This document discusses various capital budgeting techniques used to evaluate investment projects, including payback period, net present value (NPV), and internal rate of return (IRR). It explains how to calculate and use each method to make accept/reject decisions for independent projects or choose between mutually exclusive projects. While NPV and IRR typically yield the same results, they may sometimes rank projects differently, posing potential conflicts. The document also covers capital rationing, risk adjustment, and required returns that vary by project risk levels.

1. The Capital Budgeting Decision
(Chapter 12)
 Capital Budgeting: An Overview
 Estimating Incremental Cash Flows
 Payback Period
 Net Present Value
 Internal Rate of Return
 Ranking Problems
 Capital Rationing
 Risk Adjustment

2. Capital Budgeting: An Overview
 Search for investment opportunities. This process will
obviously vary among firms and industries.
 Estimate all cash flows for each project.
 Evaluate the cash flows. a) Payback period. b) Net Present
Value. c) Internal Rate of Return. d) Modified Internal rate
of Return.
 Make the accept/reject decision.
– Independent projects: Accept/reject decision for a
project is not affected by the accept/reject decisions of
other projects.
– Mutually exclusive projects: Selection of one
alternative precludes another alternative.
 Periodically reevaluate past investment decisions.

3. Estimating Incremental Cash Flows
Only changes in after-tax cash flows that would
occur if the project is accepted versus what they
would be if the project is rejected are relevant.
Initial Outlay: Includes purchase price of the asset,
shipping and installation, after-tax sale of asset to be
replaced if applicable, additional required investments in
net working capital (e.g., increases in accounts receivable
and inventory less any spontaneous increases in accounts
payable and accruals), plus any other cash flows necessary
to put the asset in working order.

4. Differential Cash Flows
Over the Project’s Life:
Change in revenue
- Change in operating expenses
= Change in operating income before taxes
- Change in taxes
= Change in operating income after taxes
+ Change in depreciation
= Differential cash flow

5. Note: Interest expenses are excluded when
calculating differential cash flow. Instead, they are
accounted for in the discount rate used to evaluate
projects.
Terminal Cash Flow: Includes after-tax salvage
value of the asset, recapture of nonexpense outlays
that occurred at the asset’s initiation (e.g., net
working capital investments), plus any other cash
flows associated with project termination.

6. Payback Period
 The number of years required to recoup the initial outlay.
What is (n) such that:
CF CF
t
t
n



 0
1
(n) = payback period (PP)
CF = initial outlay
CF after - tax cash flow in period (t)
0
t

7. Payback Period (Continued)
 Decision Rules:
– PP = payback period
– MDPP = maximum desired payback period
 Independent Projects:
– PP MDPP - Accept
– PP > MDPP - Reject
 Mutually Exclusive Projects:
– Select the project with the fastest payback, assuming PP
 MDPP.
 Problems: (1) Ignores timing of the cash flows, and
(2) Ignores cash flows beyond the payback period.

8. Net Present Value (NPV)
 The present value of all future after-tax cash flows minus
the initial outlay
return)
(required
capital
of
cost
=
k
:
where
)
1
(
...
)
1
(
)
1
(
=
)
1
(
0
2
2
1
1
0
CF
k
CF
k
CF
k
CF
CF
k
CF
NPV
n
n
n
t
t
t















 


9. NPV (Continued)
Decision Rules:
Independent Projects:
– NPV  0 - Accept
– NPV < 0 - Reject
Mutually Exclusive Projects:
– Select the project with the highest NPV,
assuming NPV  0.

10. Internal Rate of Return (IRR)
 Rate of return on the investment. That rate of discount
which equates the present value of all future after-tax cash
flows with the initial outlay. What is the IRR such that:
 When only one interest factor is required, you can solve for
the IRR algebraically. Otherwise, trial and error is
necessary.
)
1
(
1
0




n
t
t
t
CF
IRR
CF

11. IRR (Continued)
 If you are not using a financial calculator:
1. Guess a rate.
2. Calculate:
3. If the calculation = CF0 you guessed right
If the calculation > CF0 try a higher rate
If the calculation < CF0 try a lower rate
Note: Financial calculators do the trial and error
calculations much faster than we can!
CF
IRR
t
t
t
n
( )
1
1 



12. IRR (Continued)
 Decision Rules (No Capital Rationing):
– Independent Projects:
• IRR  k - Accept
• IRR < k - Reject
– Mutually Exclusive Projects:
• Select the project with the highest IRR, assuming
IRR  k.
 Multiple IRRs:
– There can be as many IRRs as there are sign reversals
in the cash flow stream. When multiple IRRs exist, the
normal interpretation of the IRR loses its meaning.

13. Ranking Problems
 When NPV = 0, IRR = k
When NPV > 0, IRR > k
When NPV < 0. IRR < k
 Therefore, given no capital rationing and independent
projects, the NPV and IRR methods will always result in
the same accept/reject decisions.
 However, the methods may rank projects differently. As a
result, decisions could differ if projects are mutually
exclusive, or capital rationing is imposed. Ranking
problems can occur when (1) initial investments differ, or
(2) the timing of future cash flows differ. (See discussion
on NPV profiles)

14. Ranking Problems (Continued)
 Ranking Conflicts: Due to reinvestment rate assumptions,
the NPV method is generally more conservative, and is
considered to be the preferred method.
 NPV - Assumes reinvestment of future cash flows at the
cost of capital.
 IRR - Assumes reinvestment of future cash flows at the
project’s IRR.
 In addition, the NPV method maximizes the value of the
firm.

15. Capital Rationing
Note:
– Capital rationing exists when an artificial
constraint is placed on the amount of funds
that can be invested. In this case, a firm may
be confronted with more “desirable” projects
than it is willing to finance. A wealth
maximizing firm would not engage in capital
rationing.

16. Capital Rationing: An Example
(Firm’s Cost of Capital = 12%)
 Independent projects ranked according to their
IRRs:
Project Project Size IRR
E $20,000 21.0%
B 25,000 19.0
G 25,000 18.0
H 10,000 17.5
D 25,000 16.5
A 15,000 14.0
F 15,000 11.0
C 30,000 10.0

17. Capital Rationing Example (Continued)
 No Capital Rationing - Only projects F and C would
be rejected. The firm’s capital budget would be
$120,000.
 Capital Rationing - Suppose the capital budget is
constrained to be $80,000. Using the IRR criterion,
only projects E, B, G, and H, would be accepted, even
though projects D and A would also add value to the
firm. Also note, however, that a theoretical optimum
could be reached only be evaluating all possible
combinations of projects in order to determine the
portfolio of projects with the highest NPV.

18. Required Returns for Individual Projects That
Vary in Risk Levels
Higher hurdle rates should be used for
projects that are riskier than the existing
firm, and lower hurdle rates should be used
for lower risk projects.
Measuring risk and specifying the tradeoff
between required return and risk, however,
are indeed difficult endeavors.
Interested students should read Chapter 13
entitled Risk and Capital Budgeting.

19. Risk Adjusted Required Returns
0
2
4
6
8
10
12
14
16
18
20
0 2 4 6
Required Return
Firm’s Risk Level
Risk
ka
Risk-Return
Tradeoff
ka = Cost of
Capital for the
existing firm.