write one essay on finance topic about 600 words
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08NPVandAlternatives.pptxTopic 8 Capital Budgeting: NPV & Alternatives
Fundamentals of Finance
Fall 2017
Zhun Liu
1
Outline
Capital budgeting and firm value
Net Present Value (NPV)
The basic idea
NPV and firm value
Calculating NPV
Examples
Other important capital budgeting techniques
Payback and Discounted Payback
Internal Rate of Return (IRR)
Evaluation and practical advice
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The Importance of Capital Budgeting
Corporations create value by making “good” real investment decisions
Real Investments == projects (usually spend now, cash later)
So the first thing you might ask is, “Hey, what’s a project?”
Pretty much everything…
Should we launch a new product?
Should we enter a new market?
Should we buy out another firm?
Should we use a new technology?
Capital budgeting is the most important issue in corporate finance
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Capital Budgeting: the process of creating a list of investments in the next period.
Net Present Value
A project is just a collection of cash flows
Projects are worth undertaking if
Benefits > Costs
We want to make more money (profits) than we spend (invest).
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2
3
4
time
0
C1
C2
C3
C4
. . .
C0
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Net Present Value
Net Present Value is the PV considering all cash flows, both positive (profits) and negative (investments)
NPV = PV of all benefits – PV of all costs
Decision Criteria: Investment projects should be accepted if the NPV of project is positive and should be rejected if the NPV is negative.
Following this rule increases firm value
Why? Because the firm is just a portfolio of existing and potential projects!
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NPV and the Goals of the Corporation
A corporation that maximizes shareholder value should undertake all investments with NPV > 0
Thus, capital budgeting is the search for projects with positive NPV
Investors value a firm taking into account:
How good are existing projects
The ability of the firm to find new projects with positive NPV (growth opportunities)
What about projects whose NPV = 0?
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Calculating NPV: Three Steps
Step 1: Calculate and plot cash flows in a timeline
Step 2: Discount all cash flows using appropriate discount rate (cost of capital)
Step 3: Sum the discounted values to find the NPV
Do project if NPV > 0
If deciding between two positive NPV, mutually exclusive projects, choose the project with the larger NPV
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Example 1
Suppose it will take two years to construct an office building. We need to invest $1.5 million in the first year, and $1 million in the second. In the third year, the building can be sold for $3 million. The discount rate is 7%.
Question: Should we construct the building?
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Look at old notes
DIY1
Suppose that instead of selling the building in the third year, you plan to rent it forever at $200,000 a year. You expect to receive the first payment during the third year and the discount rate is the same.
Question: Should we construct the building?
Hint: what would the benefits cash flow look like now?
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Look at old notes
DIY2
What if you could only rent the building for $150,000 per year, but you expect the rent to grow at 2% per year forever?
Question1: Should we construct the building?
Question2: You plan to sell the building after it is finished. How much should you get for it?
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Look at old notes
Example 2
Suppose that a real estate company is considering a renovation in one of their buildings which will allow the upper 15 floors to be used as residential space. The renovation will cost $10 million, and the new apartments (six per floor) can be sold for $500,000 each in two years. The discount rate is 7%.
Question: Should we renovate the building?
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Answer – we don’t have enough data, opportunity costs
Example 2: Alternatives
Answer: It really depends on my alternative, that is, in how much I can sell today the upper 15 floors without any renovation work
We must be really careful in identifying what are our cash flows and/or alternative projects
The rule is that we choose the project with the highest NPV
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Answer – we don’t have enough data, opportunity costs
Example 3
Suppose we are asked to decide whether or not to launch a new product. Based on projected sales and costs, the cash flows over the four-year life of the project will be $ 1,500 in the first year, $2,000 in the second year, and $2,500 in the third and fourth years. It costs $6,000 to begin production. The discount rate is 10%. Should we launch the new product?
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Use excel to show NPV function
Summary - NPV
NPV is the right capital budgeting technique
It tells us if a particular project is a good investment or not
It is consistent with maximization of shareholder value
But you must make sure you are using it correctly
Identifying the right cash flows
Using the correct discount rate
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Payback
Payback period
Length of time until the accumulated cash flows equal or exceed the original investment
Payback rule: Quicker is Better
Accept if payback is less than some pre-specified number of years
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Example - Payback
What is the payback?
