CHAPTER 9
Capital Budgeting
 PV of Cash Flows
 Payback
 NPV
 IRR
 EAA
 NPV profiles
Characteristics of Business Projects
 Project Types and Risk
 Capital projects have increasing risk according to
whether they are replacements, expansions or new
ventures
 Stand-Alone and Mutually Exclusive Projects
 A stand-alone project has no competing alternatives
 The project is judged on its own viability
 Mutually exclusive projects are involved when selecting
one project excludes selecting the other
Characteristics of Business Projects
 Project Cash Flows


The first and usually most difficult step in capital
budgeting is reducing projects to a series of cash flows
Business projects involve early cash outflows and later
inflows

The initial outlay is required to get started
 The Cost of Capital

A firm’s cost of capital is the average rate it pays its
investors for the use of their money


In general a firm can raise money from two sources: debt and
equity
If a potential project is expected to generate a return greater
than the cost of the money to finance it, it is a good investment
Capital Budgeting Techniques
 There are four basic techniques for
determining a project’s financial viability:




Payback (determines how many years it takes
to recover a project’s initial cost)
Net Present Value (determines by how much
the present value of the project’s inflows
exceeds the present value of its outflows)
Internal Rate of Return (determines the rate of
return the project earns [internally])
Equivalent annual annuity (EAA)
Capital Budgeting Techniques—
Payback
 The payback period is the time it takes to recover
early cash outflows

Shorter paybacks are better
 Payback Decision Rules
 Stand-alone projects
 If the payback period < (>) policy maximum accept
(reject)
 Mutually Exclusive Projects
 If PaybackA < PaybackB  choose Project A
 Weaknesses of the Payback Method
 Ignores the time value of money
 Ignores the cash flows after the payback period
Relevant Cash Flows
 Cash Flow (vs. Accounting Income)
 Incremental Cash Flows
 Partial budget concept
Example Projects
year
0
1
2
3
Project L
$
(100)
10
60
80
Project S
$
(100)
70
50
20
Payback for Project L
(Long: Most CFs in out years)
0
CFt
-100
Cumul
-100
PaybackL = 2
+
1
2
10
-90
60
-30
30/80
2.4
3
80
0
50
= 2.375 years
Project S (Short: CFs come
quickly)
0
1
-100
70
-100
-30
1.6
2
3
50
20
20
40
CFt
Cumul
PaybackL
0
= 1 + 30/50 = 1.6 years
Discounted Payback: Uses discounted
rather than raw CFs.
0
Project L
1
2
3
10%
CFt
-100
10
60
80
PVCFt
-100
9.09
49.59
60.11
Cumul(PV) -100
-90.91
-41.32
18.79
Disc.
payback
=
2
+ 41.32/60.11 = 2.7 yrs
Recover invest + cap costs in 2.7 yrs.
Capital Budgeting Techniques—
Payback: another example
 Consider the following cash flows
Year
Cash flow (Ci)
0
1
2
3
4
($200,000)
$60,000
$60,000
$60,000
$60,000
 Payback period is easily visualized by the cumulative cash flows
Year
0
1
2
3
4
Cash flow (Ci)
($200,000)
$60,000
$60,000
$60,000
$60,000
Cumulative cash
flows
($200,000)
($140,000)
($80,000)
($20,000)
$40,000
Payback period occurs at 3.33 years.
Capital Budgeting Techniques—
Payback— yet another example
Q: Use the payback period technique to choose between mutually exclusive
projects A and B.
Example
Project A
Project B
C0
($1,200)
($1,200)
C1
400
400
C2
400
400
C3
400
350
C4
200
800
C5
200
800
A: Project A’s payback is 3 years as its initial outlay is fully recovered in that
time. Project B doesn’t fully recover until sometime in the 4th year. Thus,
according to the payback method, Project A is better than B.
Capital Budgeting Techniques—
Payback
 Why Use the Payback Method?



It’s quick and easy to apply
Serves as a rough screening device
Indicates how long to resolve uncertainty
 The Present Value Payback Method

Involves finding the present value of the
project’s cash flows then calculating the
project’s payback
Capital Budgeting Techniques—Net
Present Value (NPV)
 NPV is the sum of the present values of a
project’s cash flows at the cost of capital
NPV

C0
PV outflows

C1
1+k 
1

C2
1+k 
2

PV inflows
 If PVinflows > PVoutflows, NPV > 0

Cn
1+k 
n
Capital Budgeting Techniques—Net
Present Value (NPV)
 NPV and Shareholder Wealth
 A project’s NPV is the net effect that
undertaking a project is expected to have on
the firm’s value



A project with an NPV > (<) 0 should increase
(decrease) firm value
Since the firm desires to maximize
shareholder wealth, it should select the capital
spending program with the highest NPV
NPV is the PV of economic profit
Capital Budgeting Techniques—Net
Present Value (NPV)
 Decision Rules

