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1. Course: Securities Markets
Topic 13:
NPV rule, cash flow calculations,
discount rates in Capital budgeting
Otabek Kurbonov, Assistant Professor of Financial
Management Department, Namseoul University
May 28, 2022, Cheonan

2. Financial theory course
schedule
• Week 1: Introduction to Finance
• Week 2: Present value and Net present value
• Week 3: Discounting and the time value of
money
• Week 4: Annuity and perpetuity
• Week 5: Introduction to Risk and Return
• Week 6: Risk Analytics
• Week 7: Portfolio Theory
• Week 8: The Capital Asset Pricing Model
• Week 9: Valuation of Fixed-Income Securities
• Week 10: Valuation of Common Stocks
• Week 11: Forward and Futures Contracts
• Week 12: Options
• Week 13: Capital budgeting criteria
• Week 14: NPV rule, cash flow calculations,
discount rates in Capital budgeting
• Week 15: Real options

3. Content
• Net present value
• IRR
• Free cash flow
• Evaluating Multiple Projects
• Comparing NPV and IRR techniques
• Choosing the discount rate

4. Net Present Value (NPV)
• Definition of NPV: The difference between the
present value of cash inflows from the project and the
present value of cash outflows (costs) of the project
• - Measured in dollars
• - Can be either positive or negative
• - We need to know the discount rate to calculate NPV

5. Net Present Value (NPV)
• - Discount rate, r, reflects the risk of the project
• - Many projects have “conventional” cash flows

6. Calculating NPV
• Suppose you are considering a project with the
following estimated cash flows
• - You believe that the appropriate discount rate for
this project is 20%
• - What is the NPV of this project?

7. Calculating NPV
• In Excel, we use NPV function to calculate NPV
• - = NPV(Discount rate, The range of cells with cash
flows)
• - Important!: NPV function assumes that the first
cash flow in the range of cells occurs in Year 1, not
in Year 0
• - Solution: When Using the NPV function, leave out
the initial outlay. Then, add the initial outlay manually
outside of the NPV function

12. NPV Decision Rule
If the NPV is positive, accept the project!
• A positive NPV means that the project is expected to
add value to the firm
• If the firm accepts a project with the NPV of $60,
for example, the firm value increases by $60

13. Criteria for Good Capital
Budgeting Decision Rules
• 1. Does the NPV rule consider the time value of
money?
• - Yes!
• 2. Does the NPV rule adjust for risk?
• - Yes!
• 3. Does the NPV rule indicate whether the project
creates value for the firm?
• - Yes!

14. Internal Rate of Return (IRR)
• Definition of IRR: The discount rate that makes
NPV of the project zero
• - Actual rate vs. hypothetical rate

15. Relationship between NPV and
Discount Rate
• - NPV changes as the discount rate changes

16. Relationship between NPV and
Discount Rate
• - NPV decreases as the discount rate increases

17. Relationship between NPV and
Discount Rate
• - NPV increases as the discount rate decreases

18. Relationship between NPV and
Discount Rate

19. Relationship between NPV and
Discount Rate

20. Calculating IRR
• In Excel, we use IRR function to calculate IRR
• - = IRR(The range of cells with cash flows)
• - Important!: Unlike NPV function, IRR function
assumes that the first cash flow in the range of cells
occurs in Year 0

23. IRR Decision Rule
• If the IRR is greater than the actual discount rate,
accept the project!
• - IRR is the annual rate of return of the project
• - The discount rate is the “hurdle rate” required by
investors or the owner of the firm

24. Criteria for Good Capital
Budgeting Decision Rules
• 1. Does the IRR rule consider the time value of
money?
• - Yes!
• 2. Does the IRR rule adjust for risk?
• - Yes!
• 3. Does the IRR rule indicate whether the project
creates value for the firm?
• - No

25. Advantages of IRR Analysis
• - Measures the rate of return (which the NPV
analysis can’t)
• - Sometimes saves you time and effort

