managerial finance exam
nimab8
Ch9Investmentvaluationmethods-NPVPIpaybackIRR.pptxDr. Ekaterina Chernobai
p. 1
FRL 3000
Instructor: Dr. Ekaterina Chernobai
Chapter 9 “Investment Valuation”
1
Dr. Ekaterina Chernobai
p. 2
In Chapter 9
Chapter 9 looks at
investment valuation
= “Capital budgeting”
= making a long-term investment decision
Means: Is it worth it to put money (or “capital”) into this project?
What method(s) do business managers use to figure this out?
Is there a single right method to figure this out?
How should we compare several different investment projects?
Dr. Ekaterina Chernobai
p. 3
Different methods of evaluating an investment opportunity:
- Net Present Value (NPV) method
- Profitability Index (PI) method
- Payback Period method
- Internal Rate of Return (IRR) method
- Modified Internal Rate of Return (MIRR) method
- Discounted Payback Period method
- Average Accounting Return method
- …
- …
In Chapter 9
today!
skip!
skip!
skip!
Dr. Ekaterina Chernobai
p. 4
The Net Present Value Rule (1 of 10)
Profit = Revenues – Costs
Idea: Accept a project if it generates profit
In a typical project:
Year 0 No revenue yet & instead just a large up-front cost
Years 1, 2,… Revenues & miscellaneous costs
The Net Present Value (NPV) approach
$ $ $
Dr. Ekaterina Chernobai
p. 5
The Net Present Value Rule (2 of 10)
today 1 2 3 4 5 ….
Let’s say, we are interested in a 4-year project
$$ $$ $$ $$
Money received
(annual profits)
Money spent
(Investment cost)
Rule: If overall $$$ coming from a project > 0, accept it
-$$$$
Dr. Ekaterina Chernobai
p. 6
The Net Present Value Rule (3 of 10)
EXAMPLE
You are thinking about opening a coffee shop. It will cost you $650,000 today to buy coffee machines and all other equipment. You estimate that your coffee sales will generate $90,000, $120,000, $170,000, $170,000 in the next 4 years. You will then sell all used equipment for an estimated $250,000 and start a different project. The appropriate discount rate is 8%.
Is the project worth it?
today 1 2 3 4
90,000
-650,000
120,000
170,000
170,000
+250,000
=420,000
Dr. Ekaterina Chernobai
p. 7
The Net Present Value Rule (4 of 10)
In year 1 =
In year 2 =
In year 3 =
The project will generate (in today’s dollars):
How much money will the project generate in the future years?
In year 4 =
90,000
120,000
170,000
420,000
= 90,000 + 120,000 + 170,000 + 420,000
629,878 – 650,000
spent today
Overall profit (in today’s dollars):
The project is ___________ .
not worth it
CF0 = –650,000
C01 = 90,000
C02 = 120,000
C03 = 170,000
C04 = 420,000
I = 8
CPT NPV
=
= -20,122
1.08
1.082
= 629,878
1.083
1.084
Dr. Ekaterina Chernobai
p. 8
The Net Present Value Rule (5 of 10)
Overall profit is nothing but the project’s Net Present Value
Net Present Value (NPV)
= Present Value of all expected future cash flows less the initial investment
Textbook definition:
NPV = difference between investment’s market value & its cost
NPV = PV of all expected futures CF’s – initial investment
-20,122 = 629,828 – 650,000
Dr. Ekaterina Chernobai
p. 9
The Net Present Value Rule (6 of 10)
NPV rule for making investment decisions:
Accept an investment if NPV > 0
Reject an investment if NPV < 0
If NPV = 0, then we should be indifferent
Dr. Ekaterina Chernobai
p. 10
The Net Present Value Rule (7 of 10)
EXAMPLE
You are considering two mutually exclusive projects with the following cash flows:
Which project(s) should you accept if the discount rate is 8.5%?
| Year | Project A | Project B |
| 0 | -$80,000 | -$80,000 |
| 1 | 31,000 | 0 |
| 2 | 31,000 | 0 |
| 3 | 31,000 | 110,000 |
Dr. Ekaterina Chernobai
p. 11
The Net Present Value Rule (8 of 10)
we can only accept ONE project among two (or more) alternatives, because we have limited resources
- limited money to invest
- limited amount of equipment that can be used for production
- limited number of people
- etc.
not mutually exclusive
= we have the resources to accept any number of profitable projects
Before we look at the solutions …
vs
Mutually exclusive projects
=
Independent projects
=
If all projects have NPV>0, then accept only ONE with the highest NPV!
