Chapter 10
The Basics of Capital
Budgeting
1
Topics

Methods




NPV
IRR, MIRR
Payback, discounted payback
EAS (EAA)
2
What is capital budgeting?


Analysis of potential projects.
Long-term decisions; involve large
expenditures.
3
Steps in Capital Budgeting



Estimate cash flows (inflows &
outflows).
Determine r = WACC for project.
Evaluate
4
Capital Budgeting Project
Categories
1. Replacement to continue profitable
operations
2. Replacement to reduce costs
3. Expansion of existing products or markets
4. Expansion into new products/markets
5. Contraction decisions
6. Safety and/or environmental projects
7. Mergers
8. Other
5
Independent versus Mutually
Exclusive Projects

Projects are:


independent, if the cash flows of one are
unaffected by the acceptance of the other.
mutually exclusive, if the cash flows of one
can be adversely impacted by the
acceptance of the other.
6
Net present value (NPV) rule
Accept project if
Net present value > 0
What is Net present value?
Net present value
= Benefits minus Costs
7
How do we measure
benefits & costs?
N
N
CIFt
COFt
NPV = B – C =  1  r t   1  r t
t 0
t 0
8
NPV: Sum of the PVs of All
Cash Flows
N
NPV = Σ
t=0
CFt
(1 + r)t
Cost often is CF0 and is negative.
N
NPV = Σ
t=1
CFt
(1 + r)t
– CF0
9
Cash Flows for Franchises
L and S
0
1
2
3
-100.00
10
60
80
0
1
2
3
70
50
20
L’s CFs:
S’s CFs:
-100.00
10%
10%
10
What’s Franchise L’s NPV?
0
L’s CFs:
-100.00
1
2
3
10
60
80
10%
9.09
49.59
60.11
18.79 = NPVL
NPVS = $19.98.
11
Calculator Solution: Enter
Values in CF Register for L
-100
CF0
10
CF1
60
CF2
80
CF3
10
I
NPV = 18.78 = NPVL
12
Rationale for the NPV Method



NPV = PV inflows – Cost
This is net gain in wealth, so accept
project if NPV > 0.
Choose between mutually exclusive
projects on basis of higher positive NPV.
Adds most value.
13
Using NPV method, which
franchise(s) should be accepted?



If Franchises S and L are mutually
exclusive, accept S because NPVs
> NPVL.
If S & L are independent, accept
both; NPV > 0.
NPV is dependent on cost of capital.
14
Internal Rate of Return: IRR
0
1
2
3
CF0
Cost
CF1
CF2
Inflows
CF3
IRR is the discount rate that forces
PV inflows = cost. This is the same
as forcing NPV = 0.
15
NPV: Enter r, Solve for NPV
N
Σ
t=0
CFt
= NPV
(1 + r)t
16
IRR: Enter NPV = 0, Solve
for IRR
N
Σ
t=0
CFt
=0
(1 + IRR)t
IRR is an estimate of the project’s rate
of return, so it is comparable to the
YTM on a bond.
17
What’s Franchise L’s IRR?
0
IRR = ?
-100.00
PV1
1
2
3
10
60
80
PV2
PV3
0 = NPV Enter CFs, then press IRR:
IRRL = 18.13%. IRRS =
23.56%.
18
Rationale for the IRR Method



If IRR > WACC, then the project’s rate
of return is greater than its cost-- some
return is left over to boost stockholders’
returns.
Example:
WACC = 10%, IRR = 15%.
So this project adds extra return to
shareholders.
19
Decisions on Franchises S
and L per IRR



If S and L are independent, accept
both: IRRS > r and IRRL > r.
If S and L are mutually exclusive,
accept S because IRRS > IRRL.
IRR is not dependent on the cost of
capital used.
20
NPV and IRR: No conflict for
independent projects.
NPV ($)
IRR > r
and NPV > 0
Accept.
r > IRR
and NPV < 0.
Reject.
IRR
r (%)
Reinvestment Rate
Assumptions



