Financial Management

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Financial Management

• Professor Jaime F Zender

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A Good Place To Start

• What is finance?
• Finance is a hybrid of economics, statistics, and
  accounting.
• It is the science of capital.
• In other words, it considers the allocation of
  money across investment opportunities.
• Necessarily draws on these underlying disciplines
  in making such decisions.
• We will concentrate on corporate finance rather
  than personal finance but the issues and concepts
  are fundamentally the same and I will often draw
  parallels.

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Typical Question

• Three years ago your cousin Ralph opened a
  brew-pub in downtown Boulder.
• While it has been operating fairly successfully
  its survival depends upon some expansion and
  upgrades in its production equipment.
• Ralph has come to you as a potential equity
  investor.
• The expansion requires 100,000 and the two of
  you are discussing the ownership stake this would
  imply for you.

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Ralphs Position

• Ralph argues that three years ago he invested
  30,000 of his own capital.
• He also argues that for three years he has been
  working at a less than competitive wage (in order
  to reinvest the generated cash).
• He estimates this amounts to 40,000 in sweat
  equity for each of the three years.
• Ralph suggests these facts imply your 100,000
  will purchase 40 of the equity.
• Is this argument valid?

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Valuation Basics Where We Are Headed

• Assets have value due to the payoffs they
  generate for those that purchase them.
• What does past investment have to do with this?
• The price you are (should be) willing to pay for
  an asset depends upon the future value you will
  receive from owning that asset.
• Another piece of the puzzle is that cash today is
  more valuable than cash tomorrow a concept we
  call the time value of money.

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Valuation

• The present value formula is a way to express
  todays value of a stream of cash payments to be
  received in the future.
• Suppose you expect to receive cash payments of
  100, 150, 180, and 210 respectively at the
  end of the next 4 years if you purchase a
  particular security. Todays value of this
  security can be expressed using a simple formula.

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Valuation
Rather
or
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Payoffs and Rates of Return

• For a given investment, the dollar payoff of that
  investment is simply the amount of cash it
  returns to the investor.
• The rate of return of the investment is the
  future payoff net of the initial investment (or
  the net payoff) expressed as a percentage of the
  initial cash outlay.
• Its like the payoff, per dollar invested, for a
  given period of time.

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Example

• An investment project that costs 10 to establish
  today will provide a cash payment of 12 in one
  year has
• time 1 payoff 12
• time 1 payoff C1
• time 1 net payoff 12 - 10 2
• time 1 net payoff C1 C0
• rate of return (12 - 10)/10 .20 20
• r0,1 (C1 C0)/C0 C1/C0 -1

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Future Value

• We can turn this formula around to answer the
  question How much money will I receive in the
  future if the rate of return is 20 and I invest
  100 today?
• The answer of course is
• 100(120) 120
• or
• r1 (C1 C0)/C0 ? C0(1r1) C1 FV1(C0)
• This is referred to as the future value of 100
  if the relevant rate of return is 20.

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Future Value

• We can use this idea to compute all sorts of
  future payoffs.
• For example an investment requiring 212 today
  and earning a holding period return (or total
  return) of 60 from now (time 0) till time 12
  would provide a payoff of
• 212(160) 339.20
• C12 C0(1r0,12) FV12(C0)

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Problems

• A project offers a payoff of 1,050 for an
  investment of 1,000. What is the rate of
  return?
• A project has a rate of return of 30. What is
  the payoff if the initial investment is 250?
• A project has a rate of return of 30. What is
  the initial investment if the final payoff is
  250? This is called the present value of the
  future 250.

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Compounding Rates of Return

• What is the two-year holding period rate of
  return if you earn a one-year rate of return of
  20 in both years?
• Note It is not 20 20 40.
• Why isnt it?
• If you invest 100 at 20 for one year you have
  120 100(120) at the end of the first year.
• If you then invest the 120 for the second year
  at 20 you end up with 144 120(120).
• This is a two-year rate of return of
• 44 (144-100)/100 r0,2

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Compounding

• This two-year rate of return of 44 is more than
  40 because you earned an additional 4 in
  interest the second year as compared to the
  first.
• During the second year you earned interest on the
  20 of interest earned during the first year.