Stand-alone Projects



NPV > 0  accept
NPV < 0  reject
Mutually Exclusive Projects

NPVA > NPVB  choose Project A over B
Capital Budgeting Techniques—Net
Present Value (NPV) Example
Example
Q: Project Alpha has the following cash flows. If the firm considering Alpha has a
cost of capital of 12%, should the project be undertaken?
C0
($5,000)
C1
$1,000
C2
$2,000
C3
$3,000
A: The NPV is found by summing the present value of the cash flows when
discounted at the firm’s cost of capital.
NPV Alpha  -5,000 
1,000
1.12
1

2,000
3,000
1.12
1.12

2
3
 -5,000  892.90  1,594.40  2,135.40
 -5,000  4,622.70
 ($377.30)
Since Alpha’s
NPV<0, it
should not be
undertaken.
Use CF on the cash flow
j
 Show on the board
Techniques—Internal Rate of
Return (IRR)
 A project’s IRR is the return it generates on the
investment of its cash outflows

For example, if a project has the following cash flows
0
1
2
3
-5,000
1,000
2,000
3,000
The “price” of receiving
the inflows


Literally the IRR is the interest rate at which the present value of the three
inflows just equals the $5,000 outflow
If you lend yourself the money to make the investment, the IRR is the
highest interest rate you could charge and the investment pay off the loan
Techniques—Internal Rate of
Return (IRR)
 Defining IRR Through the NPV Equation
 The IRR is the interest rate that makes a project’s NPV
zero
IRR :
C0
PV
Project
cost
outflows

C1
1IRR 
1

C2
1IRR 
2


Cn
1IRR 
n
PV inflows
 Solve for IRR
 one equation, one unknown, but usually impossible to
solve with algebra
Techniques—Internal Rate of
Return (IRR)
 Decision Rules

Stand-alone Projects



If IRR > cost of capital (or k)  accept
If IRR < cost of capital (or k)  reject
Mutually Exclusive Projects

IRRA > IRRB  choose Project A over Project B
(but don’t use IRR to rank mutually exclusive
projects)
Techniques—Internal Rate of
Return (IRR)
 Calculating IRRs
 Finding IRRs usually requires an iterative, trial-anderror technique
 Guess at the project’s IRR
 Calculate the project’s NPV using this interest rate
 If NPV is zero, the guessed interest rate is the project’s
IRR
 If NPV > (<) 0, try a new, higher (lower) interest rate
Techniques—Internal Rate of
Return (IRR)—Example
Q: Find the IRR for the following series of cash flows:
C0
($5,000)
C1
C2
C3
$1,000
$2,000
$3,000
Example
If the firm’s cost of capital is 8%, is the project a good idea? What if the cost of
capital is 10%?
A: We’ll start by guessing an IRR of 12%. We’ll calculate the project’s NPV at
this interest rate.
NPV
 -5,000 
1,000
1.12
1

2,000
3,000
1.12
1.12 

2
3
 -5,000  892.90  1,594.40  2,135.40
 -5,000  4,622.70
 ($377.30)
Since NPV<0,
the project’s
IRR must be <
12%.
Techniques—Internal Rate of
Return (IRR)—Example
Example
We’ll try a different, lower interest rate, say 10%. At 10%, the project’s
NPV is ($184). Since the NPV is still less than zero, we need to try a
still lower interest rate, say 9%. The following table lists the project’s
NPV at different interest rates.
Interest Rate
Guess
Calculated
NPV
12%
($377)
10
($184)
9
($83)
8
$22
7
$130
Since NPV becomes
positive somewhere
between 8% and 9%, the
project’s IRR must be
between 8% and 9%. If the
firm’s cost of capital is 8%,
the project is marginal. If
the firm’s cost of capital is
10%, the project is not a
good idea.
The exact IRR can be calculated using a financial calculator. The financial
calculator uses the iterative process just demonstrated; however it is capable of
guessing and recalculating much more quickly.
Okay, if you haven’t already pointed it
out by now, there is really no reason to
do the trial and error yourself!
 Use the CFj calculator function (IRR key)
 Cash flows
 -5000
 1000
 2000
 3000
Techniques—Internal Rate of
Return (IRR)
 Technical Problems with IRR
 Multiple Solutions
 Unusual projects can have more than one IRR
 Rarely presents practical difficulties

The number of positive IRRs to a project depends on the
number of sign reversals to the project’s cash flows
 Normal pattern involves only one sign change