NPV assumes reinvest at r (opportunity
cost of capital).
IRR assumes reinvest at IRR.
Reinvest at opportunity cost, r, is more
realistic, so NPV method is best. NPV
should be used to choose between
mutually exclusive projects.
22
Modified Internal Rate of
Return (MIRR)



MIRR is the discount rate that causes
the PV of a project’s terminal value (TV)
to equal the PV of costs.
TV is found by compounding all inflows
at WACC.
Thus, MIRR assumes cash inflows are
reinvested at WACC.
23
MIRR for Franchise L: First,
Find PV and TV (r = 10%)
0
10%
-100.0
1
2
3
10.0
60.0
80.0
10%
10%
-100.0
PV outflows
66.0
12.1
158.1
TV inflows
24
Second, Find Discount Rate
that Equates PV and TV
0
-100.0
1
2
MIRR = 16.5%
PV outflows
3
158.1
TV inflows
$100 =
$158.1
(1+MIRRL)3
MIRRL = 16.5%
25
BAII: Step 1, Find PV of
Inflows



First, enter cash inflows in CF register:
CF0 = 0, CF1 = 10, CF2 = 60, CF3 = 80
Second, enter I = 10.
Third, find PV of inflows:
Press NPV = 118.78
26
Step 2, Find TV of Inflows


Enter PV = -118.78, N = 3, I/YR = 10,
PMT = 0.
Press FV = 158.10 = FV of inflows.
27
Step 3, Find PV of Outflows


For this problem, there is only one
outflow, CF0 = -100, so the PV of
outflows is -100.
For other problems there may be
negative cash flows for several years,
and you must find the present value for
all negative cash flows.
28
Step 4, Find “IRR” of TV of
Inflows and PV of Outflows


Enter FV = 158.10, PV = -100,
PMT = 0, N = 3.
Press I/YR = 16.50% = MIRR.
29
Why use MIRR versus IRR?


MIRR correctly assumes reinvestment at
opportunity cost = WACC. MIRR also
avoids the problem of multiple IRRs.
Managers like rate of return
comparisons, and MIRR is better for this
than IRR.
30
Apply NPV, IRR

Assume a discount rate of 11%. Compute the
NPV, IRR and decide whether the project should
be accepted or rejected.
Project
C0
C1
C2
C3
C4
C5
A
T=0
-1000
T=1
400
T=2
400
T=3
400
T=4
500
T=5
500
Verify that NPV = 603.58, IRR = 31.79%,
Since NPV>0, IRR>11%, accept the project
31
Conceptual problem: NPV and
IRR

A.
B.
C.
D.
E.
Consider a project with an initial outflow at time 0
and positive cash flows in all subsequent years. As
the discount rate is decreased the _____________.
IRR
IRR
IRR
IRR
IRR
remains constant while the NPV increases.
decreases while the NPV remains constant.
increases while the NPV remains constant.
remains constant while the NPV decreases.
decreases while the NPV decreases.
32
Computational problem: NPV and IRR








You are attempting to reconstruct a project analysis
of a co-worker who was fired. You have found the
following information:
The IRR is 12%.
The project life is 4 years.
The initial cost is $20,000.
In years 1, 3 and 4 you will receive cash inflows of
$6,000.
You know there will be a cash flow in year 2, but the
amount is not in the file.
The appropriate discount rate is 10%.
What is the NPV of the project?
33
Condition 1: Cash inflows occur
before cash outflows





Thus far, we have considered projects with
normal cash flows, (i.e., a single cash outflow
in year 0 followed by cash inflows in all future
years).
With normal cash flows, IRR works fine.
However, if you have cash inflow first,
followed by cash outflow, then IRR will be
negative.
Result: You cannot use IRR to make the
accept/reject decision.
Use NPV to get the correct decision.
34
Condition 2: Cash flows change signs
more than once





Consider the following project cash flows: t = 0, $400,
t = 1, $2,500, t = 2, -$3,000. Suppose that the
company’s cost of capital is 70 percent.
NPV = $32.53. The project is, acceptable.
There are two IRR’s for this project: 61.98%, 363%.
Look at the NPV profile (next slide).
When there are multiple IRRs, the IRR method
loses meaning and is NOT appropriate.
However, the NPV method still gives the correct
accept/reject decision.
35
What is the payback period?