If all projects have NPV>0, then accept all!
Dr. Ekaterina Chernobai
p. 12
The Net Present Value Rule (9 of 10)
NPVA =
= -80,000 + 31,000 + 31,000 + 31,000
NPVB =
= -80,000 + 110,000
CF0 = -80,000
C01 = 31,000 F01 = 3
I = 8.5%
CPT NPV
CF0 = -80,000
C01 = 0 F01 = 2
C02 = 110,000 F02 = 1
I = 8.5%
CPT NPV
= -$825
1.085
1.0852
1.0853
= $6,120
1.0853
R=8.5%
| Year | Project A | Project B |
| 0 | -$80,000 | -$80,000 |
| 1 | 31,000 | 0 |
| 2 | 31,000 | 0 |
| 3 | 31,000 | 110,000 |
Choose project “B”
Dr. Ekaterina Chernobai
p. 13
The Net Present Value Rule (10 of 10)
Future cash flows are just estimates
Cash flows in more distant future are less certain
A change in riskiness of similar projects in the future may require us to revise the appropriate discount rate
(Will be covered in Ch.14)
Considers all future cash flows
Considers the time-value-of-money. I.e., future cash flows are discounted
Disadvantages:
Advantages:
Dr. Ekaterina Chernobai
p. 14
The Profitability Index Rule (1 of 8)
An alternative to the NPV rule:
The Profitability Index (P.I.) approach
= the benefit-cost ratio
= shows the value created per $1 invested
cost
benefit
Dr. Ekaterina Chernobai
p. 15
The Profitability Index Rule (2 of 8)
EXAMPLE
You are thinking about opening a coffee shop. It will cost you $650,000 today to buy coffee machines and all other equipment. You estimate that your coffee sales will generate $90,000, $120,000, $170,000, $170,000 in the next 4 years. You will then sell all used equipment for an estimated $250,000 and start a different project. The appropriate discount rate is 8%.
(same as the 1st example in the slides)
What is the Profitability Index (P.I.)? Worth it?
today 1 2 3 4
90,000
-650,000
120,000
170,000
170,000
+250,000
=420,000
Dr. Ekaterina Chernobai
p. 16
The Profitability Index Rule (3 of 8)
Profitability Index (P.I.) means:
“How many dollars do we get for each dollar invested?”
“Dollars we get” from the project =
“Dollars invested” into the project =
P.I. =
650,000
= 0.97, or 97 cents per $1 invested
CF0 = 0
C01 = 90,000
C02 = 120,000
C03 = 170,000
C04 = 420,000
I = 8 CPT NPV
629,878
650,000
= 90,000 + 120,000 + 170,000 + 420,000
1.08
1.082
= 629,878
1.083
1.084
Since we get ____ than $1 per dollar invested, ____ the project
less
reject
Same conclusion when we used the NPV approach!
Dr. Ekaterina Chernobai
p. 17
The Profitability Index Rule (4 of 8)
Profitability Index (PI)
Initial investment
PV of all expected future cash flows
Accept an investment if PI > 1
Reject an investment if PI < 1
NPV>0
NPV<0
Profitability Index rule for making investment decision:
Profitability Index calculation:
=
Dr. Ekaterina Chernobai
p. 18
The Profitability Index Rule (5 of 8)
EXAMPLE
You are choosing between two mutually exclusive investments:
“A”: costs $20, PV of all future CF’s is $40
“B”: costs $100, PV of all future CF’s is $150
Based on the P.I. Rule, which one should you choose?
Since the projects are mutually exclusive, need to choose ______________________________ .
PIA =
PIB =
Based on the “P.I. Rule” should choose ________ .
