Net Present Value, IRR and Profitability Index

1. (NPV - IRR – IP)

2. Sequence
• Introduction
• Basic terms review
• Capital budgeting introduction
• Capital budgeting technique
• Sensitivity analysis
• Scenario analysis

3. •Lets Begin

4. A review of Basics:
Present Value, Net Present value and future value
• Present value (PV) is the current worth of a future sum of money or
stream of cash flows given a specified rate of return. In other words,
present value, also known as present discounted value, is
the value of an expected income stream determined as of the date of
valuation
• Difference between a project’s value and its cost is its NPV
• Future value is the value of an asset at a specific date. It measures
the nominal future sum of money that a given sum of money is
"worth" at a specified time in the future assuming a certain interest
rate, or more generally, rate of return; it is the
present value multiplied by the accumulation function.

5. Few formulas
Discount factor; 1/(1+r)
t
PV= C1/1+r + C2/(1+r)2 . . . + Ct/(1+r)t
Present value = DF2* C2
NPV = Investment + PV

6. A review of Basic: Example
• a CEO of corporation is looking to invest $ 1 million in project X
• He asks from you (FINANCIAL MANAGER) whether to invest or not,
and if yes then what should be the grounds
Your answer may be:
first: forecast the cash flows may be generated by the project
Second: determine the appropriate opportunity cost of Capital.
That should reflect both; time value of money and Risk factor
Third: use the opportunity cost of capital to discount the
project's future cash flows
Fourth: calculate NPV by subtracting the 1 million investment
from present value: (Both formulas are given below)
PV= C1/1+r + C2/(1+r)2 . . . + Cn/(1+r)t NPV= C0 +C1/1+r + C2/(1+r)2 . . . + Cn/(1+r)t
Note: Invest in Project if its NPV is greater or equal to zero

7. Net Present Value
• Example: building costs 700,000 it can be sold for $ 800,000. if the discount
rate is 10%, calculate:
§ Present Value
§ Net Present Value
PV= C1/1+r + C2/(1+r)2 . . . + Cn/(1+r)n
=800,000/(1+.10)
PV= RS. 727273
NPV= C0 +C1/1+r + C2/(1+r)2 . . . + Cn/(1+r)n
= 700,000 -727273
NPV= $ +27273

8. NPV Strengths
and Weaknesses
Strengths:
• Cash flows
assumed to be
reinvested at the
hurdle rate.
• Accounts for TVM.
• Considers all
cash flows.
Weaknesses:
• May not include
managerial
options embedded
in the project. See
Chapter 14.

9. Net Present Value Profile
Discount Rate (%)
0 3 6 9 12 15
IRR
NPV@13%
Sum of CF’s Plot NPV for each
discount rate.
Net Present Value
$000s
15
10
5
0
-4

10. A review of Basic: Example … continue
• CEO asks, why Greater NPV is so important?
You answer:
NPV is important as if the firm does not earn equal or more than what the
shareholders expect than they might sell their share in the market.
“ Investors would forecast the dividends that Project X pay and discount
those dividends by the expected rate of return of securities having similar
risk.”
ØOnly thing to answer is where the discount rate comes from?
It is the opportunity cost of investing in the project rather than in
the capital market.
if the firm does not earn from the project what its shareholders
expect (cost of capital) than it should return the cash to the
shareholders and let them to invest in Financial Markets by
purchasing financial Asset

11. Investment
Project X
If 10% or return
Cash
Financial
Manager
Share holders
(If project return less than
10%)
Investment
(Financial Asset)
First option:
Invest
Second option:
Pay dividend to
Share holders
Shareholders
Invest
themselves
Figure 1;Deision through NPV if discount rate is 10%

12. Important Points to be remembered about Net Present Value
• First: NPV rule recognizes that a $ today is worth more than a $
tomorrow (time value of money).
• Second: NPV depends on the forecasted cash flows from the project
and the opportunity cost of capital
• Third: PV measures in todays money, therefore we add them up.
• NPV depends on Cash flows, not on book returns. Book returns are
the accounting record rather than cash as:
Book rate of Returns= book income/book assets

13. Capital Budgeting
The Capital Budgeting Process of
generating Investment Project Proposals and
estimating Project “After-Tax Incremental Operating Cash
Flows”

14. The Capital Budgeting
Process
• Generate investment proposals consistent
with the firm’s strategic objectives.
• Estimate after-tax incremental operating
cash flows for the investment projects.
• Evaluate project incremental cash flows.

