CAPITAL BUDGETING
Capital Budgeting refers to the methods that managers use to determine which projects
should be selected and which projects should be rejected.
Imagine a manager has been presented with the following projects. The first is for a new
drink called Sugar Soda and the second is for a drink called Lime Soda. Let’s call these
projects Project S and Project L.
Both drinks will cost $1000 to create and market, Sugar Soda is expected to have high
initial sales followed by a decline as parents find out what the drink does to their children
(they will bounce off the walls). Lime Soda on the other hand is an acquired taste and
sales are expected to increase as consumers begin to acquire a taste for the product. After
year 5 the formula for the drinks will be obsolete and the drinks will no longer be
marketed or sold.
The cash flows for these two projects are shown below:
Project L Cash Flows
Project S Cash Flows
1000
500
$
$
0
-500
-1000
-1500
1
2
3
4
5
800
600
400
200
0
-200
-400
-600
-800
-1000
-1200
Time
1
2
3
4
5
Time
When considering two projects a manager must know whether the projects are mutually
exclusive projects or independent projects.
 Mutually exclusive projects – when accepting one implies rejected the other.
For example if the company only has the capacity to manufacture one new soda.
 Independent projects – when the company can accept either or both projects
based only on the project’s expected cash flows. For example if the firm has the
capacity to invest in both beverages.
The following six methods are used to evaluate projects:
1. Net present value (NPV)
2. Internal Rate of Return (IRR)
3. Modified Internal Rate of Return (MIRR)
4. Profitability Index (PI)
5. Payback Period
6. Discounted Payback
Capital Budgeting
1
1. Net Present Value is also known as the discounted cash flow technique. NPV is the
amount the shareholder’s wealth would increase if the firm selected the project – if this
number is positive then the firm should select the project. 1 Using the following formula
we can find the NPV of the two projects. (Assume a cost of capital (r) of 5%).
N
NPV  
t 0
CFt
1  r 
NPVS  1000 
NPVL  1000 
t
500
1  5% 
1
100
1  5% 
1


400
1  5% 
2

2

300
1  5% 
300
1  5% 
3

3

400
1  5% 
100
1  5% 
4
 $180.42
4
 $206.50
600
1  5% 
Conclusion: Based on NPV, and if the projects are mutually exclusive (i.e. only one
project can be selected) then the firm should go with Project L (the Lime Soda).
2. Internal Rate of Return (IRR) the IRR is the discount rate that makes the net present
value of the project equal to zero.2 A project’s IRR should be compared to the
company’s cost of capital or “hurdle rate.” The hurdle rate is the rate that the project
must exceed to create positive shareholder wealth effects. (Assume the hurdle rate (r) is
5%).
N
NPV  
CFt
t  0 1  IRR 
NPVS  1000 
t
0
500
1  IRR 
1

400
1  IRR 
2

2

300
3

3

1  IRR 
100
1  IRR 
4
 $0
4
 $0
IRRS  14.5%
NPVL  1000 
100

1
1  IRR 
300
1  IRR 
400
1  IRR 
600
1  IRR 
IRRL  11.8%
Conclusion: Based on IRR, and if the projects are mutually exclusive (i.e. only one
project can be selected) then the firm should go with Project S (the Sugar Soda).
Question: Why do the NPV and IRR methods offer different decisions in this example?
 Answer: Because NPV rankings depend on the cost of capital and the timing of
the cash flows impacts their present values. Project S has higher short-term cash
1
2
Key Assumption: All cash flows are reinvested at the company’s cost of capital.
Key Assumption: All cash flows are reinvested at the project’s IRR.
Capital Budgeting
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flows while Project L has higher long-term cash flows. Note: Long-term cash
flows are much more sensitive to interest rates.
The tables below shows NPVs for the two projects at various interest rates. Notice that at
5% Project L offers a higher NPV while at 10% Project S offers a higher NPV.
NPV Sensitivity Analysis
500
400
300
200
100
0
(100)
(200)
Net Present Value
Net Present Value
NPV Sensitivity Analysis
0%
5%
10%
500
400
300
200
100
0
(100)
(200)
0%
15%
5%
10%
Cost of Capital (r)
Cost of Capital (r)
Project S
Project S
Project L
15%
Project L
Question: At what rate would we be indifferent between these two projects?
 Answer: At the crossover rate. The crossover rate is the rate below which, the
two methods offer different accept / reject solutions. To calculate the crossover
rate for two projects subtract the cash flows at each time and then solve for the
rate at which the NPV equals zero.
NPV  1000   1000  
 0
400
1  rc 
1

