Today's Lecture

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Today's Lecture

• Finish Brief Introduction to Risk
• Opportunity Cost of Capital
• Interest Rates
• Investment Decision Rules

TIP If you do not understand something, ask
me!
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How do you value risky investments?

• Consider the following example
• Risk free bond that pays 1100 for sure in one
  year
• A risky investment in the market that costs 1000
  pays an uncertain amount in a year in one of two
  equally likely events
• 800 in a weak economy
• 1400 in a strong economy
• Risk free rate of interest is 4

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Questions

• What is the price of the bond?
• What is the expected payoff of the market?

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Example contd

• Why does the investment in the market have a
  lower price than in the risk free bond, when the
  expected payoff is the same?
• What is the expected return of the investment in
  the market?

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Risk Premium

• The additional return investors expect to
  compensate them for the risk of taking on a risky
  investment opportunity

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No Arbitrage Price of a Risky Security

• Consider security A that pays off 600 if the
  economy is strong and nothing if it is weak
• What price does A sell for?
• What is As expected return?

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Another Example

• Consider security B that pays off 600 if the
  economy is weak and nothing if it is strong
• What price does B sell for?
• What is Bs expected return?
• What is going on here?

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Risk is Relative

• The risk of a security must be evaluated in
  relation to other investments in the economy!

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Extending LOP to Risky Investments

• All investment opportunities that trade in a
  normal market with the same risk and maturity
  must have the same expected return
• Why?

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Opportunity Cost of Capital

• The expected return offered in a Normal Market
  for an investment opportunity of a particular
  maturity and risk
• OR
• The expected return of best available marketed
  investment opportunity with the same risk and
  return

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The Discount Rate

• The discount rate is the correct rate to use to
  move a particular cash flow in time.
• It is calculated using the cost of capital

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Example

• Your cousin would like to buy your Acura.
  Unfortunately, he is just a student and has very
  little money. Instead of paying for the car, he
  offers to pay you 100/month forever. If your
  annual cost of capital is 10, how much is he
  offering to pay for the car?
• What monthly interest rate would you demand on
  your deposit at the bank so that you would be
  indifferent between that and being paid 10
  annually?

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Aside Annual vrs Monthly Compounding

• Say you deposit 1
• If you chose the annual interest deposit in one
  year you will have
• If you chose the monthly interest deposit in one
  year you will have
• So..

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Example - Solution
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General Idea

• Given a cost of capital of rx per x-years, the
  equivalent discount rate ry per y-years is given
  by compounding (1rx) for y/x periods
• 1 ry (1 rx)y/x.

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Interest Rate Quotes

• When a bank quotes an interest rate for a
  particular loan, it is usually not correct to use
  this quote directly as the discount rate
• The discount rate often has to be computed from
  the quoted rate based on the conventions of the
  quote.

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Annual Percentage Rate (APR)

• This is the amount of interest you would earn in
  one year assuming that you rollover the loan but
  do not reinvest any interest payment paid during
  the year, that is, the loan is not compounded.

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Example

• If a 3 month bond has a 8 APR, how much
  interest will I earn over the life of the bond?
• Since the APR quote does not include interest on
  interest and since a 3 month bond can be
  reinvested 4 times during the year, the bond will
  earn 2 interest over its life.

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Effective Annual Rate (EAR)

• This is the amount of interest you would earn in
  one year assuming that you rollover the loan and
  reinvest all interest payments as often as is
  allowed by the terms of the loan, that is, the
  loan is compounded as often as possible during
  the year.

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Example

• If a 3 month bond has a 8 EAR, how much interest
  will I earn over the life of the bond?
• Since the EAR quote does include interest on
  interest and since a 3 month bond can be
  reinvested 4 times during the year,

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Example

• Using current rates, assume that the most you can
  afford in monthly mortgage payments is 1000. If
  you plan to use a 30 year fixed rate mortgage
  with an interest rate of 7.75 and a 1
  origination fee, how large a mortgage can you
  afford?

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Internal Rate of Return

• Sometimes you know expected cash flows and the PV
  and you would like to know what discount rate
  sets them equal
• You can also think of this as the return of the
  investment

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Example

• Assume you wanted to purchase a BMW that cost
  40,000. The dealer is willing to let you have
  the car with zero down payment, so long as you
  are willing to pay off the car with 4 annual
  payments of 15,000. What interest rate is the
  dealer charging for this loan?

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Timeline
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IRR

• The internal rate of return (IRR) is the discount
  rate that sets the net present value of an
  investment opportunity equal to zero.
• For a bond, this rate is known as the yield to
  maturity.

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Investment Rules

• Thus far I have only spoken about the NPV Rule.
  But other rules exist.
• Keep in mind that any rule that disagrees with
  the NPV rule does not take the investment for
  which the benefits exceeds the costs

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Don's Laundromat

• Don is thinking of opening a laundromat. Each
  new machine costs 500. Don has been informed
  that at full capacity each machine will generate
  150 per year. However, machines require
  maintenance, so to keep the machines in working
  order Don must spend a fraction of this on
  maintenance. As might be expected this
  maintenance cost increases as the machines age.
  Don expects to do no maintenance in the first
  year, but after that he expects his net cashflow
  to decrease by 20 each year in perpetuity.
• What is the IRR of a washing machine?

