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8/17/2019 Lecture 04 NPV Rule
http://slidepdf.com/reader/full/lecture-04-npv-rule 1/24
Professor Sang Byung [email protected]
NPV rule
8/17/2019 Lecture 04 NPV Rule
http://slidepdf.com/reader/full/lecture-04-npv-rule 2/24
Last class
• The time value of money (2nd part)• PV short cuts
• Annuity
• Perpetuity
• Growing annuity/perpetuity
• Delayed annuity/perpetuity
8/17/2019 Lecture 04 NPV Rule
http://slidepdf.com/reader/full/lecture-04-npv-rule 3/24
Today
•Finish the remainder of Lecture 03• Compounding frequencies
• Investment criteria• NPV rule
8/17/2019 Lecture 04 NPV Rule
http://slidepdf.com/reader/full/lecture-04-npv-rule 4/24
Net Present Value
•NPV of a project or investment• The difference between
• PV of its future benefits
• PV of its costs
• In many cases, simply
• PV of future cash flows net of an initial investment
0 1 2 T-1 T ……3
−
where
(initial investment) is negative
8/17/2019 Lecture 04 NPV Rule
http://slidepdf.com/reader/full/lecture-04-npv-rule 5/24
NPV calculation
•Nothing special!
+ 1 + + 1 + + ⋯+ 1 +
+ =
= 1 +
0 1 2 T-1 T
……3
−
8/17/2019 Lecture 04 NPV Rule
http://slidepdf.com/reader/full/lecture-04-npv-rule 6/24
Example
• Assume that the cash flowsfrom the construction and
sale of an office building is
as follows.
• Given a 7% required rate of
return, what is the NPV?
150,000 100,0001.07 + 300,000
1.07 $18,573.67
8/17/2019 Lecture 04 NPV Rule
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NPV rule
•NPV rule• Accept projects with NPV>0
• Reject projects with NPV<0
• Result
• Following the NPV rule maximize the value of the firm.
8/17/2019 Lecture 04 NPV Rule
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NPV rule
•Is this rule really obvious?• What if a project has the positive NPV, but
• All cash flows occur 10 years from now?
• Shareholders are really old?
• Do you still think that you need to always accept a
project with the positive NPV?
• Do individuals’ preferences matter?
– Today’s consumption versus future consumption?
8/17/2019 Lecture 04 NPV Rule
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Illustrative example
•
Michael was endowed with $1M.• He can borrow or lend from a bank at 20%.
• He allocates wealth between youth and old age
• What should he do?
1. He can go on a trip around the world, and then live inpoverty in old age.
2. He can go on a smaller trip, have a moderate lifestyle in hisyouth (spending $0.5M) and still have 0.5(1.2)=0.6M for hisold age.
3. He can put it all in the bank and go for an even better triparound the world in old age ($1.2M)
8/17/2019 Lecture 04 NPV Rule
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• Choose one point on the
line depending on hispreferences
• Slope is -1.2
• Trade-off between spending
in youth vs in old age
• Every $1 dollar you do not
spend, you get $1.2 in old
age
Today vs Future
•
All these possibilities are equally “correct.”• The choice just depends on Michael’s preferences!
1.2 1 1.2 1.2
8/17/2019 Lecture 04 NPV Rule
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Opening a restaurant
•Start-up cost would be $0.7M.
• It will yield $0.8M in old age.
• Should he invest?
• No! If he puts the $0.7M in the bank, he will have
• 0.7(1.2) $0.84 > $0.8• In other words,
• 0.7 + .. 0.03 < 0
• We don’t need to know anything about Michael’s
preferences to make this decision.
8/17/2019 Lecture 04 NPV Rule
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Opening a bar
•Start-up cost would be $0.7M.
• It will yield $0.9M in old age.
• Should he invest?
• It seems that the answer should be yes.
• 0.7 + .. 0.05 > 0
• But, spending $0.7M today leaves him only $0.3M
• If he wants to spend less than $0.3M in youth, it is fine.
• But what if he wants to spend more than $0.3M in youth?
–
For example, he might want to buy a nice house.
8/17/2019 Lecture 04 NPV Rule
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After investing in a bar
•
Michael wants to consume $ in youth.• If > $0.3, he needs to borrow $(x-0.3) from the bank.
• In old age
– Earn $ 0.9M from the bar
– Need to pay back the loan
y 0.9 – 1.2( 0.3)• If < $0.3, he deposits the remainder, which is $(0.3-x).