What if the cash flow of the third year is 5,000
What does this mean?
0
1
2
3
4
-6,000
1,500
2,000
2,500
2,500
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Payback Rule Evaluated
Drawbacks
How to determine cut-off?
Bias against long term projects
Ignores time value of money
Ignores cash flows after cutoff point
Inconsistent with maximization of shareholder value
Advantages
Simple to use
No need to estimate discount rate (robust)
It is a crude measure of liquidity
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IRR – Internal Rate of Return
IRR
Discount rate that gives a project a zero NPV
IRR rule
Accept investment if IRR > Required rate of return
0
1
2
3
C0
C1
C2
C3
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What is the IRR?
We need to solve the following equation:
0
1
2
3
4
-6,000
1,500
2,000
2,500
2,500
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What is the IRR?
We need a calculator or spreadsheet to solve this problem
Check at home that R = 14.17% makes NPV = 0
Do we accept the project?
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NPV Profile and the IRR
Are the NPV and the IRR equivalent rules?
IRR = 14.17%
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IRR has several problems
Pitfall 1: Lending or borrowing?
Pitfall 2: Multiple rates of return
Pitfall 3: Mutually exclusive projects
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Pitfall 1-Are we Borrowing or Lending at IRR?
With some cash flows the NPV of the project increases as the discount rate increases
Both IRRs are 20%
If opportunity cost of capital is 8%. Do we accept case 1 or 2?
What’s the NPV at R=8%?
0
1
-1,000
1,200
0
1
1,000
-1,200
Case 1
Case 2
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Use spreadsheet.
Pitfall 2 - Multiple IRRs
Certain cash flows can generate NPV = 0 at two different discount rates.
Ex:
Why is the last cash-flow negative ?
Delays between income and taxes
Decommissioning costs (Ex: Nuclear Plants)
0
1
2
3
4
5
6
-1000
800
150
150
150
150
-150
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NPV and multiple IRRs
Do a plot at home to confirm this !
What is the decision rule?
IRR = 15.24%
IRR = -50%
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Pitfall 3-Mutually Exclusive Projects
| Project | C0 | C1 | IRR | NPV@10% | Accept |
| 1 | -10,000 | 20,000 | 100% | 8,182 | ? |
| 2 | -200,000 | 350,000 | 75% | 118,180 | ? |
This is the main reason why IRR is misleading
Which project is better?
Why does IRR give the wrong answer?
scales
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Is the IRR useful?
The IRR technique is very widely used, even as a primary method
There is a simple reason for that: communication
People like percentage measures
But percentages assume that you can scale up your project!
IRR will in most cases give the same answer as NPV
It can be used to determine a percent return on your investment
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Investment Decisions With Resource Constraints
In principle take all positive NPV projects
In practice there are limitations
Mutually exclusive projects
Budget constraints (capital rationing)
Limited production capacity
Human resource constraints
Choose best set of investments given the resources the firm has available
Capital Budgeting Techniques Summary
NPV is the right capital budgeting technique
Always correct
Always consistent with maximization of firm value
(Discounted) Payback adds information about liquidity, but should not be used on its own
IRR usually allows us to determine a percent return, but may mislead in some cases
With constraints on resources, think about value created for each unit of resource consumed (* In Appendix)
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From: J. Graham and C. Harvey, 2001, „The theory and practice of corporate finance: Evidence from the field“, Journal of Financial Economics
The Practice of Capital Budgeting
Appendix: Projects with Different Lives
An efficient method of choosing between mutually exclusive projects with different lives is to compute their equivalent annual annuity (EAA)
Accept Project B – however?
What happens after Year 2 for project A?
Appendix: Projects with Different Lives – An Example
Appendix: An Approach to Handling Different Lives: Equivalent Annual Annuity
Accept Project A
Appendix: Discounted Payback Criterion
We should at least try to account for the time value of money (Discounted Payback)
Discounted Payback Period
The length of time required for an investment’s discounted cash flows to become as large as or larger than the initial investment
Lower weights for distant cash flows (we are taking time value of money into account)
Appendix: Discounted Payback – An Example
Let R = 10%
NPV = ?