The number of years required to
recover a project’s cost,
or how long does it take to get the
business’s money back?
36
Payback for Franchise L
2.4
3
0
80
50
0
1
2
CFt
Cumulative
-100
-100
10
-90
60
-30
PaybackL
= 2 + $30/$80 = 2.375 years
37
Payback for Franchise S
0
1
1.6 2
3
-100
70
50
20
Cumulative -100
-30
20
40
CFt
PaybackS
0
= 1 + $30/$50 = 1.6 years
38
Applying the PBP criterion

Compute the payback periods for the
following two projects.
Project
C0
C1
C2
C3
C4
C5
A
-9000
2000
3000
4000
5000
6000
B
-11000
2000
3000
4000
5000
6000
Verify that PBP for A = 3 years, PBP for B = 3.4 years
(assume cash flows occur evenly throughout the year)
39
NPV + PBP Problem

Bantam Industries is considering a project which has
the following cash flows:
Year
0
1
2
3
4
Cash flow
?
$2,000
$3,000
$3,000
$1,500
The project has a payback period of 2 years. The firm's
cost of capital is 12%.
What is the project's net present value?
Verify that NPV = 2,265.91
40
Strengths and Weaknesses of
Payback

Strengths:



Provides an indication of a project’s risk.
Easy to calculate and understand.
Weaknesses:


Ignores the TVM.
Ignores CFs occurring after the payback
period.
41
PBP does not consider cash flows
after the critical number
A firm uses two years as the critical number for the
payback period.
This firm is faced with two projects whose cash flows are:
Project
A
B
C0
-1000
-1000
C1
500
0
C2
510
0
C3
10
99,000,000
According to the payback rule, project A will be accepted and B will
be rejected.
But, if you consider all cash flows, including those after 2 years,
then project B is more attractive.
42
Discounted Payback: Uses
Discounted CFs
0
10%
1
2
3
10
60
80
CFt
-100
PVCFt
-100
9.09
49.59
60.11
Cumulative -100
-90.91
-41.32
18.79
Discounted
= 2 + $41.32/$60.11 = 2.7 yrs
payback
Recover investment + capital costs in 2.7 yrs.
43
Example of discounted payback
period criterion

Example: Suppose that the discount rate is 10 percent.
Project A has the following cash flows and discounted
cash flows. Find A’s discounted PBP.
Project A
Cash flow
Discounted cash flow
C0
C1
C2
C3
-9000 3000 6000 9000
2727 4959 6762
Verify that discounted payback period = 2.194 years
44
Normal vs. Nonnormal Cash
Flows

Normal Cash Flow Project:



Cost (negative CF) followed by a series of positive
cash inflows.
One change of signs.
Nonnormal Cash Flow Project:



Two or more changes of signs.
Most common: Cost (negative CF), then string of
positive CFs, then cost to close project.
For example, nuclear power plant or strip mine.
45
When There are Nonnormal CFs and
More than One IRR, Use MIRR
0
1
2
-800,000
5,000,000
-5,000,000
PV outflows @ 10% = -4,932,231.40.
TV inflows @ 10% = 5,500,000.00.
MIRR = 5.6%
46
If the two projects have
different lifespan, then…
47
S and L are Mutually Exclusive, r
= 10%
0
1
2
S: -100
60
60
L: -100
33.5
33.5
3
4
33.5
33.5
Note: CFs shown in $ Thousands
48
NPVL > NPVS, but is L better?
CF0
S
-100
L
-100
CF1
60
33.5
NJ
I/YR
2
10
4
10
NPV
4.132
6.190
49
Method 1:mPut Projects on
Common Basis


Note that Franchise S could be repeated
after 2 years to generate additional
profits.
Use replacement chain to put on
common life.
50
Replacement Chain Approach (000s)
Franchise S with Replication
0
1
2
3
4
S: -100
60
60
-100
-40
60
60
60
60
-100
60
NPV = $7.547.
51
Method 2:Equivalent annual series (EAS)
or Equivalent Annual Annuity (EAA)

When projects are mutually exclusive but
have unequal lives
a.
b.