$40 / $20 = 2, or get $2 per $1 invested
$150 / $100 = 1.5, or get $1.5 per $1 invested
“A”
the ONE with the highest P.I.
Dr. Ekaterina Chernobai
p. 19
The Profitability Index Rule (6 of 8)
Do you think you would be making the right decision??
Why or why not??
Wrong decision, because NPV for “B” > NPV for “A” !
NPVA = PV of all future CFs – initial investment
= $40 – $20 = $20
NPVB = PV of all future CFs – initial investment
= $150 – $100 = $50
Dr. Ekaterina Chernobai
p. 20
The Profitability Index Rule (7 of 8)
Decisions based on “P.I.” and “NPV” rules may contradict each other when projects are of different scale!
i.e., different sizes of the initial investment
This example illustrates a problem with the “P.I. rule”:
Dr. Ekaterina Chernobai
p. 21
The Profitability Index Rule (8 of 8)
Disadvantages
Advantages
May lead to incorrect decisions when mutually exclusive projects are of different scale
Easy to interpret the result
Closely related to NPV: considers time-value-of-money, i.e., discounts all cash flows
Useful when available investment funds are limited
In general, when NPV Rule & PI Rule contradict each other, always go with the NPV Rule!
Dr. Ekaterina Chernobai
p. 22
The Payback Rule (1 of 12)
There’s another alternative to “NPV” and “Profitability Index” valuation methods
“The payback approach”
Idea:
Do we recover our investment within … years? If “yes”, the project is worth it.
Dr. Ekaterina Chernobai
p. 23
The Payback Rule (2 of 12)
today 1 2 3 4 5 6 ….
20 40 30 60 10
-100
Question: How soon do you recover your initial investment?
Payback period
is
3 years & 2 months
Initial investment
Recover $20
Recover $20+$40=$60
Recover $20+$40+$30 = $90
Recover the last $10
after $10 / $60=1/6th of the year (2 months)
Need to recover $10 more!
Dr. Ekaterina Chernobai
p. 24
The Payback Rule (3 of 12)
Now, let’s say you’re a manager and you are making the investment decision
You say:
…will be rejected
…will be accepted
…will be accepted
“We will accept a project if it pays back…
… within 3 years”
… within 4 years”
… within 5 years”
A project with a payback period of 3 years and 2 months…
Dr. Ekaterina Chernobai
p. 25
The Payback Rule (4 of 12)
The payback period rule for making investment decisions:
Accept an investment if its payback period is less than some prespecified number of years
Determined by project manager.
(Always given!)
Need to calculate based on given cash flows
Dr. Ekaterina Chernobai
p. 26
The Payback Rule (5 of 12)
EXAMPLE
Anna is considering adding toys to her gift shop. She estimates that the cost of inventory will be $7,500. The remodeling expenses and shelving costs are estimated at $1,800. Toy sales are expected to produce net cash inflows of $2,300, $2,900, $3,200, and $3,400 over the next 4 years, respectively.
Should Anna add toys to her store if she assigns a 3-year payback period to this project? Why or why not?
today 1 2 3 4
2,300
-7,500
-1,800
2,900
3,200
3,400
-9,300 total
Dr. Ekaterina Chernobai
p. 27
The Payback Rule (6 of 12)
today 1 2 3 4
2,300
-9,300
2,900
3,200
3,400
Payback period
is
3.26 years
Recover $2,300
Recover $2,300 + $2,900 = $5,200
Recover $2,300 + $2,900 + $3,200 = $8,400
Recover the last $900
after $900 / $3,400 = 0.26 of the year
Need to recover $9,300 – $8,400 = $900 more!
______ the project because the payback period is ____ than 3 yrs
Reject
more
Required payback period: 3 years
Dr. Ekaterina Chernobai
p. 28
The Payback Rule (7 of 12)
EXAMPLE
You are choosing between projects “A” and “B”:
Year 0 1 2 3 4 5 6 7
“A” -100 40 60 30 10 -- -- --
“B” -100 30 40 20 20 80 100 200
Payback period for “A” =
Payback period for “B” =
2 years
3.5 years
We should accept _____ and reject _____
“A”
“B”
You will accept a project if it pays back within 3 years
Based on the Payback Rule, which one should you accept?