• In old age
– Earn $ 0.9M from the bar
– Need to collect the deposit
0.9 + 1.2(0.3 )• He spends $(1.26 – 1.2x) million in old age.
8/17/2019 Lecture 04 NPV Rule
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1.2 1.2
1.26 1.2
y intercept: 1.26
x intercept: 1.05
Comparison
•
After investing a bar• Michael has better choices!
• If he wants to spend all inyouth, he can spend $1.05$,
which is $0.05M larger thanbefore.
• Recall that the NPV = $0.05M!
•
NPV rule• Accepting a positive NPV
project is equivalent toreceiving their NPV in cashtoday!
8/17/2019 Lecture 04 NPV Rule
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More than one shareholder
•
Should corporations follow the same rule?• Not one shareholder, but many
•
For example, assume two shareholders1. Grandma (100 years old and wants money now)
2. Child’s investment trust (wants money later)
• The company has two projects:
1. Produce sports cars (income now but NPV<0)
2. Develop electric cars (income later but NPV>0)
8/17/2019 Lecture 04 NPV Rule
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Conflict btw shareholders?
•Is there a conflict between the two shareholders?• NO! Both are better off if the firm develops electronic
cars.
• Why? Grandma can borrow, and then she (or her heirs)
can repay the loan using the project’s cash flows.
• Both shareholders, regardless of their preferences forcurrent or future income, want the firm to choose the
positive NPV project.
8/17/2019 Lecture 04 NPV Rule
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Fisher Separation Theorem
•Investment decision does not depend onpreferences of individual investors for current
versus future income.
• All shareholders want the firm to use the NPV rule, which
maximizes their share value.
• Then, they will use the capital market (e.g. banks) toobtain their desired consumption.
8/17/2019 Lecture 04 NPV Rule
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Importance of this theorem
•
Without it, the CFO’s job would be impossible!• The CFO would have to poll thousands of people to see when
they want their consumption, and somehow aggregate thosepreferences.
• On the other hand, individuals would have toalways be lobbying for their wishes!
• Because the NPV rule works,
• We can diversify our wealth across corporations.
• Corporations can draw from the huge amount of resourcesavailable in capital markets.
8/17/2019 Lecture 04 NPV Rule
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What have we assumed?
•This rule will be the basis of all we do.
• But, we made some simplifying assumptions.
1. The borrowing rate is equal to the lending rate.
2. All investors have the same information (or they might
disagree on NPV or even r).
3. Markets are competitive (no firm affects interest rates).
8/17/2019 Lecture 04 NPV Rule
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Another example
•Time Inc will make a profit of $45M at the endof this year, and $90M at the end of next year.
•
Assume its discount rate is 10%. What is thepresent value of these cash flows? (That is,
what is Time Inc worth today?)
• Answer:
45
1.1
+ 90
1.1 115.3
8/17/2019 Lecture 04 NPV Rule
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Example (cont’d)
• Jane Fonda is the only shareholder of Time Inc.
• All profits Time Inc generates are paid out as
dividends.
• She wants to donate $100M to the UN next year.
• Does this mean that Time Inc reconsider its
future business?
8/17/2019 Lecture 04 NPV Rule
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Example (cont’d)
•The answer is no!
• Then, how can she achieve her goal?
• Method 1: Sell shares
•
She can sell her shares for $115.3M today, invest it at 10% to get$126.8M next year, pay $100M to the UN, and reinvest the
remaining $26.8M at 10% to end up with $29.5M.
• Method 2: Dividend payment + a loan from a bank
•
She can keep her shares, get a dividend of $45M next year,borrow an additional $55M, and pay $100M to the UN. At the
end of the second year, she will get a dividend of $90M, pay
$55M*1.1=$60.5M to her lenders to repay the loan, and again be
left with $29.5M.
8/17/2019 Lecture 04 NPV Rule
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Takeaways
•Lessons for Time Inc• The management does not have to worry about Jane
Fonda’s need for cash in making their decisions about
investments.
• It does not need to generate income by speeding up
production or taking on short-term projects instead of
making long-term R&D investments.
• It does not have to worry about Jane Fonda’s desire to
save the rain forests…
8/17/2019 Lecture 04 NPV Rule
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Takeaways
•How is this possible?• Once Time Inc maximizes the value of its shares, the
capital markets allow Jane Fonda to sell or borrow
against them and do whatever she wants.
• In fact, the more the value of Time Inc’s shares, the more
Fonda can give to the UN, and the more rain forests can
be saved!