Chapter 10
The Basics of
Capital Budgeting
1
Topics


Overview
Methods



NPV
IRR, MIRR
Payback, discounted payback
2
What is capital budgeting?



A process for determining the
profitability of a capital investment.
Long-term decisions; involve large
expenditures.
Very important to firm’s future.
3
Steps in Capital Budgeting





Estimate cash flows (inflows &
outflows).
Assess risk of cash flows.
Determine r = WACC for project.
WACC = Weighted Avg. Cost of Capital
Evaluate cash flows.
4
Independent vs.
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.
5
What does this represent?
n
=
∑
t=0
CFt
(1 + r)t
6
NPV: Sum of the PVs of all
cash flows.
n
NPV = ∑
t=0
CFt
(1 + r)t
Cost often is CF0 and is negative.
n
NPV = ∑
t=1
CFt
(1 + r)t
- CF0
7
Cash Flows for project L and
project S
0
1
2
3
-100
10
60
80
0
1
2
3
70
50
20
L’s CFs:
S’s CFs:
-100
10%
10%
8
What’s project L’s NPV?
0
L’s CFs:
10%
-100
1
2
3
10
60
80
= NPVL
9
What’s project L’s NPV?
0
L’s CFs:
-100
1
2
3
10
60
80
10%
9.09
49.59
60.11
18.79 = NPVL
NPVS = $19.98.
10
Which project should be chosen?
•What if mutually exclusive? L or S?
•What if independent projects? L or S?
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 NPV. Adds
most value.
13
Using NPV method, which project(s)
should be accepted?


If project S and L are mutually
exclusive, accept S because
NPVs > NPVL .
If S & L are independent, accept both;
NPV > 0.
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
∑
t=0
CFt
= NPV .
(1 + r)t
IRR: Enter NPV = 0, solve for IRR.
n
∑
t=0
CFt
= 0.
(1 + IRR)t
16
What’s project L’s IRR?
0
-100
PV1
IRR = ?
1
2
3
10
60
80
PV2
PV3
0 = NPV Enter Cash Flows in CF, then
press IRR:
17
What’s project L’s IRR?
0
-100
PV1
IRR = ?
1
2
3
10
60
80
PV2
PV3
0 = NPV Enter Cash Flows in CF, then
press IRR: IRRL = 18.13%.
IRRS = 23.56%.
18
Find IRR if CFs are constant:
0
1
2
3
-100
40
40
40
19
Find IRR if CFs are constant:
0
1
2
3
-100
40
40
40
INPUTS
3
N
OUTPUT
-100
I/YR
PV
40
PMT
9.70%
Or, with CF, enter CFs and press
IRR = 9.70%.
20
Decisions on Projects S and L
per IRR




IRRS = 18%
IRRL = 23%
WACC = 10%
If S and L are independent, what to do?
If S and L are mutually exclusive, what
to do?
21
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.
22
Reinvestment Rate
Assumptions



NPV assumes reinvest at r (opportunity
cost of capital).
IRR assumes reinvest CFs 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.
23
Modified Internal Rate of
Return (MIRR)



MIRR is the discount rate which causes
the PV of a project’s terminal value (TV)
to equal the PV of costs.
TV is found by compounding (FV)
inflows at the WACC.
Thus, MIRR assumes cash inflows are
reinvested at the WACC.
24
MIRR for project L: First, find
PV and TV (r = 10%)
0
1
2
3
10.0
60.0
80.0
10%
-100
10%
10%
-100
PV outflows
66.0
12.1
158.1
TV inflows
25
Second, find discount rate that
equates PV and TV
0
-100
1
2
MIRR = 16.5%
PV outflows
3
158.1
TV inflows
$100 =
$158.1
(1+MIRRL)3
MIRRL = 16.5%
26
To find TV with calculator:
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
27
Step 2, find TV of inflows.

Enter PV = -118.78, N = 3, I = 10

CPT FV = 158.10 = FV of inflows.
28
Step 3, find PV of outflows.

For this problem, there is only one
outflow, CF0 = -100, so the PV of
outflows is -100.
29
Step 4, find “IRR” of TV of
inflows and PV of outflows.


Enter FV = 158.10, PV = -100, N = 3.
CPT I = 16.50% = MIRR.
30
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.
31
What is the payback period?


The number of years required to
recover a project’s cost,
or how long it takes to get the
business’s money back.
32
What is the payback period?
0
1
2
3
-100
50
50
50
33
What is the payback period?
0
1
2
3
-100
40
40
40
34
What are the payback periods
for projects L and S?
0
1
2
3
-100
10
60
80
0
1
2
3
70
50
20
L’s CFs:
S’s CFs:
-100
10%
10%
35
Payback for project L
0
CFt
-100
Cumulative -100
PaybackL
=
2
+
1
2
10
-90
60
-30
30/80
2.4
3
0
80
50
= 2.375 years
36
Payback for project 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
37
Strengths and Weaknesses of
Payback

Strengths:



Provides an indication of a project’s risk
and liquidity.
Easy to calculate and understand.
Weaknesses:


Ignores the TVM.
Ignores CFs occurring after the payback
period.
38
Discounted Payback: Uses
discounted rather than raw 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
payback
+ 41.32/60.11 = 2.7 yrs
Recovers invest. + costs in 2.7 yrs.
39