Discounted Payback = ?
Is it possible to reject a positive NPV project?
0
1
2
3
4
-6,000
1,500
2,000
2,500
2,500
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Use spreadsheet
Appendix: Discounted Payback - Summary
Useful adjustment to Payback, with similar information about liquidity
Beware of the pitfalls
We still have arbitrary cut-off rates
Again, it is biased against long term projects
Use it qualitatively, and jointly with NPV as a secondary method
Be suspicious if it takes 100 years to get your investment back
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Appendix: Modified Internal Rate of Return
Modified Internal Rate of Return (MIRR) deals with the problem of multiple IRRs.
This is done by rearranging the cash flows so that there is only one change of sign of the cash flows over the life of the project.
Appendix: Modified Internal Rate of Return
MIRR Process: 2 Steps
Modify the project’s cash flow stream by discounting the negative future cash flows back to the present using the same discount rate that is used to calculate the project’s NPV.
Appendix: Modified Internal Rate of Return
MIRR Process: 2 Steps
Calculate the MIRR as the IRR of the modified cash flow stream.
Appendix: NPV Profiles for Two Mutually Exclusive Projects
Appendix: Profitability Index
Profitability index (PI) is computed for each project
Firm chooses the set of projects with the largest profitability indices until it runs out of resources
Profitability Index is a measure of the value a project generates for unit of resource invested in that project.
Objective is to identify the bundle or combination of positive-NPV projects that creates the greatest total value for stockholders.
Appendix: Profitability Index: An Example
Calculate the profitability index for a project to acquire a lawn mower. The new mower costs $2,000 and the NPV is $20,189.
Appendix: Investment Decisions With Funding Constraint (Capital Rationing)
Using PI to choose project(s) that create the most value per dollar invested (4 step procedure):
Calculate the PI for each project.
Rank the projects from highest PI to lowest PI.
Starting at the top of the list (the project with the highest PI) and working your way down (to the project with the lowest PI), select the projects that the firm can afford.
Appendix: Profitability Index with Funding Constraint
Firm is limited to $10,000 to invest
Project Initial NPV PI Cumulative
Investment funds required
A -$5000 $5000 1.000 $5000
B -$3000 $2000 0.667 $8000
C -$3000 $1000 0.333 -
D -$2000 $500 0.250 $10000
Appendix: Shortcomings of PI
Multiple resource constraints eg budget limit (capital rationing) and human resource constraint
Multiple periods, constraints extend over more than one period
Solution is linear programming
0
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(
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(
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1
0
=
+
+
+
+
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IRR
C
IRR
C
IRR
C
C
0
)
1
(
500
,
2
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1
(
500
,
2
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1
(
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,
2
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1
(
500
,
1
000
,
6
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=
+
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-
IRR
IRR
IRR
IRR
Discount RateNPV
9%761.03
10%602.35
11%449.40
12%301.92
13%159.65
14%22.35
15%-110.19
16%-238.20
17%-361.87
-600.00
-400.00
-200.00
0.00
200.00
400.00
600.00
800.00
1000.00
9%10%11%12%13%14%15%16%17%
Discount Rate
NPV
-2000
-1500
-1000
-500
0
500
1000
1500
-60%-50%-40%-30%-20%-10%0%10%20%30%40%
Discount Rate
NPV
|
|
Shorter |
Longer |
|
|
$ |
$ |
|
Cost |
-18 000 |
-40 000 |
|
Cash inflows |
|
|
|
Year 1 |
8 400 |
11 420 |
|
2 |
8 400 |
11 420 |
|
3 |
8 400 |
11 420 |
|
4 |
– |
11 420 |
|
5 |
– |
11 420 |
|
NPV (at 10%) |
2 891 |
3 293 |
PI = Value Created
Resource Consumed =
NPV Resource Consumed
PI=
Value Created
Resource Consumed
=
NPV
Resource Consumed
PI = NPV
Resource Consumed =
20,189 2, 000
= 10.09
PI=
NPV
Resource Consumed
=
20,189
2,000
=10.09