500  100 
1  rc 
1
100
1  rc 
2


100
1  rc 
3
400   300 

1  rc 
2

300   400  100   600 

 $0
3
4
1  rc 
1  rc 
500
1  rc 
4
rc  7.17%
This is calculated easily by using the cash flow register in your financial calculator.
For the TI BAII Plus
Enter: CF (CF0) = 0; ↓ (C01) = 400; ENTER ↓ (F01) = 1; ENTER ↓ (C02) = 100;
ENTER ↓ (F02) = 1; ENTER ↓ (C03) = -100; ENTER ↓ (F03) = 1; ENTER ↓ (C04) = 500; ENTER; IRR; CPT
Answer: 7.1673%
Capital Budgeting
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3. Modified Internal Rate of Return (MIRR) – the modified IRR assumes that cash
flows are reinvested at the company’s cost of capital.3 The cash flows are first brought
forward to their future values at the company’s cost of capital. Next the “terminal value”
is calculated by summing all of the future value cash flows. Finally the terminal value is
brought to the present vale of the initial investment at the MIRR rate. (Assume a cost of
capital of 5%).
N
N

t 0
Cash Outflowt
1  r 
t

 Cash Inflow 1  r 
t 0
1  MIRR 
N 1
N
Terminal value
PV of costs =
1  MIRR 
N
 PV of terminal value
 500 1  5% 
$1000 =
$1000 =
4 1
  400 1  5% 
31
  300 1  5% 
1  MIRRS 
2 1
 100 1  5% 
2 1
  600 1  5% 
11
4
$1, 434.81
1  MIRRS 
1  MIRRs 
4

4
$1, 434.81
 1.4348
$1000
1  MIRRs  1.4348 
 1.0945
1/4
MIRRS  9.45%
100 1  5% 
$1000 =
$1000 =
4 1
  300 1  5% 
31
  400 1  5% 
1  MIRRL 
11
4
$1, 466.51
1  MIRRL 
1  MIRRL 
4

4
$1, 466.51
 1.4665
$1000
1  MIRRL  1.4665 
1/4
 1.1005
MIRRL  10.05%
Conclusion: Based on MIRR, and if the projects are mutually exclusive (i.e. only one
project can be selected) then the firm should go with Project L (the Lime Soda). Note: At
a 10% cost of capital Project S would be superior based on the MIRR calculation.
3
IRR assumes that cash flows are invested at the IRR rate.
Capital Budgeting
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4. Profitability Index (PI) – The profitability index is the present value of the project’s
cash flows divided by the cost. (Assume a 5% cost of capital) PI tells us how much
profit we can earn for each dollar invested.
N
PV of future cash flows
PI 

Initial cost
500
1  5% 

1
PI S
400

1  5% 
2

300
1  5% 
3
CFt
 1  r 
t 0
t
CF0

100
1  5% 
4
1000
$1180.42
 1.18
$1000
100
300
400
600



1
2
3
4
1  5%  1  5%  1  5%  1  5% 

PI L 
1000
$1206.50

 1.21
1000

Conclusion: Based on PI, and if the projects are mutually exclusive (i.e. only one project
can be selected) then the firm should go with Project L (the Lime Soda). According to
the Profitability Index calculation at a 5% cost of capital Project L will yield $1.21 for
every dollar invested in the project. Note: At a 10% cost of capital Project S would be
superior based on the PI calculation.
5. Payback Period – The payback period is the expected number of years required to
recover the original investment.
The payback period method has three main flaws: 1) dollars received in different years
are all given the same weight 2) cash flows beyond the payback year are not considered
3) payback period analysis does not provide an indication of how much shareholder
wealth should increase (like NPV) and 4) payback period analysis does not indicate how
much the project will yield over the cost of capital (like IRR).
Payback  Number of years prior to full recovery
Unrecovered cost at start of year

Cash flow during full recovery year
PaybackS  2 
$100
 2.33 years
$300
Capital Budgeting
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PaybackL  3 
$200
 3.33 years
$600
Project S Cash Flows
Year 0 =
-$1000
Year 1 =
500
Year 2 =
400
Year 3 =
300
Year 4 =
100
Cumulative CFs
-$1000
-500
-100
200
300
Project L Cash Flows
Year 0 =
-$1000
Year 1 =
100
Year 2 =
300
Year 3 =
400
Year 4 =
600
Cumulative CFs
-$1000
-900
-600
-200
400
Conclusion: Based on the payback method, and if the projects are mutually exclusive
then the firm should go with Project S (the Sugar Soda).
6. Discounted Payback – This method is similar to the payback period method except
the cash flows are discounted by the project’s cost of capital. The discounted payback
period is the number of years required to recover the investment from the discounted net
cash flows. (Assume a cost of capital of 5%)
Discounted Payback  Number of years prior to full recovery*

Unrecovered cost at start of year*
Cash flow during full recovery year *
*considers discounted cash flows
Project S Cash Flows
Year 0 =
-$1000
Year 1 =
500
Year 2 =
400
Year 3 =
300
Year 4 =
100
PaybackS  2 
$161.00
 2.62 years
$259.15
Project L Cash Flows
Year 0 =
-$1000
Year 1 =
100
Year 2 =
300
Year 3 =
400
Year 4 =
600
PaybackL  3 
Discounted CFs
Cumulative CFs
-1000/(1.05)0 = -$1000.00
-$1000.00
1
500/(1.05) =
476.19
-523.81
400/(1.05)2 =
362.81
-161.00
3
300/(1.05) =
259.15
98.15
100/(1.05)4 =
82.27
180.42
Discounted CFs
Cumulative CFs
0
-1000/(1.05) = -$1000.00
-$1000.00
100/(1.05)1 =
95.83
-904.76
2
300/(1.05) =
272.11
-632.65
400/(1.05)3 =
345.54
-287.12
600/(1.05)4 =
493.62
206.50
$287
 3.58 years
$493
Conclusion: Based on the discounted payback method, and if the projects are mutually
exclusive then the firm should go with Project S (the Sugar Soda).
Capital Budgeting
6