# capital budgeting

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```					Capital Budgeting
Decision Methods

October 27, 2008

1
Learning Objectives
• The capital budgeting process.
• Calculation of:
Payback
Net Present Value (NPV) \$
Internal Rate of Return (IRR) %
for proposed projects, for decision
making.
• Capital rationing, when funds are
limited.                              2
The Capital Budgeting Process
• Capital Budgeting is the process of
evaluating proposed investment projects for
a firm.
• Managers must determine which projects are
acceptable from a financial standpoint
• Examples might include:
– purchase of fixed assets,
– investments in R & D, or new businesses
3
Relevant cash flows
• The relevant cash flows are after-tax
incremental cash flows – Axiom 4
• Cash flows that will occur if the project
is done, and won’t occur if the project
isn’t done.
• Remember the brief case example
The Accept/Reject Decision
Three methods:
• Payback Period
– Time expressed in years to recoup
the initial investment
• Net Present Value (NPV)
– change in value of the firm in \$ if the
project is accepted and completed
• Internal Rate of Return (IRR) = K
– projected rate of return (%) the          4

project will earn
Capital Budgeting Methods - Payback
• Consider Projects A and B that have the
following expected cash flows:

P R O J E C T
Time       A           B
0      (10,000)   (10,000)
1        3,500        500
2        3,500        500
3        3,500      4,600
4        3,500     10,000

How long will it take for the firm to recover it’s investment?
5
Capital Budgeting Methods
• What is the payback for Project A?

P R O J E C T
Time        A           B
0       (10,000)   (10,000)
1         3,500        500
2         3,500        500
3         3,500      4,600         Payback in
4         3,500     10,000         *2.86 years

0         1          2          3           4

(10,000)     3,500      3,500     3,500        3,500
Cumulative CF -6,500     -3,000     +500        +4,000       8
*(Yr 1 + Yr 2 + 3000/3500 or 86% of Yr 3)       (or 10,000/3,500 = 2.86)
Capital Budgeting Methods
• What is the payback for Project B?

P R O J E C T
Time         A            B
0        (10,000)    (10,000)
1          3,500         500
2          3,500         500
3          3,500       4,600      Payback in
4          3,500      10,000      *3.44 years

0        1            2           3      4

(10,000)       500         500      4,600   10,000
Cumulative CF -9,500      -9,000     -4,400   +5,600      10
*(Yr 1 + Yr 2 + Yr 3 + 4,400/10,000 or 44% of Yr 4)
Payback Decision Rule
• Accept project if payback is less than
the company’s predetermined
maximum.
• If company has determined that it
requires payback in three years or less,
then you would:
– accept Project A (2.86 years)
– reject Project B (3.44 years)
11
Payback - Problems
• Does not consider cash received after
the payback period is over
Example: the remainder of the \$10,000
in year four is ignored in project B
• Does not consider the time value of
money
Example, the \$3,500 per year for the
four years in A may have a higher
present value than project B, even
though B pays back more total dollars
(\$15,600 vs. \$14,000).
Capital Budgeting Methods
Net Present Value
• Present Value of all costs and benefits
(measured in terms of after-tax incremental
cash flows) of a project.
• It is the dollar amount of the change in the
value of a firm as a result of undertaking the
project.
• A positive NPV increases firm value +\$
• A negative NPV decreases the firm’s value -\$  12
Financial Calculator:
enter Cash Flows and
compute the Net
Present Value (NPV)                       P/YR
CF    NPV   IRR

N   I/Y   PV    PMT    FV

Key used to enter expected cash flows in
order of their receipt.
Note: the initial investment (CF0) must be
entered as a negative number since it is an         23
outflow.
Financial Calculator:
enter Cash Flows and
compute the Net
Present Value (NPV)                       P/YR
CF    NPV   IRR

N   I/Y   PV    PMT    FV

Key used to calculate the net present value of
the cash flows (\$) to be received by the company
that have been entered in the calculator.
24
Financial Calculator:
enter Cash Flows and
compute the Net
Present Value (NPV)                        P/YR
and Internal                   CF    NPV   IRR

Rate of Return (IRR)       N   I/Y   PV    PMT    FV

Key used to calculate the internal rate
of return (%) for the cash flows that
have been entered in the calculator.
25
Calculate the NPV for Project B with calculator.

