $250,000 (Nominal)
Thereafter = 8% (of sales)
Corporate Tax Rate = 38%
Example: 1-Input Parameters
1) Parameters
Tax Rate
38%
Fixed Cost
$50,000
Variable Cost
$150
Initial Price
$300
Price Growth
2%
Salvage Value
$2,000,000
Working Capital Rate
12%
Inflation Rate
5%
Nominal Discount Rate
Year
15%
0
1
2
3
4
5
Units sold
50,000
100,000
80,000
60,000
20,000
MACRS Depreciation
20.00%
32.00%
19.20%
11.52%
11.52%
6
5.76%
Example: 2-Capital Spending
2) Investment
0
1
2
3
4
5
Investment
($20,000,000)
Set Up Costs
($500,000)
Factory (Opportunity
Cost)
($5,000,000)
$5,000,000
Equals: Capital
Spending
($25,500,000)
$5,000,000



Total Investment = $25,500,000
Set-up and opportunity costs are not depreciable.
Opportunity cost is ‘returned’ at project end.
Example: 3-Operating CF Year 1
3) Operating
Cash Flow
Calculation
1
Sales revenue
= units x price = 50,000 x $300 =
$15,000,000
Less: variable
costs
= units x variable cost = 50,000 x $150 =
($7,500,000)
Less: fixed costs
Equals: EBDIT
= fixed cost =
= revenue – variable cost – fixed cost =
Less: depreciation = investment x MARCS = $20,000,000 x 20% =
($50,000)
$7,450,000
($4,000,000)
Equals: EBIT
= EBDIT – depreciation =
$3,450,000
Minus: taxes
= tax rate x EBIT = 38% x $3,450,000 =
($1,311,000)
Equals: net income
= EBIT – Taxes =
$2,139,000
Plus: depreciation
”
$4,000,000
Equals: operating
cash flow
= net income + depreciation =
$6,139,000
Example: 3-Operating CF Year 2-5

Changes in Sales Revenue



Production changes
Price increases at 2% per year
1
2
3
4
5
$300
$306
$312
$318
$325
Changes in Depreciation

Follows MARCS
Example: 3-Operating CF Year 2-5

Changes in Variable Costs


Production changes
Changes in Fixed Cost

Fixed cost are stated in real terms, so inflation needs
to be taken into account:
1
2
50,000
50,000(1.05)
($50,000)
($52,500)
3
4
5
50,000(1.05)2 50,000(1.05)3 50,000(1.05)4
($55,125)
($57,881)
($60,775)
Example: 3-Operating CF Year 2-5
3) Operating Cash Flow
0
1
2
3
4
5
Sales revenue
$15,000,000
$30,600,000
$24,969,600
$19,101,744
$6,494,593
Less: variable costs
($7,500,000)
($15,000,000)
($12,000,000)
($9,000,000)
($3,000,000)
Less: fixed costs
($50,000)
($52,500)
($55,125)
($57,881)
($60,775)
Equals: EBDIT
$7,450,000
$15,547,500
$12,914,475
$10,043,863
$3,433,818
Less: depreciation
($4,000,000)
($6,400,000)
($3,840,000)
($2,304,000)
($2,304,000)
Equals: EBIT
$3,450,000
$9,147,500
$9,074,475
$7,739,863
$1,129,818
Minus: taxes
($1,311,000)
($3,476,050)
($3,448,301)
($2,941,148)
($429,331)
Equals: net income
$2,139,000
$5,671,450
$5,626,175
$4,798,715
$700,487
Plus: depreciation
$4,000,000
$6,400,000
$3,840,000
$2,304,000
$2,304,000
Equals: operating cash flow
$6,139,000
$12,071,450
$9,466,175
$7,102,715
$3,004,487
Example: 4-Working Capital
4) Working Capital
NWC requirement
0
$250,000
1
$1,200,000
2
$2,448,000
3
$1,997,568
4
$1,528,140
Liquidation of WC
Change in WC





$1,528,140
($250,000)
($950,000)
($1,248,000)
$450,432
Initial Working Capital = ($250,000)
Change in Working Capital =

5
-(New WC Requirement – Old WC Requirement)
Year 1: -($1,200,000 - $250,000) = ($950,000)
Year 3: -($1,997,568 - $2,448,000) = $450,532
In final year all working capital is returned.
$469,428
$1,528,140
Example: 5-Salvage Value

Salvage value
$2,000,000
Minus: tax on salvage value
($322,240)
Equals: after tax salvage value
$1,677,760
Remaining Book Value


Undepreciated Salvage Value


$2,000,000 - $1,152,000 = $848,000
Tax on Undepreciated Salvage Value


$20,000,000 x 5.76% = $1,152,000
$848,000 x 38% = $322,240
After Tax Salvage Value

$2,000,000 - $322,240 = $1,677,760
Example: 6-Net Project Cash
Flows
6) Net Project Cash
Flows
0
1
2
3
4
5
Operating cash flow
$0
$6,139,000
$12,071,450
$9,466,175
$7,102,715
$3,004,487
change in NWC
($250,000)
($950,000)
($1,248,000)
$450,432
$469,428
$1,528,140
after tax salvage value
$0
$0
$0
$0
$0
$1,677,760
change capital spend
($25,500,000)
$0
$0
$0
$0
$5,000,000
Project Cash Flows:
($25,750,000)
$5,189,000
$10,823,450
$9,916,607
$7,572,143
$11,210,386