26. Free Cash Flow
• Cash Flow From Assets (CFFA) =
• Operating cash flow (OCF)
• – Capital expenditure (CAPEX)
• – Change in net working capital (ΔNWC)
• + Salvage value

27. Operating Cash Flow (OCF)
Operating cash flow (OCF) =Operating income (EBIT) –
– Taxes+ Depreciation

28. Capital Expenditure (CAPEX)
• Capital expenditure is usually incurred at the
beginning of the project
• For convenience, we will include the present value of
the opportunity cost in this item

29. Change in Net Working Capital
• Net working capital = Current assets – Current
liabilities
• Key items include:
• - Account receivable, inventories, and account
payable
• Increase (decrease) in net working capital
requirement means a cash outflow (inflow)

30. Salvage Value of Fixed Assets
• Sometimes your assets could have a positive resale
value at the end of the project
• After-tax salvage
• - Consider the tax effect if resale value differs from
the net book value of the asset
• - After-tax salvage =
• Resale value – Tax rate * (Resale value – Book value)

31. Salvage Value of Net Working
Capital
Do not forget to consider the salvage value of net
working capital at the end of the project
• - Net working capital “tied up to” the project is now
freed up
• - This means a cash inflow

49. Evaluating multiple projects
(Project classifications)
• Sometimes capital budgeting decisions involve
multiple projects
- Independent projects
- Mutually exclusive projects

50. Independent projects
• Projects whose cash flows are not affected by
decisions made about other projects
• All independent projects can be undertaken if they
all are acceptable

51. Mutually exclusive projects
• Projects where the acceptance of one project means
the other(s) cannot be accepted
• Only one project can be undertaken, even if they are
all acceptable

52. Evaluating multiple projects
If projects are independent,
The same rules that are applied to a single project
should be used
• - NPV: Accept projects if NPV > 0
• - Payback period: Accept projects if the payback
period is shorter than the cutoff period
• - IRR: Accept projects if IRR > r

53. Evaluating multiple projects
If projects are mutually exclusive,
Only one project can be accepted
• - NPV: Choose the project with the highest NPV
• - Payback period: Choose the project with the
shortest payback period
• - IRR: Choose the project with the highest IRR

54. Example
• Consider the following two mutually exclusive
projects: (discount rate = 10%)

55. Example
• Consider the following two mutually exclusive
projects: (discount rate = 10%)

56. Example
• Consider the following two mutually exclusive
projects: (discount rate = 10%)

57. Example
• Consider the following two mutually exclusive
projects: (discount rate = 10%)

58. Conflict between NPV and IRR
• Generally the project with a higher NPV also has a
higher IRR
• Sometimes, however, there can be a conflict between
NPV rule and IRR rule
- This is not a problem if projects are independent
- What do we do if projects are mutually exclusive?

59. General principle
• NPV should be always preferred because
- NPV is the additional value you add to the company
- IRR is just the rate of return
• In the previous example,
- NPV(A) = $69.87; NPV(B) = $56.87
- IRR(A) = 13.78%; IRR(B) = 14.89%

60. Comparing NPV and IRR techniques I
(What do we do now?)
• More details about NPV and IRR techniques
• Why do they sometimes yield different results?

61. Overview
Comparing NPV and IRR Techniques I
• 1. Multiple IRR problem
• 2. Comparing projects with different sizes
Comparing NPV and IRR Techniques II
• 3. Comparing projects with different lives
• 4. Reinvestment rate assumptions

62. 1. Multiple IRR Problem
Sometimes a project can have multiple IRRs!
• We did not suffer from the problem in previous
examples
• Projects we have seen so far had a conventional cash
flow

63. 1. Multiple IRR Problem
What is a conventional cash flow?
• A stream of cash flows where the direction (sign) of
cash flows changes only once
• Which project has a conventional cash flow?