P R O J E C T
Time      A           B
0     (10,000)   (10,000)
1       3,500        500
P/YR
2       3,500        500
CF     NPV   IRR            3       3,500      4,600
4       3,500     10,000
N   I/Y    PV    PMT    FV

Note: First step is to press the CF
button. Then press 2nd and CE/C to
clear all prior data                              26
Calculate the NPV for Project B with calculator.

Keystrokes for TI BAII PLUS:
CF0 =         -10,000
CF 10000    +/- ENTER
P/YR
CF    NPV   IRR

N     I/Y   PV    PMT    FV

27
Calculate the NPV for Project B with calculator.

Keystrokes for TI BAII PLUS:
C01 =               500
CF 10000    +/- ENTER
P/YR               500       ENTER
CF    NPV   IRR

N    I/Y   PV    PMT     FV

28
Calculate the NPV for Project B with calculator.

Keystrokes for TI BAII PLUS:
F01 =               2
CF 10000     +/- ENTER
P/YR                  500       ENTER
CF    NPV   IRR
2       ENTER
N    I/Y    PV   PMT        FV

F stands for “frequency”. Enter 2 since there
are two adjacent payments of 500 in periods 1
and 2.
29
Calculate the NPV for Project B with calculator.

Keystrokes for TI BAII PLUS:
C02 =               4600
CF 10000     +/- ENTER
P/YR                500       ENTER
CF    NPV   IRR
2       ENTER
N    I/Y   PV    PMT     FV
4600        ENTER

30
Calculate the NPV for Project B with calculator.

Keystrokes for TI BAII PLUS:
F02 =               1
CF 10000     +/- ENTER
P/YR                  500       ENTER
CF    NPV   IRR
2       ENTER
N    I/Y    PV   PMT        FV
4600        ENTER
1       ENTER

31
Calculate the NPV for Project B with calculator.

Keystrokes for TI BAII PLUS:
C03 =               10000
CF 10000     +/- ENTER
P/YR                 500       ENTER
CF    NPV   IRR
2       ENTER
N    I/Y   PV    PMT     FV
4600        ENTER
1       ENTER
10000        ENTER

32
Calculate the NPV for Project B with calculator.

Keystrokes for TI BAII PLUS:
F03 =               1
CF 10000     +/- ENTER
P/YR                  500       ENTER
CF    NPV   IRR
2       ENTER
N    I/Y    PV   PMT        FV
4600        ENTER
1       ENTER
10000        ENTER
1       ENTER
33
Calculate the NPV for Project B with calculator.

Keystrokes for TI BAII PLUS:
I =                 10
NPV      10      ENTER

P/YR
CF    NPV   IRR

k = 10%
N     I/Y   PV    PMT    FV

34
Calculate the NPV for Project B with calculator.

Keystrokes for TI BAII PLUS:
NPV =         1,153.95
NPV      10      ENTER

P/YR                CPT
CF     NPV   IRR

N     I/Y   PV    PMT    FV

The net present value of Project B =
\$1,154 as we calculated previously.
Note: If you press the IRR key, and
35
CPT, it will calculate the IRR for you,
i.e. 13.5%
Calculate the NPV for project A with calculator

• CF             -10,000           ENTER
down arrow
• CO1              3,500           ENTER
down arrow

• FO1                 4            ENTER
• Down arrow
•   CO2                            NPV
•   I=                10           ENTER
•   NPV =                          CPT
•   NPV =        \$1,094.53
For IRR, punch the IRR key and then CPT
NPV Decision Rule
• Accept the project if the NPV is greater than
or equal to 0.

Example:
NPVA = \$1,095      >0      Accept
NPVB = \$1,154      >0      Accept

•If projects are independent, accept both projects.
•If projects are mutually exclusive, or you don’t
have enough money to do both, accept the project
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with the higher NPV, in this case project B.
Capital Budgeting Methods
• IRR (Internal Rate of Return) = K
– IRR is the discount rate (K) that forces the NPV
to equal zero.
– It is the rate of return on the project given its
initial investment and future cash flows.
• We use the same equation as for NPV, except that
NPV = zero, and we solve for k
• Using the table method, and you have unequal
amounts of cash flow, it can only be done by trial and
error. For example, substitute values for k until the
NPV comes out to zero. Ugh! So don’t even try.
37
• Use your financial calculator! 
Calculate the IRR for project A using the
financial calculator – an annuity
• If the payments are \$3,500 each for four periods, and
the present value is \$10,000, the initial outlay, then
• IRR = \$3,500(PVIFA k, 4), solving for k
• N=4
• PMT = 3,500
• PV = -10,000
• FV = 0
• CPT I/Y = 14.96%
• You can also use Cash Flow method
Calculate the IRR for Project B with calculator.
Not an Annuity

P R O J E C T
Time      A           B
0     (10,000)   (10,000)
1       3,500        500
P/YR
2       3,500        500
CF    NPV   IRR                3       3,500      4,600
4       3,500     10,000
N   I/Y   PV    PMT    FV

See slides 17 – 23 for entering
the unequal amounts in project B
39
Calculate the IRR for Project B with calculator.