Dr. Ekaterina Chernobai
p. 29
The Payback Rule (8 of 12)
Do you think you would be making the right decision??
Why or why not??
Wrong decision, because NPV for “B” is obviously much higher!
Higher cash flows after the prespecified cutoff are being ignored!
Dr. Ekaterina Chernobai
p. 30
The Payback Rule (9 of 12)
This example illustrates a problem with the “payback rule”:
Cash flows after the cutoff period are ignored
So, decisions based on “payback” and “NPV” rules may contradict each other!
=_______________
Dr. Ekaterina Chernobai
p. 31
The Payback Rule (10 of 12)
EXAMPLE
| Year | A | B | C | D | E |
| 0 | -100 | -200 | -200 | -200 | -50 |
| 1 | 30 | 40 | 40 | 100 | 100 |
| 2 | 40 | 20 | 20 | 100 | -50,000,000 |
| 3 | 50 | 10 | 10 | -200 | |
| 4 | 60 | 130 | 200 |
Payback periods:
=__________
=_________
=_______
=__________
2.6 years
never
4 years
2 or 4 years
6 months or never
Dr. Ekaterina Chernobai
p. 32
The Payback Rule (11 of 12)
This example illustrates additional problems with the “payback rule”:
There may be multiple payback periods!
There may be no payback period!
Dr. Ekaterina Chernobai
p. 33
The Payback Rule (12 of 12)
Disadvantages
Advantages
Ignores CF’s after the prespecified payback period We may be rejecting a project which should be accepted The rule will tend to bias us toward shorter-term projects
May be several payback periods Which one do we use??
The prespecified payback time is arbitrary
Ignores time-value-of-money We may be accepting a project which should be rejected when the discount rate is taken into account
Easy to use
Good enough for small-scale projects, for which the cost of a detailed analysis exceeds the possible loss from making a wrong decision
Because future CF’s are ignored, it adjusts for the uncertainty of future CF’s
Biased toward short-term projects biased toward projects that free up cash quickly biased toward liquidity
Dr. Ekaterina Chernobai
p. 34
The IRR Rule (1 of 26)
The most important alternative to NPV
Often used in practice & is intuitively appealing
Internal Rate of Return (IRR) approach
Dr. Ekaterina Chernobai
p. 35
EXAMPLE
The IRR Rule (2 of 26)
You are considering an investment with the following cash flows:
| Year | 0 | 1 | 2 | 3 | 4 |
| Cash flow | $-10 (initial investment) | $6 | $5 | $8 | $8 |
Calculate NPV for several different discount rates. Let’s try 30%, 50%, 70%
At which rate do we “break even”?
Dr. Ekaterina Chernobai
p. 36
The IRR Rule (3 of 26)
NPV @ R=30% is _________
NPV @ R=50% is _________
NPV @ R=70% is _________
$ 4.02
$ 0.17
$-2.15
Calculate NPV separately at a few different discount rates R of 30%,
50%,
70%
NPV = -10 + + + +
5
(1+R)2
8
(1+R)3
8
(1+R)4
6
1+R
CF0 = –10
C01 = 6
C02 = 5
C03 = 8
C04 = 8
I = R
CPT NPV
Dr. Ekaterina Chernobai
p. 37
The IRR Rule (4 of 26)
At this rate we “break even”!
