CAPITAL BUDGETING

Net Present Value and Other

Investment Criteria
Net Present Value (NPV)

• Net present value is the difference between an

investment’s market value (in today’s dollars) and
its cost (also in today’s dollars).

• Net present value is a measure of how much value

is created by undertaking an investment.

• Estimation of the future cash flows and the

discount rate are important in the calculation of the
NPV.
Net Present Value

Steps in calculating NPV:

• The first step is to estimate the expected future

cash flows.
• The second step is to estimate the required return
for projects of this risk level.
• The third step is to find the present value of the
cash flows and subtract the initial investment.
NPV Illustrated
0 1 2

Initial outlay Revenues $1000 Revenues $2000

($1100) Expenses 500 Expenses 1000
Cash flow $500 Cash flow $1000

– $1100.00
1
$500 x
1.10
+454.55
1
$1000 x
1.102
+826.45

+$181.00 NPV
NPV

• An investment should be accepted if the NPV is

positive and rejected if it is negative.

• NPV is a direct measure of how well the

investment meets the goal of financial
management—to increase owners’ wealth.

• A positive NPV means that the investment is

expected to add value to the firm.
Payback Period
• The amount of time required for an investment to generate
cash flows to recover its initial cost.

• Estimate the cash flows.

• Accumulate the future cash flows until they equal the initial
investment.

• The length of time for this to happen is the payback period.

• An investment is acceptable if its calculated payback is less

than some prescribed number of years.
Payback Period Illustrated
Initial investment = –$1000
Year Cash flow
1 $200
2 400
3 600

Accumulated
Year Cash flow
1 $200
2 600
3 1200

Payback period = 2 2/3 years

Advantages of Payback Period

• Easy to understand.

• Adjusts for uncertainty of later cash flows.

• Biased towards liquidity.

Disadvantages of Payback Period

• Time value of money and risk ignored.

• Arbitrary determination of acceptable payback

period.

• Ignores cash flows beyond the cut-off date.

• Biased against long-term and new projects.

Discounted Payback Period

• The length of time required for an investment’s

discounted cash flows to equal its initial cost.

• Takes into account the time value of money.

• More difficult to calculate.

• An investment is acceptable if its discounted

payback is less than some prescribed number of
years.
Example—Discounted Payback
Initial investment = —$1000
R = 10%
PV of
Year Cash flow Cash flow
1 $200 $182
2 400 331
3 700 526
4 300 205
Example—Discounted Payback
(continued)

Accumulated
Year discounted cash flow
1 $182
2 513
3 1039
4 1244

Discounted payback period is just under three years

Ordinary and Discounted Payback
Initial investment = –$300
R = 12.5%
Cash Flow Accumulated Cash Flow
Year Undiscounted Discounted Undiscounted Discounted

1 $ 100 $ 89 $ 100 $89

2 100 79 200 168
3 100 70 300 238
4 100 62 400 300
5 100 55 500 355

• Ordinary payback?
• Discounted payback?
Advantages and Disadvantages of
Discounted Payback

• Advantages • Disadvantages

- Includes time value of - May reject positive NPV

money investments
- Easy to understand - Arbitrary determination of
- Does not accept negative acceptable payback period
estimated NPV investments - Ignores cash flows beyond
- Biased towards liquidity the cutoff date
- Biased against long-term
and new products
Accounting Rate of Return (ARR)

• Measure of an investment’s profitability.

average net profit

ARR 
average book value
• A project is accepted if ARR > target average
accounting return.
Example—ARR
Year
1 2 3

Sales $440 $240 $160

Expenses 220 120 80
Gross profit 220 120 80
Depreciation 80 80 80
Taxable income 140 40 0
Taxes (25%) 35 10 0
Net profit $105 $30 $0

Assume initial investment = $240

Example—ARR (continued)

$105  $30  $0
Average net profit 
3
 $45

Initial investment  Salvage value

Average book value 
2
$240  $0

2
 $120
Example—ARR (continued)

Average net profit

ARR 
Average book value
$45

$120
 37.5%
Disadvantages of ARR

• The measure is not a ‘true’ reflection of return.

• Time value is ignored.

• Arbitrary determination of target average return.

