ASPEK KEUANGAN
Capital Budgeting
MANAJEMEN PROYEK
Investment decisions
y Objectives for this session :
y Review investment rules
y NPV, IRR, Payback
y BOF Project
P j t
y Free Cash Flow calculation
y Sensitivity analysis, break even point
y Inflation
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Investment rules
y Net Present Value (NPV)
NPV
y Di
Discounted
t d incremental
i
t l free
f cashh flflows
y Rule: invest if NPV>0
y Internal Rate of Return (IRR)
y IRR: discount rate such that NPV=0
y Rule: invest if IRR > Cost of capital
y Payback period
y Numbers of year to recoup initial investment
y No precise rule
y Profitability
P fi bili Index
I d (PI)
y PI = NPV / Investment
y Useful to rank projects if capital spending is limited
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IRR
r
Internal Rate of Return
y Alternative rule: compare the internal rate of return for the
project to the opportunity cost of capital
y Definition of the Internal Rate of Return IRR : (1-period)
IRR = Profit/Investment = (C1 - I)/I
y In
I our example:
l
IRR = (125 - 100)/100 = 25%
y The Rate of Return Rule: Invest if IRR > r
y In this simple setting, the NPV rule and the Rate of Return Rule
lead to the same decision:
y NPV = -I+C1/(1+r) >0 ⇔ C1>I(1+r) ⇔ (C1-I)/I>r ⇔ IRR>r
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MBA 2007 Capital Budgeting (1)
IRR: a general definition
y The Internal Rate of Return is the discount
rate such that the NPV is equal
q to zero.
30.00
y -I + C1/(1+IRR) ≡ 0
25.00
20.00
y -100 + 125/(1+IRR)=0
y
⇒ IRR=25%
2 %
15.00
Net Present Value
y In our example:
10.00
5.00
IRR
0.00
0.0%
2.5%
5.0%
7.5%
10.0%
12.5%
15.0%
-5.00
-10.00
Discount Rate
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MBA 2007 Capital Budgeting (1)
17.5%
20.0%
22.5%
25.0%
27.5%
30.0%
Internal Rate of Return IRR
y Can be viewed as the “yield to maturity” of the project
y Remember: the yield to maturity on a bond is the rate that set the present
value of the expected cash flows equal to its price
y Consider the net investment as the p
price of the pproject
j
y The IRR is the rate that sets the present value of the expected cash flows
equal to the net investment
y The IRR is the rate that sets the net present value equal to zero
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MBA 2007 Capital Budgeting (1)
What do CFOs Use?
% Always or Almost Always
y
y
y
y
y
y
y
Internal Rate of Return
N t Present
Net
P
t Value
Vl
Payback period
Discounted payback period
Accounting rate of return
Profitability index
75.6%
74 9%
74.9%
56.7%
29.5%
30.3%
11.9%
y Based on a survey of 392 CFOs
Source: Graham, John R. and Harvey R. Campbell, “The Theory and Practice of Corporate Finance: Evidence from the Field”, Journal of Financial Economics 2001
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MBA 2007 Capital Budgeting (1)
IRR Pitfall 1: Lending or borrowing?
y Consider following projects:
IRR: borrowing or lending?
-30.00
Discount rate
Project A
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MBA 2007 Capital Budgeting (1)
Project B
%
%
-20.00
30
%
%
27
24
21
Rule IRR<r
%
y B: borrowing
-10.00
%
Rule IRR>r
0.00
18
y A: lending
10.00
%
-9.09
9 09
20.00
15
20%
9.09
12
y B +100 -120
120
20%
30.00
9%
-100 +120
NPV(10%)
6%
IRR
3%
1
0%
y A
0
N e t P re se n t V a llu e
y
IRR Pitf
Pitfallll 2 Multiple
M lti l Rates
R t off Return
R t
y Consider the following project
y Year
y CF
0
1
2
Multiple Rates of Return
-1,600 10,000 -10,000
-1500.00
y To overcome problem, use modified IRR
method
h d
y Reinvest all intermediate cash flows at the cost of
capital till end of project
y Calculate IRR using the initial investment and the
future value of intermediate cash flows
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MBA 2007 Capital Budgeting (1)
-2000.00
Discount Rate
495%
4
450%
4
405%
4
360%
3
315%
3
270%
2
-1000.00
225%
2
-500.00
180%
0.00
135%
sign off cashh flflows
500.00
90%
y This happens if more than one change in
1000.00
45%
+400%
0%
y 2 “IRR
“IRRs”” : +25% &
Net Present Value
1500.00
IRR Pitfall 3 - Mutually Exclusive
P j t
Projects
y Scale Problem
y Timing Problem
C0
C0
y
C1 NPV10% IRR
y Small
S ll
-10
10
+20
y Large
-50
+80
y L-S
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-40
22.7
60%
C1 NPV10% IRR
+60
NPV8% IRR
-100 +20 +120
19.8 20%
B
-100 +100 +30
17.0 24.2%
88.22 100%
y To choose, look at incremental cash flows
C0
C2
A
y Look at incremental cash flows
C0
y
C1
14.5
50%
MBA 2007 Capital Budgeting (1)
A-B 0
C1
C2
-80 +90
NPV8% IRR
2.9 12.5%
M t ll Exclusive
Mutually
E l i P
Project
j t - Illustration
Ill t ti
50.0
40.0
A
30.0
20.0
B
10 0
10.0
0.0
0.0%
2.5%
5.0%
7.5%
-10.0
-20.0
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MBA 2007 Capital Budgeting (1)
10.0%
12.5%
15.0%
17.5%
20.0%
22.5%
25.0%
27.5%
30.0%
32.5%
Payback
y The payback period is the number of years it takes before the
cumulative
l ti fforcasted
t d cashh flflows equals
l th
the initial
i iti l iinvestment.