The Reinvestment Assumption
 IRR method implicitly assumes cash inflows will be reinvested
at the project’s IRR
 For projects with extremely high IRRs, this is unlikely
When NPV and IRR disagree
 Only when comparisons must be made
 Not stand alone analysis
 Use the NPV rankings, not the IRR
rankings
NPV Profile
 A project’s NPV profile is a graph of its
NPV vs. the cost of capital
 It crosses the horizontal axis at the IRR
Construct NPV Profiles
Enter CFs in CFLO and find NPVL and
NPVS at several discount rates:
k
0
5
10
15
20
NPVL
50
33
19
7
(4)
NPVS
40
29
20
12
5
k
0
NPV ($)
60
5
10
15
50
Crossover
Point = 8.7%
40
NPVL
50
33
19
7
(4)
20
30
20
NPVS
40
29
20
12
5
S
10
IRRS = 23.6%
L
0
0
5
10
15
20
23.6
-10
IRRL = 18.1%
Discount Rate (%)
Mutually Exclusive Projects
NPV
k< 8.7: NPVL> NPVS , IRRS > IRRL
CONFLICT
L
k> 8.7: NPVS> NPVL , IRRS > IRRL
NO CONFLICT
S
k
8.7
Crossover
rate = 8.7%
IRRs
%
k
IRRL
Rankings of S and
L were consistent
because K was 10%
To find the crossover rate:
1.
Find cash flow differences
between
the projects. Project L minus
Project S
CashL
(100)
10
60
80
CashS
(100)
70
50
20
Difference
0
-60
10
60
2.
3.
4.
Enter these differences in CFLO
register, then press IRR. Crossover
rate = 8.68, rounded to 8.7%.
Can subtract S from L or vice versa,
but better to have first CF negative.
If profiles don’t cross, one project
dominates the other.
Two reasons NPV profiles cross:
1)
2)
Size (scale) differences. Smaller
project frees up funds at t = 0 for
investment. The higher the discount
rate, the more valuable these funds,
so high k favors small projects.
Timing differences. Project with
faster payback provides more CF in
early years for reinvestment. If k is
high, early CF especially good, NPVS
> NPVL.
Reinvestment Rate Assumptions
 NPV assumes reinvest at k.
 IRR assumes reinvest at a rate
greater than the crossover rate.
 Reinvest at opp. cost, k, is more
realistic, so NPV method is best.
NPV should be used to choose
between mutually exclusive projects.
Comparing Projects with Unequal
Lives
 If a significant difference exists between
mutually exclusive projects’ lives, a direct
comparison of the projects can be in error
 The problem arises using the NPV method


Longer lived projects often have higher NPVs
Or shorter projects lower net present cost
 Must consider if the investments are really a
sequence
 If not a sequence then NPV is correct.
Comparing Projects with Unequal
Lives
 Two solutions exist
 Replacement Chain Method
 Extends projects until a common time horizon is
reached
 For example, if mutually exclusive Projects A (with a life of
3 years) and B (with a life of 5 years) are being compared,
both projects will be replicated so that they each last 15
years

Equivalent Annual Annuity (EAA) Method
 Replaces each project with an equivalent annuity
(PMT) that equates to the project’s original NPV
 That is, annualize the NPV (or net present cost)
 Both methods give the same conclusion so I only
use EAA
Comparing Projects with Unequal
Lives—Example
Q: Which of the two following mutually exclusive projects should a firm
purchase?
C0
C1
C2
C3
C4
C5
C6
Short-Lived Project (NPV = $432.82 at an 8% discount rate; IRR = 23.4%)
Example
($1,500)
$750
$750
$750
-
-
-
$750
$750
Long-Lived Project (NPV = $867.16 at an 8% discount rate; IRR = 18.3%)
($2,600)
$750
$750
$750
$750
A: The IRR method argues for undertaking the Short-Lived Project
while the NPV method argues for the Long-Lived Project. We’ll
correct for the unequal life problem by using the EAA Method. Both
the EAA and Replacement Chain methods will lead to the same
decision.
Example
Comparing Projects with Unequal
Lives—Example
The EAA Method equates each project’s original NPV to an equivalent
annual annuity. For the Short-Lived Project the EAA is $167.95 (the
equivalent of receiving $432.82 spread out over 3 years at 8%); while
the Long-Lived Project has an EAA of $187.58 (the equivalent of
receiving $867.16 spread out over 6 years at 8%). Since the LongLived Project has the higher EAA, it should be chosen. This is the
same decision reached by the Replacement Chain Method.
Review Steps:
1. Create ideas for capital investment
2. Estimate CFs (inflows & outflows).
3. Assess riskiness of CFs.
4. Determine k = WACC (adj. for risk).
5. Find NPV and/or IRR.
6. Accept if NPV > 0 and/or IRR > WACC.
7. If mutually exclusive, take the highest NPV
8. If mutu. excl. & lives differ take highest EAA