15. The Capital Budgeting
Process
• Select projects based on a value-maximizing
acceptance criterion.
• Reevaluate implemented investment projects
continually and perform post audits for completed
projects.

16. Classification of Investment
Project Proposals
1. New products or expansion of existing
products
2. Replacement of existing equipment or
buildings
3. Research and development
4. Exploration
5. Other (e.g., safety or pollution related)

17. Payback method
• Payback period in capital budgeting refers to the period of time
required to recoup the funds expended in an investment, or to reach
the break-even point.
For example, a $1000 investment which returned $500 per year would
have a two-year payback period. The time value of money is not taken
into account.

18. Payback method
Cash flows
NPV at 10%Payback period
(years)
3C2C1C0CProject
2,62435,000500500-2000A
-58201,800500-2000B
50205001,800-2000C
Payback is calculated by taking the accumulated of all CFs
NPV is calculated with the help of the following formula
nr)+1/(nC. . . + 2r)+1/(2Cr + +1/1C+0C= NPV

19. Discounted payback
Some companies discount the cash flows before they compute payback
period
Discounted Cash flows Rs
NPV at 10%Payback period
(years)
C3C2C1C0Project
2,62435,000/1.13500/1.12
=413
500/1.12
=455
-2000A
-58-01,800/1.12
=1,488
500/1.1
=455
-2000B
5020500/1.12
=413
1,800/1.1
= 1,636
-2000C

20. Why payback can give misleading answers
• Payback rule ignores all cash flows after the cutoff date.
• Its rule gives equal weight to all cash flows before the cutoff date
• Companies still frequently use it because it is the simplest way to
communicate the idea.
• Everyone can understand it
• Manager like it as it tell short span period; good for their promotion

21. PBP Strengths
and Weaknesses
Strengths:
• Easy to use and
understand
• Can be used as a
measure of
liquidity
• Easier to forecast ST
than LT flows
Weaknesses:
• Does not account
for TVM
• Does not consider
cash flows beyond
the PBP
•

22. Internal Rate of Return (IRR)
IRR is the discount rate that equates the present
value of the future net cash flows from an
investment project with the project’s initial
cash outflow.
tCF2CF1CF
t)IRR+1(2)IRR+1(1)IRR+1(
+ . . . ++ICO =

23. Example Project Data
A financial manager is evaluating a new
project for her firm. She has determined
that the after-tax cash flows for the project
will be $10,000; $12,000; $15,000;
$10,000; and $7,000, respectively, for each
of the Years 1 through 5. The initial cash
outlay will be $40,000.

24. Independent Project
• Independent -- A project whose acceptance (or
rejection) does not prevent the acceptance of other
projects under consideration.
◆ For this project, assume that it is
independent of any other potential
projects.

25. $15,000 $10,000 $7,000
IRR Solution
$10,000 $12,000
2)IRR+1(1)IRR+1(
Find the interest rate (IRR) that causes the
discounted cash flows to equal $40,000.
+ +
++$40,000 =
5)IRR+1(4)IRR+1(3)IRR+1(

26. IRR Solution (Try 10%)
$40,000 = $10,000(PVIF10%,1) + $12,000(PVIF10%,2) +
$15,000(PVIF10%,3) + $10,000(PVIF10%,4) + $
7,000(PVIF10%,5)
$40,000 = $10,000(.909) + $12,000(.826) +
$15,000(.751) + $10,000(.683) +
$ 7,000(.621)
$40,000 = $9,090 + $9,912 + $11,265 +
$6,830 + $4,347
= $41,444 [Rate is too low!!]