We construct the equivalent annual series (EAS)
of each project and
We choose the project with the highest EAS
A project’s EAS is the payment on an annuity
whose life is the same as that of the project
and whose present value, using the discount
rate of the project, is equal to the project’s
NPV.
52
Equivalent Annual Annuity
Approach (EAA)




Convert the PV into a stream of annuity
payments with the same PV.
S: N=2, I/YR=10, PV=-4.132, FV = 0.
Solve for PMT = EAAS = $2.38.
L: N=4, I/YR=10, PV=-6.190, FV = 0.
Solve for PMT = EAAL = $1.95.
S has higher EAA, so it is a better
project.
53
Calculating EAS

Consider Projects J & K, with the following cash
flows. The discount rate is 10%.
Project
C0
C1
C2
C3
J
-12000
6000
6000
6000
K
-18000
7000
7000
7000
C4
7000
54
EAS for Project J
To compute Project J’s EAS, do the following:
 Compute Project J’s NPV
• Verify that NPV(J) = $2,921.11
 Find the payment on the 3-year (life of project J) annuity
whose PV is equal to $2,921.11.
Enter the following values:
N=3, I/Y=10, PV=-2921.11, FV=0, Then CPT, PMT.
PMT = 1,174.62, which is Project J’s EAS.
So, finding EAS is nothing more than finding the payment of
an annuity.

55
EAS for Project K
Verify that Project K’s NPV= $4,189.06
 Find the payment on the 4-year (life of project K)
annuity whose PV is equal to $ 4,189.06.
Enter the following values:
N=4, I/Y=10, PV=- 4,189.06, FV=0, Then CPT, PMT.
PMT = 1,321.53, which is Project K’s EAS.
Recall that Project J’s EAS=1174.62
So, choose Project K since it has the higher EAS.

56
Another application of EAA


We can use the EAA concept to choose
between two machines that do the
same job but have different costs and
lives.
Consider the following problem.
57
Problem

Suppose that your firm is trying to decide
between two machines, that will do the same
job. Machine A costs $90,000, will last for ten
years and will require operating costs of
$5,000 per year. At the end of ten years it
will be scrapped for $10,000. Machine B costs
$60,000, will last for seven years and will
require operating costs of $6,000 per year. At
the end of seven years it will be scrapped for
$5,000. Which is a better machine? (discount
rate is 10 percent)
58
Step 1: compute the PV of the costs
of each machine
PV of costs (A)
= $90,000 + PV of $5,000 annuity for ten years
- PV of the scrap (at t = 10) value of $10,000
= 90000 + 30722.84 – 3855.43 = $116,867.41
PV of costs (B)
= $60,000 + PV of $6,000 annuity for seven years
- PV of the scrap (at t = 7) value of $5,000
= $60,000 + $29,210.51 - $2,565.79 =$86,644.72
59
Step 2: compute equivalent annual
cost (EAC) series of each machine
The equivalent annual cost series is the payment of an
annuity that has the same present value as the PV of
the machine’s cost.
EAC of machine A, EAC(A):
 N = 10, I/Y = 10, PV = -116867.41, FV = 0. Then CPT,
PMT. This yields EAC(A) = $19,019.63.
EAC of machine B, EAC(B):
 N = 7, I/Y = 10, PV = -86644.72, FV = 0. Then CPT,
PMT. This yields EAC(B) = $17,797.30.
 Choose machine B because it has the lower cost.

60
Homework Assignment

Problems:
1,2,3,4,5,6,7,9,11,13(a,b,c),16,17,21(a,
b,c,d)
61