P R O J E C T
IRR =                13.5%   Time       A           B
0      (10,000)   (10,000)
1        3,500        500
P/YR
2        3,500        500
CF     NPV   IRR             3        3,500      4,600
4        3,500     10,000
N     I/Y   PV    PMT     FV

Enter Cash Flows as for NPV

IRR    CPT
Calculate IRR for project A
with calculator. = 14.96%                                         40
IRR Decision Rule
• Accept the project if the IRR is greater than
or equal to the required rate of return (k).
• Reject the project if the IRR is less than the
required rate of return (k).

Example:
If k = 10%
IRRA = 14.96% > 10%             Accept
IRRB = 13.50% > 10%             Accept
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What if NPV and IRR give different results?

• Which project(s) should the firm accept?
NPV         IRR
• A \$1,095       14.96%
• B \$1,154       13.5%

48
NPV/IRR Decision Rules
•If projects A & B are independent, and you
have enough money, accept both projects
•If projects A & B are mutually exclusive,
meaning you can only pick one or the other,
or you don’t have enough money to do
both,
•Always choose the project with the highest
NPV. See page 257 (280), mid-page             49
What is capital rationing?
• Capital rationing is the practice of
placing a dollar limit on the total size of
the capital budget.
• This practice may not be consistent
with maximizing shareholder value but
may be necessary for other reasons,
like lack of cash.
• Choose between projects by selecting
the combination of projects that yields
the highest total NPV without exceeding
the capital budget cash outlay limit.
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Capital Rationing example p. 261 (284)
• Project        Cash Outlay        NPV
–A            \$20,000            \$8,000
–B            \$50,000            \$7,200
–C            \$40,000            \$6,500
–D            \$60,000            \$5,100
–E            \$50,000            \$4,200
–F            \$30,000            \$3,800
–G            \$30,000            \$2,000
\$280,000
If cash outlay spending limit is \$200,000,
which combination of projects should be
chosen to maximize NPV?
Capital Rationing example p. 261 (284)
• Project     Cash Outlay    NPV
A,B,C,D     \$170,000       \$26,800
A,B,C,D,F   \$200,000       \$30,600
A,B,C,D,G   \$200,000       \$28,800
B,C,D,E     \$200,000       \$23,000
B,C,E,F,G   \$200,000       \$23,700
A,C,D,E,F   \$200,000       \$27,600
A,C,D,E,G   \$200,000       \$25,500
Mutually Exclusive Projects With
Unequal Lives
• Mutually exclusive projects with unequal
project lives can be compared by using
the Replacement Chain method

68
Replacement Chain Approach
• Assumes each project can be replicated
until a common period of time has
passed, allowing the projects to be
compared.
• Example
– Project Cheap Talk has a 3-year life,
with an NPV of \$4,424.
– Project Rolles Voice has a 12-year
life, with an NPV of \$12,000.
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Replacement Chain Approach
• Project Cheap Talk could be repeated
four times during the life of Project
Rolles Voice. (4 x \$4,424 = \$17,696?)

• The NPVs of Project Cheap Talk, in
years t3, t6, and t9, need to be
discounted back to year t0.

70
Replacement Chain Approach
• The NPVs of Project Cheap Talk, in years t3,
t6, and t9, are discounted back to year t0,
which results in an NPV of \$12,121. So
choose project Cheap Talk
k=10%
0           3      6      9

4,424    4,424    4,424   4,424

3,324
2,497
1,876
71
12,121
Disparate sizes

•   Suppose capital budget is \$10,000
•   Project A: \$2,000 with NPV of \$1,000
•   Project B: \$10,000 with NPV of \$3,000
•   Which should you choose? Say you
only have \$10,000 and can’t do both.
Disparate Sizes
• Ans: depends on what you can earn on
the extra \$8,000 if you choose Project
A. If the combined NPV’s for project A
plus what you earned on the other
\$8,000 exceeds the NPV of project B,
then do project A plus others.
• Otherwise, choose project B
• Always choose the option with the
highest NPV!

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