27. IRR Solution (Try 15%)
$40,000 = $10,000(PVIF15%,1) + $12,000(PVIF15%,2) +
$15,000(PVIF15%,3) + $10,000(PVIF15%,4) + $
7,000(PVIF15%,5)
$40,000 = $10,000(.870) + $12,000(.756) +
$15,000(.658) + $10,000(.572) +
$ 7,000(.497)
$40,000 = $8,700 + $9,072 + $9,870 +
$5,720 + $3,479
= $36,841 [Rate is too high!!]

28. .10 $41,444
.05 IRR $40,000 $4,603
.15 $36,841
($1,444)(0.05)
$4,603
IRR Solution (Interpolate)
$1,444X
X =
X = .0157
IRR = .10 + .0157 = .1157 or 11.57%

29. IRR Acceptance Criterion
No! The firm will receive 11.57% for each
dollar invested in this project at a cost of
13%. [ IRR < Hurdle Rate ]
The management of a company has
determined that the hurdle rate is 13% for
projects of this type.
Should this project be accepted?

30. IRRs on the Calculator
We will use the cash
flow registry to solve
the IRR for this
problem quickly and
accurately!

31. Actual IRR Solution Using Your
Financial Calculator
Steps in the Process
Step 1: Press CF key
Step 2: Press 2nd CLR Work keys
Step 3: For CF0 Press -40000 Enter ¯ keys
Step 4: For C01 Press 10000 Enter ¯ keys
Step 5: For F01 Press 1 Enter ¯ keys
Step 6: For C02 Press 12000 Enter ¯ keys
Step 7: For F02 Press 1 Enter ¯ keys
Step 8: For C03 Press 15000 Enter ¯ keys
Step 9: For F03 Press 1 Enter ¯ keys

32. Actual IRR Solution Using Your
Financial Calculator
Steps in the Process (Part II)
Step 10:For C04 Press 10000 Enter ¯ keys
Step 11:For F04 Press 1 Enter ¯ keys
Step 12:For C05 Press 7000 Enter ¯ keys
Step 13:For F05 Press 1 Enter ¯ keys
Step 14: Press ¯ ¯ keys
Step 15: Press IRR key
Step 16: Press CPT key
Result: Internal Rate of Return = 11.47%

33. IRR Strengths
and Weaknesses
Strengths:
• Accounts for
TVM
• Considers all
cash flows
• Less
subjectivity
Weaknesses:
• Assumes all cash
flows reinvested at
the IRR
• Difficulties with
project rankings and
Multiple IRRs

34. NPV on the Calculator
We will use the cash flow
registry to solve the NPV
for this problem quickly
and accurately!
Hint: If you have not cleared
the cash flows from your
calculator, then you may skip
to Step 15.

35. Actual NPV Solution Using Your
Financial Calculator
Steps in the Process
Step 1:PressCFkey
:2Step Pressnd2CLR Workkeys
40000-Press 0CFFor : 3Step keys¯Enter
Press01CFor : 4Step 10000keys¯Enter
Press01FFor : 5Step 1keys¯Enter
Press02CFor : 6Step 12000keys¯Enter
Press02FFor : 7Step 1keys¯Enter
Press03CFor : 8Step 15000keys¯Enter
Press03FFor : 9Step 1keys¯Enter

36. Part II)Steps in the Process (
Press04CFor :10Step 10000keys¯Enter
Press04FFor :11Step 1keys¯Enter
Press05CFor :12Step 7000keys¯Enter
Press05FFor :13Step 1keys¯Enter
Step 14: Press¯¯keys
Step 15: PressNPVkey
Enter, For I=: 16Step 13Enter¯keys
Step 17: PressCPTkey
Result:1,424.42$-= Net Present Value
Actual NPV Solution Using Your
Financial Calculator

37. Creating NPV Profiles Using the
Calculator
Hint: As long as you do
not “clear” the cash
flows from the registry,
simply start at Step 15
and enter a different
discount rate. Each
resulting NPV will
provide a “point” for
your NPV Profile!