discount rate R, %
NPV, $
30%
50%
70%
$4.02
$0.17
-$2.15
51.2%
NPV profile
51.2% is the Internal Rate of Return (IRR)
= a graphical representation of the relationship between NPV & various discount rates
NPV = $0
NPV = -10 + + + +
= 0
5
1.5122
8
1.5123
8
1.5124
6
1.512
NPV > $0
NPV < $0
Dr. Ekaterina Chernobai
p. 38
The IRR Rule (5 of 26)
Internal Rate of Return (IRR) definition
IRR is the discount rate at which NPV = 0
IRR is based entirely on the estimated cash flows & is independent of interest rates found elsewhere
Hence, “internal”
Dr. Ekaterina Chernobai
p. 39
The IRR Rule (6 of 26)
Calculate IRR:
Trial and error
Financial calculator
In this example IRR = 51.2%
CF0 = –10
C01 = 6
C02 = 5
C03 = 8
C04 = 8
IRR
CPT
Dr. Ekaterina Chernobai
p. 40
The IRR Rule (7 of 26)
discount rate R, %
NPV, $
30
50
70
4.02
0.17
-2.15
51.2%
IRR
NPV profile
NPV > 0
Accept the project
NPV < 0
Reject the project
If required R < IRR, then
If required R > IRR, then
Dr. Ekaterina Chernobai
p. 41
The IRR Rule (8 of 26)
Internal Rate of Return (IRR) rule:
Accept a project if the required return < IRR
Reject a project if the required return > IRR
NPV>0
NPV<0
Need to find
Always given
Dr. Ekaterina Chernobai
p. 42
The IRR Rule (9 of 26)
EXAMPLE
WalMarket is considering a project with an initial cost of $118,400. The project’s cash inflows for years 1~3 are $37,200, $54,600, and $46,900, respectively
Should it accept or reject this project if it requires a 10% return? Use the IRR approach
Solution:
IRR = 8.04%
CF0 = –118 400
C01 = 37 200
C02 = 54 600
C03 = 46 900
IRR
CPT
Since the required return of 10% is _________ than the IRR, ___________.
greater
reject
discount rate R, %
NPV, $
NPV profile
NPV<$0
Reject!
8.04%
10%
Dr. Ekaterina Chernobai
p. 43
The IRR Rule (10 of 26)
EXAMPLE
Issue #1:
Non-conventional cash flows: cash inflow followed by cash outflows
Consider the following project cash flows:
| Year | 0 | 1 | 2 | 3 | 4 |
| Cash flow | $ 10 | $ –6 | $ –5 | $ –8 | $ –8 |
In which case should be accept / reject this project?
a.k.a. “financing” type project.
So far our projects have been “investing” type
Dr. Ekaterina Chernobai
p. 44
The IRR Rule (11 of 26)
discount rate, %
NPV, $
30
50
70
- 4.02
- 0.17
2.15
51.2%
NPV = 0
NPV profile
Again, try a few discount rates. E.g., 30%, 50%, 70%
This is the IRR
reject
accept
Dr. Ekaterina Chernobai
p. 45
The IRR Rule (12 of 26)
“Investing” type projects
“Financing” type projects
Conventional cash flows: cash outflow, then cash inflows
Accept project
Accept project
Non-conventional cash flows: cash inflow, then cash outflows
Dr. Ekaterina Chernobai
p. 46
The IRR Rule (13 of 26)
the traditional IRR Rule doesn’t work!
The new rule should say:
Accept the project if ____________________________
Reject the project if _____________________________
In this example,
IRR < required return
IRR > required return
Dr. Ekaterina Chernobai
p. 47
The IRR Rule (14 of 26)
EXAMPLE
Issue #2:
| Year | 0 | 1 | 2 |
| Cash flow | $ –60 | $ 155 | $ –100 |
| Year | 0 | 1 | 2 |
| Cash flow | $ 60 | $–155 | $ 100 |
discount rate, %
NPV, $
10
30
50
- 1.74
- 1.11
0.06
IRR#1
25%
NPV profile
IRR#2
33.33%
reject
reject
accept
Non-conventional cash flows:
cash flows change signs more than once
discount rate, %
NPV, $
10
30
50
1.74
1.11
- 0.06
IRR#1
25%
NPV profile
IRR#2
33.33%
reject
accept
accept
Dr. Ekaterina Chernobai
p. 48
The IRR Rule (15 of 26)
In fact,
# of IRRs equals # of times cash flows change signs
Dr. Ekaterina Chernobai
p. 49
The IRR Rule (16 of 26)
EXAMPLE
Issue #3: Mutually exclusive projects
A real estate company has $100 million that it would like to invest into a new real estate market. It is choosing between two mutually exclusive projects:
| Year | 0 | 1 | 2 | 3 | 4 |
| Market A | $-100 Initial cost | $50 | $40 | $40 | $30 |
| Market B | $-100 Initial cost | $20 | $40 | $50 | $60 |
Which market should it invest into?