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Compounding

• We can represent this more generally using the
  compounding (or the one plus) formula.
• This can be expanded to consider an arbitrary
  number of periods

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Problems

• If for the first year the one year interest rate
  is 20 and for the second year the one year
  interest rate is 30, what is the two-year total
  interest rate?
• If the per-year interest rate for all years is
  5, what is the two-year interest rate?
• If the per-year interest rate is 5, what is the
  100-year interest rate?

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Annualized Return

• Suppose that you earn interest for three years.
  In the first year you earn a 20 return, 30 in
  the second year, and 10 in the third year.
• This means a total three-year holding period
  return of 71.6. Why?
• We want to convey the return for this investment
  on an annualized basis. We can do this by asking
  what return, if received for each of the three
  years, would provide the same holding period
  (three-year) return?

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Annualized Return

• Note that it is not 71.6/3 23.87.
• This is because if we received 23.87 for each of
  three years we would receive a three-year return
  of
• We are looking for
• If you receive 19.72 for three years you will
  have a three-year return of 71.6
• If the total holding period return is 50 for a
  5-year investment, what is the annualized rate of
  return?

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Quoting Rates of Return

• When compounding is done for periods different
  than a year things can get complex.
• To try and avoid confusion the industry language
  concerning return has been standardized.
• Interest rates are commonly put on a stated
  annual or quoted annual basis.
• Then if compounding is done more frequently than
  annually we can calculate the interest you will
  actually receive for a one-year investment.
• We have assumed till now and for simplicity we
  will continue to assume that compounding is
  always done annually.

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Ex. Quarterly Compounding

• Your bank quotes a stated annual 10 interest
  rate on your CD. The interest on the CD however
  is compounded quarterly.
• If you invest 1,000 in the CD how much will you
  have at the end of a year?
• There are 4 quarters in a year so for a stated
  annual 10 rate one divides the stated 10 by 4
  to find a stated 2.5 per quarter.

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Ex. Quarterly Compounding

• With quarterly compounding this implies a payoff
  on your investment of
• 1,000(1.025)(1.025)(1.025)(1.025) 1,103.81
• This means a one-year return of
• (1,103.81 - 1,000)/1,000 10.381
• This is called the effective annual return. It
  is the interest rate you effectively receive when
  you invest for one year when the stated rate is
  10 and compounding is quarterly.

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The Yield Curve

• The term structure of interest rates.
• Todays average annualized interest rate that
  investments pay as a function of their maturity.
• The important message here is that investments of
  different maturities have different rates of
  return.
• This is true even for Treasury securities.
• The following graph and chart provide a view of a
  recent yield curve.

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The Yield Curve
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The Yield Curve
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The Yield Curve

• On June 29th 2005 how much money did an
  investment of 100,000 in a 2-year U.S. Treasury
  note promise to payout in two years time?
• r0,2 (13.65)(13.65) 1 7.43
• Thus in two years the 100,000 will turn into
• (1.0743) ? 100,000 107,430

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The Yield Curve

• What if you invested 100,000 in 30-year Treasury
  bonds?
• The 30-year total holding period return is
• r0,30 (1 4.26)30 1 3.4957 - 1 249.57
• Your 100,000 investment will payoff
• 100,000 ? (1 249.57) 349,570
• in 30 years.
• Note The Yield curve is usually upwards sloping
  but may occasionally have other shapes. We will
  usually speak as if it is flat.

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Problems

• Use the yield curve from 6/29/05.
• What is the future value of 100 invested in a
  three-year Treasury security?
• What is the total holding period return for a
  five-year investment?
• What is r2,3 ?

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Evaluating Investments

• Finance views all investments as if they were a
  series of cash payments received at different
  times.
• The actual costs or benefits may not be in cash,
  however for a proper evaluation of an investment,
  the costs and benefits must all be assigned a
  monetary value.
• Once all incremental cash flows for an investment
  are listed finance can take over and evaluate the
  desirability of the project.
• The decision of whether to make an investment
  will always entail a comparison of that
  investment to an alternative use of the required
  cash.
• How do we make such a comparison?