38. Profitability Index (PI)
PI is the ratio of the present value of a
project’s future net cash flows to the
project’s initial cash outflow.
CF1 CF2 CFn
(1+k)1 (1+k)2 (1+k)n
+ . . . ++ ICOPI =
PI = 1 + [ NPV / ICO ]
<< OR >>

39. PI Acceptance Criterion
This. 1.00less than is PIThe No! means
that the project is not profitable. [Reject as PI <
1.00 ]
PI= $38,572 / $40,000
= .9643 (Method #1, 13-33)
Should this project be accepted?

40. PI Strengths and Weaknesses
:Strengths
•Same as NPV
•Allows
comparison of
different scale
projects
:Weaknesses
•Same as NPV
•Provides only
relative profitability
•Potential Ranking
Problems

41. Other Project Relationships
• Mutually Exclusive -- A project whose
acceptance precludes the acceptance
of one or more alternative projects.
◆ Dependent -- A project whose
acceptance depends on the
acceptance of one or more other
projects.

42. Potential Problems
Under Mutual Exclusivity
A. Scale of Investment
B. Cash-flow Pattern
C. Project Life
Ranking of project proposals may create contradictory
results.

43. A. Scale Differences
Compare a small (S) and a large (L) project.
NET CASH FLOWS
Project S Project LEND OF YEAR
0 -$100 -$100,000
1 0 0
2 $400 $156,250

44. Scale Differences
Calculate the PBP, IRR, NPV@10%, and PI@10%.
Which project is preferred? Why?
PINPVIRRProject
S 100% $ 231 3.31
L 25% $29,132 1.29

45. B. Cash Flow Pattern
Let us compare a decreasing cash-flow (D) project and
an increasing cash-flow (I) project.
NET CASH FLOWS
Project D Project IEND OF YEAR
0 -$1,200 -$1,200
1 1,000 100
2 500 600
3 100 1,080

46. D 23% $198 1.17
I 17% $198 1.17
Cash Flow Pattern
Calculate the IRR, NPV@10%, and PI@10%.
Which project is preferred?
Project IRR NPV PI

47. C. Project Life Differences
Let us compare a long life (X) project
and a short life (Y) project.
NET CASH FLOWS
Project X Project YEND OF YEAR
0 -$1,000 -$1,000
1 0 2,000
2 0 0
3 3,375 0

48. X 50% $1,536 2.54
Y 100% $ 818 1.82
Project Life Differences
Calculate the PBP, IRR, NPV@10%, and PI@10%.
Which project is preferred? Why?
Project IRR NPV PI

49. Another Way to Look at
Things
1. Adjust cash flows to a common terminal
year if project “Y” will NOT be replaced.
Compound Project Y, Year 1 @10% for 2 years.
Year 0 1 2 3
CF -$1,000 $0 $0 $2,420
Results: IRR* = 34.26% NPV = $818
*Lower IRR from adjusted cash-flow stream. X is still Best.

50. Replacing Projects with Identical Projects
2. Use Replacement Chain Approach (Appendix B) when
project “Y” will be replaced.
0 1 2 3
-$1,000 $2,000
-1,000 $2,000
-1,000 $2,000
-$1,000 $1,000 $1,000 $2,000
Results:IRR* = 100% NPV* = $2,238.17
*Higher NPV, but the same IRR. Y is Best.

51. Capital Rationing
Capital Rationing occurs when a constraint (or
budget ceiling) is placed on the total size of
capital expenditures during a particular
period.
Example: Julie Miller must determine what
investment opportunities to undertake for Basket
Wonders (BW). She is limited to a maximum
expenditure of $32,500 only for this capital
budgeting period.