What should be the IRR decision rule?
Dr. Ekaterina Chernobai
p. 50
The IRR Rule (17 of 26)
discount rate, %
NPV, $
5
50
43
48
-31
NPV profile for A
-42
IRRA= 24%
NPV profile for B
IRRB= 21%
NPV@5%
NPV@50%
=___
=___
=___
=___
43
-31
48
-42
A B
Try a couple different discount rates & calculate the NPVs:
Traditional IRR rule says:
Accept “A” if required return < 24%
Accept “B” if required return < 21%
Can we use this rule?? No!!
Reject A
Reject B
Accept A
Reject B
Reject A
Accept B
50
Dr. Ekaterina Chernobai
p. 51
The IRR Rule (18 of 26)
With mutually exclusive projects, we can never accept both projects. If both are worth it, we need to pick only one!
What should be the correct IRR decision rule?
Accept only “A” if ____________________________________
Accept only “B” if ____________________________________
Reject both “A” and “B” if _____________________________
Accept both “A” and “B” if _____________________________
____________________________________________
crossover rate < required return < IRRA
required return < crossover rate
required return > IRRA
NEVER! Because “A” & “B” are
mutually exclusive!
Dr. Ekaterina Chernobai
p. 52
The IRR Rule (19 of 26)
Calculate the “crossover rate”:
Step 1
Step 2 Find IRR based on CF differences
IRR = __________
| Year | 0 | 1 | 2 | 3 | 4 |
| Market A | -100 | 50 | 40 | 40 | 30 |
| Market B | -100 | 20 | 40 | 50 | 60 |
| A – B | =____ | =____ | =____ | =____ | =____ |
0
30
0
-10
-30
11.07%
(Can also do “B – A” instead!)
CF0 = 0
C01 = 30
C02 = 0
C03 = -10
C04 = -30
IRR CPT
Dr. Ekaterina Chernobai
p. 53
The IRR Rule (20 of 26)
At the crossover rate, we are indifferent between the two projects
discount rate, %
NPV, $
11.07
NPV profile for A
NPV profile for B
Crossover rate = 11.07%
NPV”A” = NPV”B”
Dr. Ekaterina Chernobai
p. 54
The IRR Rule (21 of 26)
EXAMPLE
You are analyzing the following two mutually exclusive projects and have developed the following information:
Calculate the crossover rate
| Year | Project A | Project B |
| 0 | -$75,000 | -$75,000 |
| 1 | 26,300 | 24,000 |
| 2 | 29,500 | 26,900 |
| 3 | 45,300 | 51,300 |
Dr. Ekaterina Chernobai
p. 55
The IRR Rule (22 of 26)
Solution:
Step 1 Find the difference between cash flows:
Step 2 Find IRR for “A – B” cash flows
IRR = _______
14.6%
A – B
= _______
= _______
= _______
= _______
0
2,300
2,600
-6,000
CF0 = 0
C01 = 2300
C02 = 2600
C03 = -6000
IRR CPT
| Year | Project A | Project B |
| 0 | -$75,000 | -$75,000 |
| 1 | 26,300 | 24,000 |
| 2 | 29,500 | 26,900 |
| 3 | 45,300 | 51,300 |
Dr. Ekaterina Chernobai
p. 56
The IRR Rule (23 of 26)
EXAMPLE
| Year | Project “A” | Project “B” |
| 0 | -400 | -500 |
| 1 | 325 | 325 |
| 2 | 200 | 325 |
| IRR | 22.17% | 19.43% |
| NPV @ 10% | 60.74 | 64.05 |
“A” and “B” are mutually exclusive. Which project should you accept? Why?
Based on IRR rule:
IRRA > IRRB. And so choose __ because ________________________________
________________________________.
it has a wider range of acceptable required returns
Based on NPV rule:
NPVA < NPVB. And so choose __ because ________________________________.
“B”
it generates a higher profit amount
“A”
Means: can only accept ONE!
Dr. Ekaterina Chernobai
p. 57
The IRR Rule (24 of 26)
NPV directly measures the increase in $$$ value to the firm
Whenever there is a conflict between NPV and IRR rule, you should always use NPV
Conflict between the NPV and IRR valuation methods!
