Capital budgeting techniques are used to evaluate long-term investment projects. The key techniques discussed are net present value (NPV), internal rate of return (IRR), profitability index (PI), and payback period. NPV discounts future cash flows to determine if a project adds value. IRR is the discount rate that results in an NPV of zero. PI divides NPV by project cost. Payback period determines how long until costs are recovered. Relevant cash flows consider sunk costs, opportunity costs, working capital changes, capital expenditures and taxes, and inflation adjustments.

1. Capital Budgeting

2. Revision basic techniques
Compounding Discounting
 1 
FV = PV (1 + r )
n
PV = FV 
 (1 + r ) n 

 
FV = Future Value
PV = Present Value
r = rate
n = number of periods

3. Example
John deposits £200 in an account that
pays 6% per year. At the end of 6 years
what will he have?

4. Annuity
An equal sum of money (AMT) received or paid over
a fixed period of time.
Compounding Discounting
 1 
 (1 + r ) − 1 
n 1− 
FV = AMT   (1 + r ) n
  PV = AMT  
 r   r 
 
 

5. Example: Annuity
Jill has been faithfully depositing $2,000 at
the end of each year for the past 10 years
into an account that pays 8% per year.
How much money will she have
accumulated in the account?

6. Example: Annuity
John wants to make sure that he has saved up
enough money for college expenses: $40,000
per year for 4 years. How much money will John
need to have accumulated in an account that
earns 7% per year?

7. Perpetuity
A perpetuity is an equal sum of money (AMT), received or
paid over an infinite period (will never cease).
AMT
PV =
r
Eg: You are considering the purchase of a
bond that pays $60 per year forever, and the
rate of interest you want to earn is 10% pa, what
is the present value of the bond?

8. Capital Budgeting Decisions
• Long-term decisions - go or no-go decision on
a product, service, facility, or activity of the firm.
– Involve longer time horizons
– cost larger sums of money
– require a lot more information to be collected
e.g. estimates of the timing and amount of
cash flow
– Models used have a pre-determined accept
or reject criterion.

9. Methods
1. Net Present Value (NPV)
2. Internal Rate of Return (IRR)
3. Profitability Index (PI)
4. Payback Period

10. 1. Net Present Value (NPV)
• Discounts all the cash flows from a project
back to time 0 using an appropriate discount
rate, r:
CF1 CF2 CF3 CFn
NPV = − CF0 + + + + ... +
(1 + r ) (1 + r ) (1 + r )
1 2 3
(1 + r ) n
A +NPV implies that the project is adding value
to the firm’s bottom line, therefore, the higher
the NPV the better.
RULE: Accept if NPV>0 reject if NPV<0

11. Example 1
• The owner of Perfect Images Salon is
considering the purchase of a new tanning bed.
• It costs $10,000 and is likely to bring in after-tax
cash inflows of $4,000 in the first year, $4,500 in
the second year, $10,000 in the third year, and
$8,000 in the fourth year.
• The company’s cost of capital is 10%.
• Calculate the NPV for the new tanning bed.

12. 2. Internal Rate of Return (IRR)
• The IRR is the discount rate which when applied to the
cash flows gives a nil (zero) NPV:
CF1 CF2 CF3 CFn
£0 = −CF0 + + + + ... +
(1 + r ) (1 + r ) (1 + r )
1 2 3
(1 + r ) n
RULE: Accept if IRR > hurdle rate
Reject if IRR < hurdle rate
Hurdle rate = company’s cost of capital (WACC)
• Note that the IRR is measured as a percent, while the
NPV is measured in money terms.

13. IRR Method
1. Find the NPV(a) at one discount rate (a%)
2. Find the NPV(b) at a second discount rate
(b%)
3. Interpolate between the two NPV’s to find
the approximate IRR
 NPVa 
IRR ≈ a % +  ( b% − a % ) 
 ( NPVa − NPVb ) 

14. Example 2: Calculating IRR
Yr Cash flow PV factor PV PV Factor PV
0 (5,000,000)
1 2,000,000
2 2,000,000
3 2,460,000

15. Problems with the IRR
• In most cases, NPV decision = IRR decision
– i.e. a project with a positive NPV will have an IRR that
exceeds its hurdle rate - similarly, the highest NPV
project will also have the highest IRR.
• There are some cases where the IRR method is
problematic - Multiple IRR’s -Projects that have non-
normal cash flows i.e. --multiple sign changes, often end
up with multiple IRR’s. (normal = negative followed by
positive cash flows)
• IRR ignores the relative size of investments
RULE: select the project if it has a positive NPV

16. Multiple Internal Rates of Return

17. 3. Profitability Index (PI)
• If faced with a constrained budget, we should choose
projects that makes the best use of the scarce resource
• The PI can be used to calculate the ratio of the NPV the
cost of a project as follows:
NPV
PI =
cos t
• In essence, how NPV we are getting per pound invested.

18. Example 3: PI
Using the cash flows and NPVs @ 10%, calculate the PI of
each project. Which one should be accepted, if they are
mutually exclusive? Why?
Year A£ B£
0 -10,000 -7,000
• 5,000 9,000
• 7,000 5,000
• 9,000 2,000
NPV £7,092.41 £6,816.68

19. Capital Rationing
Often associated with general problems of cash shortage:
i. the business has become loss making implying that there will be
insufficient cash with which to replace these assets when
necessary.
ii. High inflation may mean that even though the business is
profitable it is still failing to generate sufficient funds to replace
assets.
iii.Growing businesses may face a shortage of working capital with
which to finance expansion, result in a period of capital rationing.
iv. Seasonal or cyclical businesses may face times of cash
shortage causing periodic capital rationing.
v. A large one-off item of expenditure e.g. property, may mean a
temporary shortage of cash for further investment.
vi. Investment opportunities – there are more investment
opportunities available than the funds allocated to the capital
budget permit. This means that projects must be ranked for
investment.