52. Available Projects for BW
Project ICO IRR NPV PI
A $ 500 18% $ 50 1.10 B
5,000 25 6,500 2.30 C
5,000 37 5,500 2.10 D
7,500 20 5,000 1.67 E
12,500 26 500 1.04 F
15,000 28 21,000 2.40 G
17,500 19 7,500 1.43 H
25,000 15 6,000 1.24

53. Choosing by IRRs for BW
Project ICO IRR NPV PI
C $ 5,00037% $ 5,500 2.10 F
15,000 28 21,000 2.40 E
12,500 26 500 1.04 B
5,000 25 6,500 2.30
Projects C, F, and E have the three
largest IRRs.
The resulting increase in shareholder wealth is
$27,000 with a $32,500 outlay.

54. Choosing by NPVs for BW
Project ICO IRR NPV PI
F $15,000 28% $21,000 2.40 G
17,500 19 7,500 1.43 B
5,000 25 6,500 2.30
Projects F and G have the two
largest NPVs.
The resulting increase in shareholder wealth is
$28,500 with a $32,500 outlay.

55. Choosing by PIs for BW
Project ICO IRR NPV PI
F $15,000 28% $21,000 2.40
B 5,000 25 6,500 2.30
C 5,000 37 5,500 2.10
D 7,500 20 5,000 1.67
G 17,500 19 7,500 1.43
Projects F, B, C, and D have the four largest PIs.
The resulting increase in shareholder wealth is $38,000
with a $32,500 outlay.

56. Summary of Comparison
Method Projects Accepted Value Added
PI F, B, C, and D $38,000
NPV F and G $28,500
IRR C, F, and E $27,000
PI generates the greatest increase in shareholder
wealth when a limited capital budget exists for a
single period.

57. Post-Completion Audit
Post-completion Audit
A formal comparison of the actual costs and benefits
of a project with original estimates.
• Identify any project weaknesses
• Develop a possible set of corrective actions
• Provide appropriate feedback
Result: Making better future decisions!

58. Multiple IRR Problem*
Two!! There are as many potential IRRs as
there are sign changes.
Let us assume the following cash flow pattern
for a project for Years 0 to 4:
-$100 +$100 +$900 -$1,000
How many potential IRRs could this project
have?
* Refer to Appendix A

59. Project analysis
• Investment process starts with the preparation of an annual capital
budget.
• Project authorization and problem of biased forecasts
• Post audits
• Identification of problems
• Accuracy of forecast
Any suggestion

60. Sensitivity analysis
• Uncertainty means more things can happen than will happen.
• Example
A company is introducing new scooters for city use with Rs. 15 b Net
investment for 10 years, producing NCF of Rs. 3 B in ten years. Staff have
prepared the forecasts at 10% NPV.
= (-15)+3/(1.1)10 = Rs. +3.43 billions
Production department estimated cost per unit is Rs. 300,000 and 100,00
scooter can be made in the year. If calculated the revenue as the firm has 1%
market share, it will be:
Unit sales= new product share in market*size of scooter market
37.5 billions(Revenue) = 100,000*375,000
Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or
system (numerical or otherwise) can be apportioned to different sources of uncertainty in its inputs.

61. Sensitivity analysis
Preliminary cash-flow forecast for company
Year 1- 10 (one to ten years)Year 0 (zero)Description
NIL15 billionInvestment
37.5NILRevenue
30NILVariable cost
3NILFixed cost
1.5NILDepreciation
3NILPretax profit
1.5NILTax
1.5NILNet profit
3NILOperating cash flow
3NILNet cash flow
1. Investment is depreciated over 10 years straight line
2. Income is taxed at a rate of 50%

62. Sensitivity analysis…
• Value Information
• Suppose that production department is worried about the machine which will
not work properly and the firm has to purchase another method which incure
per unit cost an extra Rs. 20,000:
units sales*additional unit cost*(1-tax rate)
Rs.1 Billion = 100,000*20,000*.50
It will reduce the NPV by:
1/(1.10)10
• Limits of sensitivity analysis
• Giving ambiguous results

63. Scenario analysis
• Scenario analysis is a process of analyzing possible future events by
considering alternative possible outcomes (sometimes called
"alternative worlds").
• Thus, the scenario analysis, which is a main method of projections,
does not try to show one exact picture of the future.