So, choose “B”!
Dr. Ekaterina Chernobai
p. 58
The IRR Rule (25 of 26)
EXAMPLE
| Year | Project “A” | Project “B” |
| 0 | -400 | -500 |
| 1 | 325 | 325 |
| 2 | 200 | 325 |
| IRR | 22.17% | 19.43% |
| NPV @ 10% | 60.74 | 64.05 |
“A” & “B” are independent. Which project should you accept? Why?
Based on IRR rule:
Both IRRA and IRRB are > required return of 10%. And so choose ___________.
both
Based on NPV rule:
Both NPVs are > $0. And so choose ____.
both
No disagreement between “NPV” & “IRR” rules. Accept both
Means: okay to accept BOTH!
Dr. Ekaterina Chernobai
p. 59
The IRR Rule (26 of 26)
Closely related to NPV: considers time-value-of-money, i.e., discounts all cash flows
Easy to understand & communicate
If the IRR is high enough, you may not need to estimate a required return (from various similar investments), which is often a difficult task
Advantages
Disadvantages
The traditional IRR rule stops working…
…when we have non-conventional cash flows
(1) A “financing” type project, rather than an “investing” type project
OR
(2) Cash flows change signs more than once
…when we deal with mutually exclusive projects may lead to incorrect decisions
Dr. Ekaterina Chernobai
p. 60
Summarize (1 of 6)
Review capital budgeting decision criteria
| Technique | Units | Accept if: |
| Net Present Value (NPV) | $ | NPV > $0 |
| Profitability Index (PI) | None | PI > 1.0 |
| Payback Period | Time | Payback period < Manager’s # |
| Internal Rate of Return | % | IRR > required return R |
Dr. Ekaterina Chernobai
p. 61
Summarize (2 of 6)
Want to know how to do these in Excel??
| Technique | Function in Excel | |
| Net Present Value (NPV) | ||
| Profitability Index (PI) | ||
| Payback Period | ||
| Internal Rate of Return |
Come up to me after class, and I’ll explain in a minute how these work!
=npv(……)
=irr(……)
Dr. Ekaterina Chernobai
p. 62
Summarize (3 of 6)
In general,
- Different valuation methods may be in conflict
- With an exception of NPV, other valuation methods have many issues
When in doubt, always go with the NPV approach!
Dr. Ekaterina Chernobai
p. 63
Summarize (4 of 6)
Table 9.6
Which valuation method is used in real world?
Large firms………Almost always use “IRR” & “NPV” techniques
Small firms………Almost always use “payback period” technique
Dr. Ekaterina Chernobai
p. 64
Summarize (5 of 6)
John has analyzed two mutually exclusive projects of similar size and has compiled the following information based on his analysis. Both projects have 3-year lives.
John has been asked for his best recommendation given this information.
His recommendation should be to accept ______
because ________________________________.
EXAMPLE
it has a higher NPV
“B”
| Project A | Project B | |
| Net Present Value | $81,406 | $82,909 |
| Payback period | 2.48 years | 2.31 years |
| Required return | 11.5% | 12.0% |
independent
both
both NPVs > $0
(a) The discount rate used in computing the NPV was less than 11.63 %.
(b) The discounted future cash flows cover the initial investment after exactly 2.98 years.
(c) The discount rate used in the computation of the PI index was 11.63 %.
(d) This project should be accepted as the IRR exceeds the required return.
Dr. Ekaterina Chernobai
p. 65
Summarize (6 of 6)
EXAMPLE
You are considering a project with conventional cash flows and the following characteristics:
| Net Present Value (NPV) | $ 987 |
| Profitability Index (PI) | 1.04 |
| Payback period | 2.98 years |
| Internal rate of return (IRR) | 11.63% |
Which of the following is (are) correct?
Conventional CFs & positive NPV. This can only happen if discount rate <IRR
The word “discounted” is wrong!
11.63% is IRR. At this rate we should have NPV=$0 and PI=1. But our PI=1.04
We have conventional CFs. So traditional IRR rule holds
