Capital budgeting is the process of planning for long-term investments. Key criteria for evaluating capital projects include payback period, net present value (NPV), internal rate of return (IRR), and profitability index (PI). NPV discounts future cash flows to determine if a project's value exceeds its cost. IRR is the discount rate that sets NPV to zero. PI is NPV divided by the initial investment. Multiple IRRs can occur if cash flows change signs more than once. The modified IRR (MIRR) assumes reinvestment at the required rate of return rather than the IRR.

1. Capital Budgeting
Decision
Criteria

2. Capital Budgeting: the process of
planning for purchases of long-
term assets.
• example:
Suppose our firm must decide whether to
purchase a new plastic molding machine
for $125,000. How do we decide?
• Will the machine be profitable?
• Will our firm earn a high rate of return
on the investment?

3. Decision-making Criteria in
Capital Budgeting
How do we decide
if a capital
investment
project should
be accepted or
rejected?

4. Decision-making Criteria in
Capital Budgeting
• The Ideal Evaluation Method
should:
a) include all cash flows that occur
during the life of the project,
b) consider the time value of money,
c) incorporate the required rate of
return on the project.

5. Payback Period
• How long will it take for the project
to generate enough cash to pay for
itself?

6. Payback Period
• How long will it take for the project
to generate enough cash to pay for
itself?
(500) 150 150 150 150 150 150 150 150
0 1 2 3 4 5 6 7 8

7. Payback Period
• How long will it take for the project
to generate enough cash to pay for
itself?
(500) 150 150 150 150 150 150 150 150
0 1 2 3 4 5 6 7 8
Payback period = 3.33 years.

8. Payback Period
• Is a 3.33 year payback period good?
• Is it acceptable?
• Firms that use this method will compare
the payback calculation to some
standard set by the firm.
• If our senior management had set a cut-
off of 5 years for projects like ours,
what would be our decision?
• Accept the project.

9. Drawbacks of Payback Period
• Firm cutoffs are subjective.
• Does not consider time value of
money.
• Does not consider any required
rate of return.
• Does not consider all of the
project’s cash flows.

10. Drawbacks of Payback Period
• Does not consider all of the
project’s cash flows.
(500) 150 150 150 150 150 (300) 0 0
0 1 2 3 4 5 6 7 8
• Consider this cash flow stream!

11. Drawbacks of Payback Period
• Does not consider all of the
project’s cash flows.
(500) 150 150 150 150 150 (300) 0 0
0 1 2 3 4 5 6 7 8
• This project is clearly unprofitable,
but we would accept it based on a 4-
year payback criterion!

12. Discounted Payback
• Discounts the cash flows at the firm’s
required rate of return.
• Payback period is calculated using
these discounted net cash flows.
Problems:
• Cutoffs are still subjective.
• Still does not examine all cash flows.

13. Discounted Payback
(500) 250 250 250 250 250
0 1 2 3 4 5
Discounted
Year Cash Flow CF (14%)
0 -500 -500.00
1 250 219.30

14. Discounted Payback
(500) 250 250 250 250 250
0 1 2 3 4 5
Discounted
Year Cash Flow CF (14%)
0 -500 -500.00
1 250 219.30 1 year
280.70

15. Discounted Payback
(500) 250 250 250 250 250
0 1 2 3 4 5
Discounted
Year Cash Flow CF (14%)
0 -500 -500.00
1 250 219.30 1 year
280.70
2 250 192.37

16. Discounted Payback
(500) 250 250 250 250 250
0 1 2 3 4 5
Discounted
Year Cash Flow CF (14%)
0 -500 -500.00
1 250 219.30 1 year
280.70
2 250 192.37 2 years
88.33

17. Discounted Payback
(500) 250 250 250 250 250
0 1 2 3 4 5
Discounted
Year Cash Flow CF (14%)
0 -500 -500.00
1 250 219.30 1 year
280.70
2 250 192.37 2 years
88.33
3 250 168.74

18. Discounted Payback
(500) 250 250 250 250 250
0 1 2 3 4 5
Discounted
Year Cash Flow CF (14%)
0 -500 -500.00
1 250 219.30 1 year
280.70
2 250 192.37 2 years
88.33
3 250 168.74 .52 years

19. Discounted Payback
(500) 250 250 250 250 250
0 1 2 3 4 5
Discounted
Year Cash Flow CF (14%)
The Discounted
0 -500
Payback-500.00
1 250 219.30 1 year
is 2.52 years
280.70
2 250 192.37 2 years
88.33
3 250 168.74 .52 years

20. Other Methods
1) Net Present Value (NPV)
2) Profitability Index (PI)
3) Internal Rate of Return (IRR)
Each of these decision-making criteria:
• Examines all net cash flows,
• Considers the time value of money, and
• Considers the required rate of return.

21. Net Present Value
• NPV = the total PV of the annual net
cash flows - the initial outlay.
n
Σ
FCFt
NPV = - IO
(1 + k) t
t=1

22. Net Present Value
• Decision Rule:
• If NPV is positive, accept.
• If NPV is negative, reject.

23. NPV Example
• Suppose we are considering a capital
investment that costs $250,000 and
provides annual net cash flows of
$100,000 for five years. The firm’s
required rate of return is 15%.

