Ch10. The Basic of Capital
Budgeting
• Goal: To understand the advantage and
disadvantage in different investment analyzing
tools
• Tool:
- Net Present Value (NPV)
- Payback period
- Discounted payback period
- Internal Rate of Return (IRR)
- Modified Internal Rate of Return (MIRR)
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1. Project classification
Replacement
Expansion of existing products
Expansion into new products or markets
Safety and/or environmental projects
• 2. Types of projects
• Mutually exclusive project: if one project is taken,
the other will be rejected.
• Independent project: projects’ cash flows are
independent of one another
•
Basic concept in criteria: To find the
profitable projects to corporations or
investors
3. Net Present Valuation (NPV)
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Def of NPV:difference between an
investment’s market value and its costs
= PV of cash flow from a project – PV
of the initial costs and other costs
- Here, Cost of capitals is used as a discount rate
- Rule: acceptable if the NPV > 0.
Ex) You believe the cash revenues from the fertilizer
business will be $20,000 per year. And cash costs
will be $14,000 per year. You will close the
business in eight years with $2000 salvage value.
The project costs $30000 to launch. Assume 15%
discount rate.
Q1) Do you think that this business should be
launched?
• Answer:
NPV = -30,000+27578 = - 2422
Therefore, it is not a good investment.
Q2) What is the impact of taking this project
on the stock if there are 1000 outstanding
shares?
Answer: loss of stock value, -2422/1000
= -2.42 per share
1) Problem of NPV:
- Accurate cash flow?
- Discount rate (cost of capitals)?
- Market price?
4. Payback rule
- Def of payback:the length of time it takes to
recover our initial investment.
• Rule: acceptable if its calculated payback
period is less than pre-specified number of
years
• Ex) Cash flow with the initial costs of $500.
1st year:$100, 2nd year: $200
and 3rd year: $500.
Q1) How long it will take to pay back the
initial cost?
Answer: 2 years + 200/500 =2.4 yrs. If the
cutoff period is 3 years, a project with this
cash flow may be accepted
1) Disadvantages
• Ignore the time value of money
Ex) $30 on the second year is not the same as
$30 on the third year
• Arbitrary Cutoff period
• Ignore cash flow beyond the cutoff period
Ex) A: -100, 50, 50
B:-100, 10, 30, 70, 200
With a rule, you have to pick up “A”. But this
decision ignore $200 in B.
• Biased against long-term projects
Ex) Only accept investments within the cutoff
period
2) Advantage
• Easy to understand
• Adjusted for uncertainty of later cash flows
• Biased toward liquidity.
5. Discounted payback
• Def: the length of time until the sum of the
discounted cash flow is equal to the initial
investment. This is a variation of payback
to cover the time value problem.
• Rule: acceptable if its discounted payback is
less than some pre-specified number of
years
• Ex) The initial costs are $300 with 12.5% of
WACC. 1st year: $100, 2nd year: $200 and
3rd year:$300.
1) Disadvantages
• Arbitrary Cutoff
• Reject the positive NPV
• Ignore the cash flow after the cut off
• Biased against the long term projects
2) Advantages
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Include the time value of money
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Easy to understand
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Not accept the negative NPV
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Biased toward liquidity
V. Internal Rate of Return (IRR)
• Def: the discount rate that makes the NPV
of investment zero. In other word, it is
break-even discount rate and minimum
return
• Rule: acceptable if the IRR exceeds the prespecified return (required rate of return)
• How to calculate IRR: Trial and Error
method or NPV profile
Ex) Initial costs :$100
1st year: $60 and 2nd year:$60
0 = -100+60/(1+r)+60/((1+r)^2)
Here r=13.1%. If the cutoff rate is 12%, then
a project with this cash flow may be
accepted
6. Comparison of NPV to IRR.
1) NPV profile
Using the previous example, we are able to
calculate NPV with different IRRs
Rate: 0% 5% 10% 15% 20%
NPV:20 11.5 4.1 -2.4 -8.3
Using this information, we are able to make a
graph called “net present value profile”
• From the NPV profile, we indirectly realize
that a point crossing X-axiom is the IRR
2)NPV rankings: comparing more than two
projects’ NPV profiles
- Cross rate: cost of capital at which the
project’s NPVs are equal
- Why the NPV profiles are crossing each
other: Due to cash flows patterns
• 3) Independent Projects
• They always have the same conclusion
(acceptance or rejection) from NPV and
IRR.
• 4) Mutually Exclusive Projects
• Two basic conditions that can cause NPV
profile to cross and thus conflicts to arise
between NPV and IRR
- When project size (or scale) difference
exist. That is, the cost of one project is
larger than that of the other.
- When timing differences exist. That is,
timing of cash flows from the two projects
differs.
Any other reason of conflicts? Due to
reinvestment rate
• NPV assume that cash flows will be reinvested at
the cost of capital whereas the IRR assumes that
the firm can reinvest at IRR.
• The best reinvestment rate is the cost of capital
• (5) Multiple IRRs
• Normal cash flows: one or more cash outflows
(costs) followed by a series of cash inflows.
• Nonnormal cash flows: a large cash outflow
during or at the end of its life.
• Nonnormal cash flows may lead to multiple IRRs
• Ex) Figure 11-5
• 7. Modified IRR.
• Using the cost of capital as a reinvestment
rate, recalculate IRR.
• Practitioners prefer a percentage return
(IRR & MIRR) to dollar amounts (NPV).
n
• PV of costs =  CIFt (1  k ) nt /(1  MIRR ) n
t 1
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• Ex) S company tries to launch a project. That
project needs the initial outlay of $1000. It will
produce a series of profits for next 4 years. (1st
year: 500, 2nd year: 400, 3rd year: 300 and 4th
year: 100). Its cost of capital is 10%.
• What is MIRR?
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500 1.13  400 1.12  100 1.1  100
 1579.50
1000  1579.50 /(1  MIRR )
MIRR  12.10%
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(1) Advantage of using MIRR over IRR
Reinvestment at the cost of capitals
Solve Multiple IRR issue
In mutually exclusive case, if the projects have
same size & life, the NPV and MIRR always lead
to the same decision
• If the projects are of equal size but differ in lives,
the MIRR will always lead to the same decision as
the NPV if MIRRs are calculated using the life of
longer project as the terminal year (just fill zeros
for the shorter projects’ missing cash flows)
• If the size differ, the conflicts happen
• Among the tools, NPV is the best one.