Annual, net project cash flows are sum of operating cash flows,
changes in working capital, salvage value and change in capital
spending.
Example: 7-Decision Criteria
7) Decision Criteria
Net Present Value
$3,369,528
Internal Rate of Return
19.98%
Complete Example

You cannot read this–but you can paste it into a word
document and expand it!
1) Parameters
Tax_Rate
Fixed_Cost
Variable_Cost
Initial_Price
Price_Growth
Salvage_Value
Working_Capital_Rate
Inflation_Rate
Nominal_Discount_Rate
Year
Units sold
MACRS Depreciation
38%
$50,000
$150
$300
2%
$2,000,000
12%
5%
15%
0
1
50,000
20.00%
2
100,000
32.00%
3
80,000
19.20%
4
60,000
11.52%
5
20,000
11.52%
2) Investment
Investment ($20,000,000)
Set Up Costs
($500,000)
Factory (Opportunity Cost) ($5,000,000)
Equals: Capital Spending ($25,500,000)
$5,000,000
$5,000,000
3) Operating Cash Flow
Sales revenue
Less: variable costs
Less: fixed costs
Equals: EBDIT
Less: depreciation
Equals: EBIT
Minus: taxes
Equals: net income
Plus: depreciation
Equals: operating cash flow
4) Working Capital
Net working capital requirement
Liquidation of working capital
Change in working capital
$250,000
($250,000)
$15,000,000
($7,500,000)
($50,000)
$7,450,000
($4,000,000)
$3,450,000
($1,311,000)
$2,139,000
$4,000,000
$6,139,000
$30,600,000
($15,000,000)
($52,500)
$15,547,500
($6,400,000)
$9,147,500
($3,476,050)
$5,671,450
$6,400,000
$12,071,450
$24,969,600
($12,000,000)
($55,125)
$12,914,475
($3,840,000)
$9,074,475
($3,448,301)
$5,626,175
$3,840,000
$9,466,175
$1,200,000
$2,448,000
$1,997,568
$1,528,140
$450,432
$469,428
($950,000) ($1,248,000)
$19,101,744
$6,494,593
($9,000,000) ($3,000,000)
($57,881)
($60,775)
$10,043,863
$3,433,818
($2,304,000) ($2,304,000)
$7,739,863
$1,129,818
($2,941,148)
($429,331)
$4,798,715
$700,487
$2,304,000
$2,304,000
$7,102,715
$3,004,487
$1,528,140
$1,528,140
5) Salvage Value
Salvage value
Minus: tax on salvage value
Equals: after tax salvage value
$2,000,000
($322,240)
$1,677,760
6) Net Project Cash Flows
Operating cash flow
$0
Minus: change in net working capital
($250,000)
Plus: after tax salvage value
$0
Minus: change capital spend ($25,500,000)
Project Cash Flows: ($25,750,000)
7) Decision Criteria
Net Present Value
Internal Rate of Return
Profitability Index
$3,369,528
19.98%
1.13
$6,139,000 $12,071,450
($950,000) ($1,248,000)
$0
$0
$0
$0
$5,189,000 $10,823,450
$9,466,175
$450,432
$0
$0
$9,916,607
$7,102,715
$469,428
$0
$0
$7,572,143
$3,004,487
$1,528,140
$1,677,760
$5,000,000
$11,210,386
6
5.76%
Other Methods for Computing OCF

Bottom-Up Approach



Top-Down Approach



Works only when there is no interest expense
OCF = NI + depreciation
OCF = Sales – Costs – Taxes
Don’t subtract non-cash deductions
Tax Shield Approach

OCF = (Sales – Costs)(1 – T) + (Depreciation * T)
NOTE: Cautions about ‘Formulae’ Approach
Investments of Unequal
Lives
Investments of Unequal Lives



Air cleaner is mandated by law.
Two choices:
Model
Cadillac Cleaner
Cheapskate Cleaner
Price
$4,000
$1,000
Annual Cost
$100
$500
Life
10 years
5 years
Assuming a 10% discount rate, which one
should we choose?
Investments of Unequal Lives

Replacement Chain



Repeat projects until they begin and end at
the same time.
Compute NPV for the “repeated projects.”
The Equivalent Annual Cost Method
Replacement Chain Approach
The Cadillac cleaner time line of cash flows:
-$4,000 –100 -100
0
1
2
-100 -100 -100
3
4
5
-100 -100
6
7
-100
8
-100
-100
9
10
The Cheapskate cleaner time line of cash flows
over ten years:
-$1,000 –500 -500
0
1
2
-500 -500 -1,500
3
4
5
-500 -500
6
7
-500
8
-500
-500
9
10
Equivalent Annual Cost (EAC)



Greater Applicability
The EAC is the value of the level payment annuity
that has the same PV as our original set of cash
flows.
EAC like Average Annual Cost to Operate
Equivalent Annual Cost (EAC)

Cadillac Air Cleaner
1) Find PV of Annual Cost
P/Y = 1; N = 10; I/Y = 10; PMT = -100; FV = 0
→ PV = $614.47
2) Add Price $4,000.00 + 614.47 = $4,614.47
3) Find EAC
P/Y = 1; N = 10; I/Y = 10; PMT = - 4,614.47; FV = 0
→ PMT = $750.98 = EAC

Problem: Cheapskate Air Cleaner flows.