24. NPV Example
• Suppose we are considering a capital
investment that costs $250,000 and
provides annual net cash flows of
$100,000 for five years. The firm’s
required rate of return is 15%.
(250,000) 100,000 100,000 100,000 100,000 100,000
0 1 2 3 4 5

25. Net Present Value (NPV)
NPV is just the PV of the annual cash
flows minus the initial outflow.
Using TVM:
P/Y = 1 N = 5 I = 15
PMT = 100,000
PV of cash flows = $335,216
- Initial outflow: ($250,000)
= Net PV $85,216

26. Profitability Index

27. Profitability Index
n
Σ
FCFt
NPV = t - IO
(1 + k)
t=1

28. Profitability Index
n
Σ
FCFt
NPV = t - IO
(1 + k)
t=1
n
Σ
FCFt
PI = IO
(1 + k) t
t=1

29. Profitability Index
• Decision Rule:
• If PI is greater than or equal
to 1, accept.
• If PI is less than 1, reject.

30. Internal Rate of Return (IRR)
• IRR: the return on the firm’s
invested capital. IRR is simply the
rate of return that the firm earns on
its capital budgeting projects.

31. Internal Rate of Return (IRR)

32. Internal Rate of Return (IRR)
n
Σ
FCFt
NPV = - IO
(1 + k) t
t=1

33. Internal Rate of Return (IRR)
n
Σ
FCFt
NPV = - IO
(1 + k) t
t=1
n
FCFt
IRR:
Σ
t=1
(1 + IRR) t = IO

34. Internal Rate of Return (IRR)
n
FCFt
IRR:
Σt=1
(1 + IRR) t = IO
• IRR is the rate of return that makes the
PV of the cash flows equal to the initial
outlay.
• This looks very similar to our Yield to
Maturity formula for bonds. In fact, YTM

35. Calculating IRR
• Looking again at our problem:
• The IRR is the discount rate that
makes the PV of the projected cash
flows equal to the initial outlay.
(250,000) 100,000 100,000 100,000 100,000 100,000
0 1 2 3 4 5

36. IRR with your Calculator
• IRR is easy to find with your
financial calculator.
• Just enter the cash flows as you did
with the NPV problem and solve for
IRR.
• You should get IRR = 28.65%!

37. IRR
• Decision Rule:
• If IRR is greater than or equal to
the required rate of return,
accept.
• If IRR is less than the required
rate of return, reject.

38. • IRR is a good decision-making tool as
long as cash flows are conventional.
(- + + + + +)
• Problem: If there are multiple sign
changes in the cash flow stream, we
could get multiple IRRs. (- + + - + +)

39. • IRR is a good decision-making tool as
long as cash flows are conventional.
(- + + + + +)
• Problem: If there are multiple sign
changes in the cash flow stream, we
could get multiple IRRs. (- + + - + +)
(500) 200 100 (200) 400 300
0 1 2 3 4 5

40. • IRR is a good decision-making tool as
long as cash flows are conventional.
(- + + + + +)
• Problem: If there are multiple sign
changes in the cash flow stream, we
could get multiple IRRs. (- + + - + +)
1
(500) 200 100 (200) 400 300
0 1 2 3 4 5

41. • IRR is a good decision-making tool as
long as cash flows are conventional.
(- + + + + +)
• Problem: If there are multiple sign
changes in the cash flow stream, we
could get multiple IRRs. (- + + - + +)
1 2
(500) 200 100 (200) 400 300
0 1 2 3 4 5

42. • IRR is a good decision-making tool as
long as cash flows are conventional.
(- + + + + +)
• Problem: If there are multiple sign
changes in the cash flow stream, we
could get multiple IRRs. (- + + - + +)
1 2 3
(500) 200 100 (200) 400 300
0 1 2 3 4 5

43. Summary Problem
• Enter the cash flows only once.
• Find the IRR.
• Using a discount rate of 15%, find NPV.
• Add back IO and divide by IO to get PI.
(900) 300 400 400 500 600
0 1 2 3 4 5

44. Summary Problem
• IRR = 34.37%.
• Using a discount rate of 15%,
NPV = $510.52.
• PI = 1.57.
(900) 300 400 400 500 600
0 1 2 3 4 5

45. Modified Internal Rate of Return
(MIRR)
• IRR assumes that all cash flows are
reinvested at the IRR.
• MIRR provides a rate of return
measure that assumes cash flows are
reinvested at the required rate of
return.

46. MIRR Steps:
• Calculate the PV of the cash outflows.
– Using the required rate of return.
• Calculate the FV of the cash inflows at
the last year of the project’s time line.
This is called the terminal value (TV).
– Using the required rate of return.
• MIRR: the discount rate that equates
the PV of the cash outflows with the PV
of the terminal value, ie, that makes:
• PVoutflows = PVinflows

47. MIRR
• Using our time line and a 15% rate:
• PV outflows = (900)
• FV inflows (at the end of year 5) = 2,837.
• MIRR: FV = 2837, PV = (900), N = 5
• solve: I = 25.81%.
(900) 300 400 400 500 600
0 1 2 3 4 5

48. MIRR
• Using our time line and a 15% rate:
• PV outflows = (900)
• FV inflows (at the end of year 5) = 2,837.
• MIRR: FV = 2837, PV = (900), N = 5
• solve: I = 25.81%.
• Conclusion: The project’s IRR of
34.37%, assumes that cash flows are
reinvested at 34.37%.

49. MIRR
• Using our time line and a 15% rate:
• PV outflows = (900)
• FV inflows (at the end of year 5) = 2,837.
• MIRR: FV = 2837, PV = (900), N = 5
• solve: I = 25.81%.
• Conclusion: The project’s IRR of
34.37%, assumes that cash flows are
reinvested at 34.37%.
• Assuming a reinvestment rate of 15%,
the project’s MIRR is 25.81%.