64. 1. Multiple IRR Problem
Multiple IRR problem
• If a project has a conventional cash flow, it has only
one IRR
• If a project has a non-conventional cash flow, it has
multiple IRRs
We cannot use the IRR rule when cash flow is non-
conventional!
• NPV rule should be used

65. 2. Comparing projects with
different sizes

66. 2. Comparing projects with
different sizes
• NPV is likely to be greater for large projects

67. 2. Comparing projects with
different sizes
• NPV is likely to be greater for large projects
• IRR is likely to be greater for small projects

68. General principle revisited
NPV should be always preferred because
• NPV is the additional value you add to the company
• IRR is just the rate of return

69. Sometimes IRR could make more
sense
A startup company could prefer IRR as the main
decision rule
• Limited resources
• More opportunities to invest in value projects
• Greater uncertainty

70. Comparing NPV and IRR
Techniques II
Comparing NPV and IRR Techniques I
• 1. Multiple IRR problem
• 2. Comparing projects with different sizes
Comparing NPV and IRR Techniques II
• 3. Comparing projects with different lives
• 4. Reinvestment rate assumptions

71. 3. Comparing projects with
different lives
• Generally, NPV is greater for a longer-life project
• Is it fair to use the NPV rule?

72. 3. Comparing projects with
different lives
Yes, if:
• You believe that you have no other investment
opportunities on the horizon after these two projects
are undertaken
No, if:
• You believe that investment opportunities similar to
these projects can be found consistently
• You believe that the project can be rolled over for a
long time

73. Equivalent Annual Cost (EAC)
• The value of the annual payment in the annuity that
has the same present value as our original project
- Average “annualized” net cash flow
- To compute EAC, we need to know the project’s
1) NPV, 2) length, and 3) discount rate
- Use PMT function in Excel
- = PMT(Rate, Number of payments, Present value,
[Future value], [Type])

79. 4. Reinvestment rate assumptions
Both NPV and IRR assume that intermediate cash
flows of a project are reinvested
• NPV assumes that they are reinvested at the actual
discount rate
• IRR assumes that they are reinvested at the IRR

80. 4. Reinvestment rate assumptions
• How can we verify those assumptions?
• What are the implications of those assumptions?

88. 4. Reinvestment rate assumptions
• - NPV assumption: The company can find projects
whose rate of return equals the discount rate of the
company
• - IRR assumption: The company can find projects
whose rate return equals the IRR of this specific
project
• Which assumption is more realistic?
• - NPV…

89. Choosing the discount rate
• How do we determine the appropriate discount rate
of a project?
• - So far the discount rate was given in problems
• - Discount rate is determined by risk of the project
or the company
• - The meaning of the discount rate?
• - How to choose the discount rate?

90. Other names for discount rate
Discount rate = Required rate of return= Cost of capital
Required rate of return
• - Rate of return investors demand when investing in the
firm
Cost of capital
• - The return to investors is the company’s “cost of capital”

91. Cost of capital
The cost of capital is the hurdle rate for the company’s
investment
• - IRR decision rule: IRR > r
What are the components that constitute a company's
capital?
• - Debt and equity
• - Cost of debt and cost of equity
• - Estimation of cost of debt and cost of equity is out
of scope of this course

92. Cost of capital
• Cost of capital
• = Weighted average cost of debt and cost of equity
• - The weights of debt and equity are determined by
the company’s capital structure
• This is the “discount rate” we use in a project
analysis

93. Example
Consider the following information:
• - Total assets: $100M; Debt: $30M; Equity: $70M
• - Weight of debt: 30M / 100M = 0.3
• - Weight of equity: 70M / 100M = 0.7
• - We are told that the company’s after-tax cost of
debt is 3%, and the cost of equity is 8%. What is the
cost of capital of this company?
• - 0.3 x 3% + 0.7 x 8% = 6.5%

94. Company risk vs. Project risk
The cost of capital reflects the overall risk of the
company
• Technically, the discount rate used in a project
analysis should reflect the risk of the specific project
• In practice, the company’s cost of capital is widely
used as the discount rate for a project
• Assumption: the project has the same risk as the firm
• If the project risk is significantly different from the
overall company risk, use a different rate