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IRR Rule

• What do you think the rule is?
• Accept the project if its IRR is greater than the
  discount rate
• Reject the project if its IRR is less than the
  discount rate
• What should Don do?

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What is the NPV of Don's Laundromat as a function
of r?

• Does the NPV Rule always give the same answer as
  the IRR rule?

IRR
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IRR and discount rate estimation

• The difference between the IRR and the discount
  rate is the amount your estimate of the discount
  rate can be off without changing the investment
  decision

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Problems with IRR

• Negative investments lead to the wrong conclusion
• Negative cashflows lead to multiple IRRs
• For mutually exclusive projects
• Timing Matters
• Scale Matters
• We will use examples to illustrate each problem

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Negative Investments

• Mr Mankiw, an economist at Harvard, recently
  accepted the following deal to write an
  introductory economics text. He took an up front
  payment of 1,000,000 and was expected to deliver
  a completed text within three years. Mankiw
  figures that based on his consulting rates, his
  disutility from writing and the amount of time
  that he will spend, it will cost him 500,000 a
  year to complete the book (i.e., for this amount
  he is indifferent between writing and not writing
  the book). If current interest rates are 10,
  based on the IRR method what should he have done.
  What about the NPV method?

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NPV of Mankiw Deal
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Multiple Values

• Assume that the deal also includes royalties that
  are expected to be 20,000 a year in perpetuity
  once the book is completed. Now what should he do?

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NPV of Mankiw (Part 2)
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Scale Problem

• Lets go back to Don and assume that he has as an
  alternative investment, the opportunity to invest
  500 in his girlfriend's business. In a year he
  expects to get 1000 back. What should he do if
  the interest rate is 8?

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What are the NPVs of the investment alternatives
as a function of r?

• Blue Girlfriend
• Red One Machine Laundromat

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NPV of Don's Laundromat

• Blue Girlfriend
• Red 20 Machine Laundromat

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Timing Problem

• Assume that Don also has the option of purchasing
  a maintenance contract on the machines. Now he
  is not responsible for maintenance, however the
  cost of the maintenance contract is 107.14 per
  year. This leaves him with a cashflow of 42.86
  per year in perpetuity. Now what does IRR say?

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NPV of 1 Machine Laundromat

• Red Maint. Cont.
• Blue No Maint. Cont.

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Can IRR be fixed?

• NO

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OK, but if it is so bad, why do people still use
it?

• "Advantage" of IRR
• You do not need to know the discount rate
• Is this really true?
• Still, the IRR itself can be calculated without
  the discount rate
• You can do the same thing with NPV by calculating
  the NPV for a range of discount rates!

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IRR Rule vrs the IRR

• Although using the IRR rule is a mistake, the IRR
  itself is a very useful piece of information
• Tells you how far your discount rate estimate can
  be off without changing the decision
• A measure of the expected return

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Payback Rule

• Find out by adding the cashflows how long it
  takes to payback the initial investment
• If this period is less then some prespecified
  period, invest
• Otherwise, do not invest

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Problems

• How do you get your payback period
• Ignores
• Time value of money for the payments before the
  break-even date
• all payments after that date.

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Redeeming Features

• Simple
• Might be useful for small projects that would not
  justify an NPV analysis
• Early cashflows are emphasized --- provides
  liquid investments

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EVA

• Many companies use an investment rule called
  Economic Value Added or EVA.
• The rule says invest when the present value of
  the EVA is positive.
• EVA is just a method for applying the NPV rule.

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Motivation

• When companies were evaluating ongoing projects,
  they noticed that just looking whether or not the
  project made a profit was not good enough?
• Why?

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Answer (by Peter Drucker)

• "Until a business returns a profit that is
  greater than its cost of capital, it operates at
  a loss. Never mind that it pays taxes as if it
  had a genuine profit. The enterprise still
  returns less to the economy than it devours in
  resourcesUntil then it does not create wealth
  it destroys it."
• This is the basis of the NPV rule!

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EVA Cashflow

• EVAt Cashflowt
• (Capital x cost of
  Capital)
• OR

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Relation to NPV

• Take a case where the cashflows are a perpetuity
  and the capital is investment is made at the
  beginning and never changed.
• The PV of the EVA is

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In General

• This holds more generally as well. For homework,
  try to show this in other cases.
• There are two things to remember
• If the project has a finite life, you must
  remember to recoup the (market) scrap value of
  capital at the end of the project.
• If capital investments are made during the
  project you must take the cash flow at the time
  of the investment into account and also increase
  the capital terms from then on out.

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Next Lecture

• The basics of Capital Budgeting
• Reading
• Chapter 7