Capital Budgeting Process
1. Estimate the cash flows.
2. Assess the riskiness of the cash flows.
3. Determine the appropriate discount
rate.
4. Find the PV of the expected cash
flows.
5. Accept the project if PV of inflows >
costs.
Capital Budgeting
1. Basic Data
Expected Net Cash Flow
Year
Project L
Project S
0
($100)
($100)
1
10
70
2
60
50
3
80
20
2. Evaluation Techniques
A. Payback period
B. Discounted payback period
C. Net present value (NPV)
D. Internal rate of return (IRR)
E. Modified internal rate of return (MIRR)
Capital Budgeting - Illustration
I. Basic Data
Expected Net Cash Flow
Year
Project L Project S
0
($100)
($100)
1
10
70
2
60
50
3
80
20
Capital Budgeting
Weakness of Payback:
1. Ignores the time value of money. This
weakness is eliminated with the
discounted payback method.
2. Ignores cash flows occurring after the
payback period.
Capital Budgeting
NPV = 
CFt
(1+k) t
Project L:
0 10% 1
-100.00 10
2
3
60
80
9.09
49.59
60.11
NPVL= 18.79
NPVS = $19.98
If the projects are independent, accept both.
If the projects are mutually exclusive, accept Project S
since NPVS > NPVL
Capital Budgeting
IRR =
CFt
 (1+IRR)
t =
1
2
3
-100.00 10
8.47
43.02
48.57
0.06 = $0
60
80
$0 = NPV
Project L:
0
IRR
IRRL=18.1% IRRS=23.6%
If the projects are independent, accept both because IRR>k.
If the projects are mutually exclusive, accept Project S since
IRRS > IRRL
Capital Budgeting
Project L:
0 10% 1
-100.00 10
100.00
3
80.00
66.00
12.10
MIRR = 16.5% $158.10
$0.00 = NPV
PV outflows = $100
TV inflows =$158.10
(pvif)
2
60
TVof
inflows
$100=158.10
Capital Budgeting - Illustration
II. Evaluation Techniques
A. Payback period
B. Discounted payback period
C. Net present value (NPV)
D. Internal rate of return (IRR)
E. Modified internal rate of return
(MIRR)
Capital Budgeting - Payback Period
Payback period = Expected number of
years required to recover a project’s cost.
Project L
Expected Net Cash Flow
Year Annual
Cumulative
0 ($100)
($100)
1
10
(90)
2
60
(30)
3
80
50
Capital Budgeting - Payback Period
PaybackL= 2 + $30 / $80 years
= 2.4 years
PaybackS= 1.6 years.
Weaknesses of Payback:
1. Ignores the time value of money. This
weakness is eliminated with the
discounted payback period.
2. Ignores cash flows occurring after the
payback period.
Capital Budgeting - Net Present Value (NPV)
n
CFt
NPV = 
Project L:
t=0 (1+k)t
0 10% 1
2
-100.00 10
60
9.09
49.59
60.11
NPVL= $18.79
3
80
Capital Budgeting - Net Present Value (NPV)
n
CFt
NPV = 
Project S:
t=0 (1+k)t
0 10% 1
2
-100.00 70
50
63.64
41.32
15.03
NPVS= $19.99
3
20
Capital Budgeting - Net Present Value (NPV)
NPVS = $19.99
NPVL= $18.79
If the projects are independent, accept
both.
If the projects are mutually exclusive,
accept Project S since NPVS > NPVL.
Note:
NPV declines as k increases and NPV
rises as k decreases.
Internal Rate of Return (IRR)
n
CFt
IRR = 
= $0 = NPV
Project L:
t=0 (1+IRR)t
0 IRR 1
2
3
-100.00 10 60
80
8.47
18.13%
43.00
18.13%
48.54
18.13%
$ 0.01  $0
Internal Rate of Return (IRR)
n
CFt
IRR = 
= $0 = NPV
Project S:
t=0 (1+IRR)t
0 IRR 1
2
3
-100.00 70 50
20
56.65
23.56%
32.75
23.56%
10.60
23.56%
$ 0.00
Internal Rate of Return (IRR)
IRRL = 18.13%
IRRS = 23.56%
If the projects are independent, accept
both because IRR > k.
If the projects are mutually exclusive,
accept Project S since IRRS > IRRL.
Note:
IRR is independent of the cost of capital.
Capital Budgeting - NPV Profiles
k
NPVL NPVS
0% $50
$40
5
33
29
10
19
20
15
7
12
20
(4)
5
Modified IRR (MIRR)
Project L:
0 10% 1
-100
10
2
60
3
80.00
66.00
12.10
$158.10 =TV of
100.00
MIRR=16.5%
inflows
$ 0.00 = NPV
Modified IRR (MIRR)
Project S:
0 10% 1
-100
70
2
50
3
20.00
55.00
84.70
$159.70 =TV of
100.00
MIRR=16.9%
inflows
$ 0.00 = NPV
Modified IRR (MIRR)
PV outflows = $100
TV inflows = $158.10
$100 = $158.10 (PVIFMIRRL,3)
MIRRL = 16.5%
MIRRS = 16.9%
Modified IRR (MIRR)
Project L:
0
5% 1
-100
10
2
60
3
80.00
63.00
11.03
$154.03 =TV of
100.00
MIRR=15.48%
inflows
$ 0.00 = NPV
Modified IRR (MIRR)
Project S:
0
5% 1
-100
70
2
50
3
20.00
52.50
77.18
$149.68 =TV of
100.00
MIRR=14.39%
inflows
$ 0.00 = NPV
Modified IRR (MIRR)
MIRR is better than IRR because:
1. MIRR correctly assumes reinvestment
at project’s cost of capital.
2. MIRR avoids the problem of multiple
IRRs.
NPV Profile: Nonnormal Project P with
Multiple IRRs
Year
0
1
2
Cash Flow (‘000)
($800)
5,000
(5,000)
NPV @10% = -$386,777. Do not accept; NPV < 0.
IRR = 25% and 400%.
MIRR = 5.6%. Do not accept; MIRR < k.
Debt
$120
$100
1 year
Bank
IRR = 20%
wacc=10%
Equity
$100
%
20% A=20%
IOS
wacc = 10%
0
100
MCC
$
IF IRR > WACC THEN ACCEPT PROJECT
Debt
$110
$100
1 year
Bank
IRR = 10%
wacc=10%
Equity
$100
PV(CASH IN) = 100 = CASH OUTFLOW
IN
120
IN
110
1 YEAR
1 YEAR
WACC = 10%
100
OUT
PV(IN) = 109.09
PV(OUT) = 100
NPV
= 9.09
CF0= -100 i=10%
CF1= 120
NPV = 9.09
WACC = 10%
100
OUT
PV(IN) = 100
PV(0UT) = 100
NPV
=0
CF0= -100 i=10%
CF1= 110
NPV = 0
10%
IN
105
WACC = 10%
100
OUT
IRR
CF0 = -100
CF1 = 105
IRR = 5%
NPV
PV(IN) = 95.45
PV(OUT) = 100
NPV = -4.55
CF0 = -100
CF1=105
i = 10% NPV = -4.55