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Present Value and Net Present Value

• Recall our basic rate of return formula
• Just as we can turn this around to determine the
  future value of the current cash flow we can also
  use it to determine the present value of the
  future cash flow

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Example

• A project has an annual rate of return of 30.
  If we invest 100 for one year what is the future
  value of our investment?
• Ans 100(1 30) 100(1.3) 130.
• If a project has an annual rate of return of 30
  and will payoff 130 in one year, what is the
  initial investment?
• Ans 130/(1 30) 100 C1/(1 r0,1)
• 100 is the present value of 130 to be received
  in one year if the relevant rate of return is
  30. This is true because if you had 100 today
  it would become 130 in one year investing at
  30. Alternatively, we charge next years 130
  the 30 rate of return we could receive if we had
  money now.

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Extension

• This technique can be used to find the present
  value of cash at any future date.
• For example, suppose the annual interest rate is
  15 (for years one and two) and you will receive
  300 in two years, what is the present value of
  this future cash flow?
• r0,2 (1 r0,1)(1 r1,2) 1.15?1.15 - 1
  32.25
• The present value of the 300 is
• PV(C2) 300/(1.3225) C2/(1 r0,2) 226.84

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So What?

• How does this help us evaluate a project?
• Investment projects have lots of cash flows at
  different points in time. To make an investment
  decision we need a way to compare cash flows
  received at different times.
• We cant compare 100 today with 120 next year
  but we can compare 100 today with the present
  value (todays value) of 120 next year.
• The present values of future cash flows are all
  in terms of dollars today.
• Investment decisions are all made by comparison
  with a comparable alternative. Is it better than
  an alternative use of the upfront investment?

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Present Value

• Consider a project that will generate a payoff of
  15 in one years time and 10 in two years.
  What is the present value of these payments if
  the annual interest rate on Treasury bills is 10
  for both years?
• The present value of the first payoff is
• r0,1 10 so PV0(C1) C1/(1 r0,1) 15/1.1
  13.64 (, today)
• The present value of the second payoff is
• r0,2 (1.1)(1.1) 1 21 so PV0(C2)
  10/1.21 8.26 (, today)
• Their sum is 13.64 8.26 21.90 (, today)
• Would you undertake this project if it cost 20?

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Net Present Value

• This is just the net present value (NPV) rule.
• If the sum of the present values of a projects
  future cash flows is greater than its initial
  cost, then taking it is creating value.
• This is just like being able to buy 10 bills for
  5 or 8 or 9.98.
• Alternatively, we can think of a positive NPV
  project as providing a return higher than the
  available alternative.
• If the NPV of an investment is negative you are
  paying 10.05 for the 10 bill.

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Precision

• The Net Present Value formula is
• The net present value capital budgeting rule
  states that you should accept projects with a
  positive NPV and reject those with a negative NPV.

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The NPV Rule

• It is important to note that the timing of the
  projects cash flows are irrelevant once you find
  that the NPV is positive.
• What if you are 90 years old and find a positive
  NPV investment that provides payoffs only in 30
  years?
• What if you are saving for your childs college
  expenses and there is a positive NPV investment
  that provides a payoff immediately?
• All agents agree on the desirability of positive
  NPV projects. Nice in the corporate world.

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Implementation

• For today and tomorrow we will assume that agents
  in the economy are risk neutral.
• This means they do not require extra payment for
  taking on risk.
• It also implies that when evaluating an
  investment project the relevant interest rate is
  given by the Treasury yield curve.
• If you are evaluating an investment project a
  relevant alternative is always investing in
  Treasury (risk free) securities in this
  simplified case.

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Problem

• For simplicity assume the relevant interest rate
  is 5 annually for all years.
• What is the present value of the future cash
  flows of a project if it has payoffs of 150 in
  one year, 200 in two years, 600 in three years,
  and 100 in four years?
• What is the most you would pay for such an
  investment?
• If it costs 800 to purchase this investment what
  is its NPV? What is todays value of being able
  to invest in this project?

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Handy Short Cuts

• A growing perpetuity
• A growing annuity

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Examples

• The interest rate is 10. Your aunt Maude just
  promised to give you 150 every year for
  Christmas, forever. If it is now New Years eve
  how generous is she being?
• What if the promise is for the next 10 years?
• What if the promise is for 10 years but the
  amount will grow by 5 after the first year to
  account for inflation?
• What if the promise lasts forever and grows by 5
  after the first years payment?