t
t
0
1
2
3
Payback
N PV
y Example:Y e a r
r= 1 0%
A
- 1 ,0 0 0
500
500
1 ,0 0 0
2
619
B
- 1 ,0 0 0
0
1 ,0 0 0
0
2
-1 7 4
C
- 1 ,0 0 0
500
500
0
2
-1 3 2
y A very flawed method, widely used
y Ignores time value of money
y Ignores
g
cash flows after cutoff date
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MBA 2007 Capital Budgeting (1)
Profitability Index
y Profitability Index = PV(Future Cash Flows) / Initial
Investment
y A useful
f l tooll for
f selecting
l
among projects when
h capitall
budget limited.
y The highest weighted average PI
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MBA 2007 Capital Budgeting (1)
NPV - Review
y NPV: measure change in market value of company if project
accepted
y As market value of company V = PV(Future
Free Cash Flows)
ΔFCF
NPV = ΔV = ∑
t (1 + r )
y ΔV =Vwith project - Vwithout project
y Cash flows to consider:
t
t
y cash flows (not accounting numbers)
y do not forget depreciation and changes in WCR
y incremental (with project - without project)
y forget sunk costs
y include opportunity costs
y include all incidental effects
y beware of allocated overhead costs
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MBA 2007 Capital Budgeting (1)
Inflation
y Be consistent in how you handle inflation
y Discount nominal cash flows at nominal rate
y Discount real cash flows at real rate
y Both approaches
pp
lead to the same result.
y
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Example: Real cash flow in year 3 = 100 (based on price level at time 0)
y Inflation rate = 5%
y Real discount rate = 10%
Discount real cash flow using real rate
Discount nominal cash flow using nominal rate
PV = 100 / (1.10)3 = 75.13
Nominal cash flow = 100 (1.05)3 = 115.76
Nominal discount rate = (1.10)(1.05)-1 = 15.5%
PV = 115.76 / (1.155)3 = 75.13
MBA 2007 Capital Budgeting (1)
Interest rates and inflation: real
i t
interest
t rate
t
Nominal interest rate = 10%
Date 0
Date 1
Indi idual in
Individual
invests
ests
$ 1,000
1 000
Individual receives
$ 1,100
Hamburger sells for
$1
$1.06
Inflation rate = 6%
Purchasing power (# hamburgers)
H1,000
H1,038
y Real interest rate = 3.8%
(1+Nominal interest rate)=(1+Real interest
) (
rate))
rate)×(1+Inflation
y Approximation:
Real interest rate ≈ Nominal interest rate - Inflation rate
y
y
y
y
y
y
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MBA 2007 Capital Budgeting (1)
Investment Project Analysis:
BOF
Big Oversea Firm is considering the project
Year
0
Initial Investment
60
1
2
Resale value
3
20
Sales
100
100
Cost of sales
50
50
Corporate
C
t tax
t rate
t = 40%
Working Capital Requirement = 25% Sales
Discount rate = 10%
MBA 2007 Capital Budgeting (1)
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BOF: Free Cash Flow
Calculation
Year
0
1
2
100
100
C off sales
Cost
l
50
50
EBITDA
50
50
Depreciation
30
30
EBIT
20
20
Taxes
8
8
8
Net income
12
12
-8
Net income
12
12
-8
D
Depreciation
i ti
30
30
0
DWCR
25
0
-25
Sales
CFInvestment
-60
Free Cash Flow
-60
3
20
17
MBA 2007 Capital Budgeting (1)
42
37
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BOF: go ahead?
y NPV calculation:
NPV = −60 +
17
42
37
+
+
= 17.96
2
3
1.10 (1.10)
(1.10)
y Internal Rate of Return = 24%
y Payback period = 2 years
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MBA 2007 Capital Budgeting (1)
BOF: checking the numbers
y Sensitivity analysis
y What if expected sales below expected value?
Sales
60
70
80
90
100
NPV
-1.28
3.53
8.34
13.15
17.97
y Break-even point
y What is the level of sales required to break even?
y Break even sales = 62.7
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MBA 2007 Capital Budgeting (1)
BOF Project with inflation rate
= 100%
Nominal free cash flows
Year
Sales
Cost of sales
EBITDA
Depreciation
EBIT
Taxes
Net income
0
Net income
Depreciation
ΔWCR
CFInvestment
Free Cash Flow
-60
-60
1
200
100
100
30
70
28
42
2
400
200
200
30
170
68
102
42
30
50
102
30
50
22
82
3
64
-64
64
-64
0
-100
160
196
Nominal discount rate = (1+10%)(1+100%)-1 = 120%
NPV = -14.65
IRR = 94%
MBA 2007 Capital Budgeting (1)
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REFERENSI
y Solvay Business School
y Université Libre de Bruxelles
y Fall 2007
MBA 2007 Capital Budgeting (1)
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