20. Hard capital rationing – a firm is prevented from undertaking
attractive investments for reasons external to the firm.
Soft capital rationing – management places a limit on the
amount of capital investment that may be undertaken: it is
due to factors internal to the firm, such as:
• management may decide to limit funds to retained earnings:
– They do not wish to issue further equity to prevent
outsiders from gaining control of the business or to avoid
earnings dilution
– They do not wish to commit the company to meeting large
fixed interest payments on additional debt capital.
• number of projects undertaken restricted in order to ensure
adequate management resources available for them to
realise their full potential.

21. 4. Payback Period
• The length of time in which an investment pays back its
original cost.
RULE: Accept if Payback period ≤ the cutoff
period
• Main focus is on cost recovery or liquidity.
• Assumes that all cash outflows occur right at the
beginning of the project’s life, followed by a stream of
inflows that occur uniformly over the year.

22. Payback Period Flaws
• The payback period method has two major
flaws:
-It ignores all cash flow after the initial cash
outflow has been recovered
-It ignores the time value of money – this
can be solved by calculating the payback
period using discounted cash flows.

23. Example 4 - Payback Period
Calculate the payback period for the following cash
flows:
Yr Cash Flow
0 -470,000
1-5 140,000pa

24. Overview of Decision Models
1. Net present value (NPV)
– economically sound
– properly ranks projects across various sizes, time
horizons, and levels of risk, without exception for all
independent projects.
2. Internal rate of return (IRR)
– provides a single measure (return)
– has the potential for errors in ranking projects
– can also lead to an incorrect selection when there are two
mutually exclusive projects or incorrect acceptance or rejection
of a project with more than a single IRR
3. Profitability index (PI)
– incorporates risk and return
– but the NPV-to-cost ratio is actually just another way of
expressing the NPV

25. Overview of Decision Models
4. Payback period
– simple and fast, but economically unsound
– ignores all cash flow after the cutoff date
– ignores the time value of money
4a. Discounted (Adjusted) payback period
– incorporates the time value of money
– still ignores cash flow after the cutoff date.

26. Importance of Cash Flow
• Cash flow measures the actual inflow and outflow
• While profits represent merely an accounting measure
of periodic performance.
- A firm can spend its operating cash flow but not its
net income.
- Some firms have net losses (due to high depreciation
write-offs) and yet can pay dividends from cash
balances, while others show profits and may not have
the cash available.
Thus, cash flow is broader than net income.

27. Relevant Project Cash Flows
Incremental Cash Flow
Relevant cash flows are: the incremental cash
flows of the company as a whole as a result of
accepting the project.
Those cash flows which would have arisen anyway,
irrespective of whether or not the project is
undertaken, can be ignored, e.g. apportioned costs
and money already spent or committed.
RULE: We are only concerned with the
timing and size of future cash flows

28. 5 important issues
1. sunk costs
2. opportunity cost
3. working capital
4. capital expenditures and
tax implications
5. inflation

29. 1. Sunk Costs
• Expenses already incurred, or that will be
incurred, regardless of the decision to accept or
reject a project.
-e.g. marketing research exploring business
possibilities in a region would be a sunk cost,
since its expenditure has taken place prior to
undertaking the project and will have to be paid
whether or not the project is taken on.
RULE: do not considered as part of the
relevant cash flows when evaluating
the project

30. 2. Opportunity Costs
• Costs that may not be obvious
• Result from benefits lost as a result of a project
-e.g. a project uses existing equipment rather
than selling it, the value that could be realized
by selling would be a relevant opportunity cost
RULE: include opportunity costs as
relevant cash flows

31. 3. Working Capital
• Additional cash flows arising from changes in current
assets (inventory and receivables) and current liabilities
(accounts payables) - as a result of a new project.
• At the end of the project, these additional cash flows are
recovered and must be shown as cash inflows.
• Even though the net cash outflows--due to increase in net
working capital at the start-- may equal the net cash inflow
at the end, the time value of money effects make these
costs relevant.
RULE: include changes in working capital as
relevant cash flows

32. 4. Capital Spending & Tax Implications
• Capital expenditures are expensed on an annual
basis giving the company tax relief
• The portion written off each year is called the
depreciation expense; a accumulated total is kept
in the balance sheet - Accumulated Depreciation.
• The book value of an asset equals its original cost
minus its accumulated depreciation and allows the
gain or loss at disposal to be calculated.
RULE: -include capital expenditure and sales
proceeds as relevant cash flows
-include tax relief as a relevant cash flow
-do not include depreciation as it is not a
cash flow

33. 5. Inflation – cash flows
To find the future cash flow with inflation (nominal):
FV = PV × (1 + r )
n
Where:
r = inflation rate n = number of periods
FV = future value with inflation – nominal cash flow
PV = present value without inflation – real cash flow
RULE: future cash flows must include the
effects of inflation

34. 5. Inflation – discount rate
If the cash flows include inflation then the discount rate
must include inflation:
n = (1 + r )(1 + i ) − 1
Where:
n = nominal discount rate
r = real discount rate
i = inflation rate
RULE: discount rate must include the
effects of inflation