Chapter 11. The Basics of Capital Budgeting. Net Present Value (NPV) Internal Rate of Return (IRR) Modified Internal Rate of Return (MIRR) Regular Payback Discounted Payback. What is capital budgeting?. Analysis of potential additions to fixed assets.
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Chapter 11
Net Present Value (NPV)
Internal Rate of Return (IRR)
Modified Internal Rate of Return (MIRR)
Regular Payback
Discounted Payback
Projects we’ll examine:
CF is the difference between CFL and CFS. We’ll use CF later.
Year flow streams?
CFt
PV of CFt
0

100

$100.00
1
10
9.09
2
60
49.59
3
80
60.11
NPVL
=
$ 18.79
What is Project L’s NPV?WACC = 10%
Excel: =NPV(rate,CF1:CFn) + CF0
Here, CF0 is negative.
Year flow streams?
CFt
PV of CFt
0

100

$100.00
1
70
63.64
2
50
41.32
3
20
15.02
NPVS
=
$ 19.98
What is Project S’ NPV?WACC = 10%
Excel: =NPV(rate,CF1:CFn) + CF0
Here, CF0 is negative.
Enter CFs into the calculator’s CFLO register.
CF0 = 100
CF1 = 10
CF2 = 60
CF3 = 80
Enter I/YR = 10, press NPV button to get NPVL = $18.78.
NPV = PV of inflows – Cost
= Net gain in wealth
IRR is the discount rate that forces PV of inflows equal to cost, and the NPV = 0:
Solving for IRR with a financial calculator:
Enter CFs in CFLO register.
Press IRR; IRRL = 18.13% and IRRS = 23.56%.
Solving for IRR with Excel:
=IRR(CF0:CFn,guess for rate)
Internal Rate of Return (IRR)If IRR > WACC, accept project.
If IRR < WACC, reject project.
WACC cost, and the NPV = 0:
NPV
NPV
L
S
0
$50
$40
5
33
29
10
19
20
15
7
12
20
(4)
5
NPV ProfilesNPV cost, and the NPV = 0: ($)
IRR > r
and NPV > 0
Accept.
r > IRR
and NPV < 0.
Reject.
r = 18.1%
r (%)
IRRL = 18.1%
Independent ProjectsNPV and IRR always lead to the same accept/reject decision for any given independent project.
NPV cost, and the NPV = 0:
L
S
%
r 8.7 r
IRRL
IRRs
Mutually Exclusive ProjectsIf r < 8.7%: NPVL> NPVSIRRS> IRRL
CONFLICT
If r > 8.7%: NPVS> NPVL,
IRRS> IRRL
NO CONFLICT
0
1
2
3
Excel: =MIRR(CF0:CFn,Finance_rate,Reinvest_rate)
We assume that both rates = WACC.
10%
100.0
10.0
60.0
80.0
10%
66.0
12.1
10%
MIRR = 16.5%
100.0
158.1
PV outflows
TV inflows
$158.1
(1 + MIRRL)3
$100
=
MIRRL = 16.5%
Project L’s Payback Calculation
0
1
2
3
CFt
100
10
60
80
30
Cumulative
100
90
50
80
30
PaybackL = 2 + /
= 2.375 years
PaybackS = 1.600 years
Uses discounted cash flows rather than raw CFs.
0
1
2
3
10%
CFt
100
10
60
80
PV of CFt
100
9.09
49.59
60.11
Cumulative
100
90.91
41.32
18.79
Disc PaybackL = 2 + / = 2.7 years
41.32
60.11
0 1 2
WACC = 10%
800 5,000 5,000
Find Project P’s NPV and IRRProject P has cash flows (in 000s): CF0 = $800, CF1 = $5,000, and CF2 = $5,000.