• Uses profit and book value instead of cash flow

and market value.
Advantages of ARR

• Easy to calculate and understand.

• Accounting information almost always available.

Internal Rate of Return (IRR)
• The discount rate that equates the present value of
the future cash flows with the initial cost.

• Generally found by trial and error.

• A project is accepted if its IRR is > the required

rate of return.

• The IRR on an investment is the required return

that results in a zero NPV when it is used as the
discount rate.
Example—IRR
Initial investment = –$200
Year Cash flow
1 $ 50
2 100
3 150

n Find the IRR such that NPV = 0

50 100 150
0 = –200 + + +
(1+IRR) 1 (1+IRR)2 (1+IRR)3

50 100 150
200 = + +
(1+IRR) 1 (1+IRR)2 (1+IRR)3
Example—IRR (continued)
Trial and Error
Discount rates NPV
0% $100
5% 68
10% 41
15% 18
20% –2

IRR is just under 20%—about 19.44%

NPV Profile
Net present value

120 Year Cash flow

0 – $275
100 1 100
2 100
80 3 100
4 100
60

40

20

– 20

– 40 Discount rate
2% 6% 10% 14% 18% 22%
IRR
Problems with IRR

• More than one negative cash flow  multiple rates

of return.

• Project is not independent  mutually exclusive

investments. Highest IRR does not indicate the
best project.

Advantages of IRR
• Popular in practice
• Does not require a discount rate
Multiple Rates of Return
Assume you are considering a project for
which the cash flows are as follows:

Year Cash flows

0 –$252

1 1431
2 –3035
3 2850
4 –1000
Multiple Rates of Return
n What’s the IRR? Find the rate at which
the computed NPV = 0:

at 25.00%: NPV = 0
at 33.33%: NPV = 0
at 42.86%: NPV = 0
at 66.67%: NPV = 0

n Two questions:
u 1. What’s going on here?
u 2. How many IRRs can there be?
Multiple Rates of Return
NPV
$0.06

$0.04

IRR = 25%
$0.02

$0.00

($0.02) IRR = 33.33% IRR = 66.67%

IRR = 42.86%
($0.04)

($0.06)

($0.08)

0.2 0.28 0.36 0.44 0.52 0.6 0.68

Discount rate
IRR and Non-conventional Cash
Flows

• When the cash flows change sign more than once,

there is more than one IRR.
• When you solve for IRR you are solving for the root
of an equation and when you cross the x axis more
than once, there will be more than one return that
solves the equation.
• If you have more than one IRR, you cannot use
any of them to make your decision.
IRR, NPV and Mutually-exclusive
Projects
Net present value
Year
160 0 1 2 3 4
140 Project A: – $350 50 100 150 200
120
100 Project B: – $250 125 100 75 50
80
60
40
Crossover Point
20
0
– 20
– 40
– 60
– 80
– 100 Discount rate
0 2% 6% 10% 14% 18% 22% 26%

IRR A IRRB
 Present Value Index (PVI)

• Expresses a project’s benefits relative to its initial

cost.
PV of inflows
PVI 
Initial cost
• Accept a project with a PVI > 1.0.
Example—PVI

Assume you have the following information on Project X:

Initial investment = –$1100 Required return = 10%

Annual cash revenues and expenses are as follows:

Year Revenues Expenses
1 $1000 $500
2 2000 1000
Example—PVI (continued)
500 1 000
NPV    1100
1.10 1.10 2

 $181

181  1100
PVI 
1100
 1.1645

Net Present Value Index

= 181
1100
= 0.1645
Example—PVI (continued)

Is this a good project? If so, why?

• This is a good project because the present value of

the inflows exceeds the outlay.

• Each dollar invested generates $1.1645 in value or

$0.1645 in NPV.
Advantages and Disadvantages of
PVI (and NPVI)

• Advantages • Disadvantages

- Closely related to NPV, - May lead to incorrect

generally leading to decisions in comparisons of
identical decisions. mutually exclusive
investments.
- Easy to understand.

- May be useful when

available investment funds
are limited.
Capital Budgeting in Practice

• We should consider several investment criteria

when making decisions.

• NPV and IRR are the most commonly used primary

investment criteria.

• Payback is a commonly used secondary

investment criteria.