THE INVESTMENT DECISION

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THE INVESTMENT DECISION
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TIME VALUE OF MONEY
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Opportunity Costs

• The rate that can be earned on alternative
  investments of similar risk.
• Not the source of funds, but what you do with the
  funds.

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Comparison
FV Grows to its
PV Is discounted to its
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Time Value

• A dollar today is worth more than a dollar in the
  future. Why?
• Certainty
• Inflation
• Opportunity Cost

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Interest Comparison

• Future Value Single Sum
• Present Value Single Sum
• Future Value Annuity
• Present Value - Annuity

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Future Value

• Any simple compound interest problem requires 3
  of these 4 variables
• Number of periods which compounding occurs (n)
• Present value of future sum (p)
• Future value of present sum (f)
• Interest rate per period (i)

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Future Value

• What an amount invested today will be worth at a
  certain time (compounding)
• f p X f(i,n) or
• FV PV X (1I)n
• P or PV initial investment amount
• I interest rate
• N of time periods of the investment
• So if we invest 10,000 for 5 years at 10

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Future Value

• The Future Value Factor (1I)n or f(I,n) can also
  be derived from the table (15-1).
• In the previous case the FVF 10,5 would follow
  the top row to 10 and the side row to 5 periods.

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Present Value

• The value today of payments which will be
  received in the future (known as discounting)
• p f X p(I,n) or
• PV FV (1I)n
• So if we have 16,105 at 10 for 5 years

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Present Value

• The Present Value Factor 1/(1I)n or p(I,n) can
  also be derived from the table (15-2).
• In the previous case the PVF 10,5 would follow
  the top row to 10 and the side row to 5 periods.

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Future/Present Value - Annuity

• Multiple payments/receipts
• F R X F(I,n)
• P R X P(I,n)
• In this case, R refers to the periodic deposits
  into the annuity account.

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Future Value of an Annuity

• Suppose you received 10,000 each year for 3
  years? What would it be worth if at each year it
  earned 10?
• Table 15-3

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Present Value of an Annuity

• Suppose a donor wants to give 10,000 each year
  for 3 years? What is it worth today if at each
  year it earned 10?
• Table 15-4

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Combo Problem

• A Hospital has a sinking fund payment required
  for the last 10 years of a bonds life. At the
  end of that period, there must be 45 million
  available to retire the debt. Luckily, the
  hospital has created a 5 million fund today, 20
  years before debt retirement. If the yield is
  expected to be 10, what annual deposit must be
  made?

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Combo Problem

• 1st Determine future value of the 5 million
  deposit
• F P X F(I,n) ? Z
• 2nd Determine remainder
• 45,000,000 - Z
• 3rd Calculate solution
• Z R X F(I,n)

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Using Decision Making

• Strategic Decisions
• Expansion Decisions
• Replacement Decisions

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Capital Investment Objectives
Financial Return
Non-Financial Benefit
Future Funding
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Capital Expenditures

• Relatively small percentage of total costs
  often 6 to 10.
• Usually land, land improvements, buildings, fixed
  equipment, major movable equipment, major repairs
  that extend useful life.
• Replacement New (for budgeting)

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Payback Rule

• Feasibility of investment determined by how long
  it would take to be recovered
• Initial investmentAnnual Cash Flows

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Payback Rule

• Acceptable if calculated payment is less than
  some prespecified number of years
• One alternative
• Two alternatives

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Example

• If it costs 1,000,000 either way, do we
• Buy an existing physician practice and renovate
  it to our needs (333,333 for 6 years) OR
• Build our own satellite clinic (200, 250, 300,
  350, 450, 650)?

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The Good and Bad

• GOOD ?
• Simple to calculate and understand
• BAD ?
• Answers in years, not
• Disregards cash flow after payback
• Time value of money

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Net Present Value

• Relies on discounting cash flows
• Difference between initial amount paid for an
  investment and the future cash flows the
  investment brings in

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NPV Equation

• In this formula t is the time of the cash flow, n
  the total time of the project, r the discount
  rate and C is the cash flow at that point in
  time.

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Example

• Launch a new consumer product?
• Cash flows for Year 1 2000
• Year 2 2000
• Year 3 4000
• Year 4 4000
• Year 5 5000
• Cost of Capital 10
• Production Cost 10,000

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Answer

• PV 2000/1.1 2000/1.12 4000/1.13
  4000/1.14 5000/1.15
• 12,313
• NPV 12313-10000 2313

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NPV of Physician Practice

• Lets say we have 1,000,000 to invest in either
  upgrading our physician practice or setting up a
  satellite clinic.
• For our practice, we would bring in
• 333,333 for 6 years with a capital cost of 10
• PV Factor is 4.3553
• Thus Answer - 1,000,000 NPV

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NPV of Satellite Clinic
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NPV Total

• Initial Investment 1,000,000
• PV of Cash Flows 1,499,202
• Net Present Value/SC 499,202
• Net Present Value/PP 451,765

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The Good and Bad

• Good ?
• Answers in , not years
• Accounts for cash flows
• Discounts cost of capital
• Bad ?
• Estimates are difficult to develop
• Discount rate not always determinable

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Profitability Index

• Equals NPV/Investment Cost
• Values greater than zero imply earnings are
  greater than discount rate
• Thus it should be funded.

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Average Accounting Return

• Average Net IncomeAverage Book Value
• Ignores time value, no meaningful economic sense

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Internal Rate of Return

• The Internal Rate of Return (IRR) is defined as
  the discount rate that makes the project have a
  zero Net Present Value (NPV).
• IRR is an alternative method of evaluating
  investments without estimating the discount rate.
  
• IRR takes into account the time value of money by
  considering the cash flows over the lifetime of a
  project. The IRR and NPV concepts are related but
  they are not equivalent.
• Trial Error insert different discount factors
  until sum equals zero
• The IRR uses the NPV equation as its starting
  point

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Equation
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Graph
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Equation
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• Calculate NPVs at different rates
• 0 164.56
• 5 100.36
• 10 46.15
• 15 0.00
• 20 -39.61
• 15 is IRR. Can we make 18?

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The Good and Bad

• Good ?
• Considers all relevant cash flows
• Time value of money based
• Widely used
• Bad ?
• Assumes reinvestment of proceeds at IRR
• Estimates difficult
• Can have multiple rates of return

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EAC

• In finance the equivalent annual cost (EAC) is
  the cost per year of owning and operating an
  asset over its entire lifespan.
• EAC is often used as a decision making tool in
  capital budgeting when comparing investment
  projects of unequal lifespans. For example if
  project A has an expected lifetime of 7 years,
  and project B has an expected lifetime of 11
  years it would be improper to simply compare the
  net present values (NPVs) of the two projects,
  unless neither project could be repeated.
• EAC is calculated by dividing the NPV of a
  project by the present value of an annuity
  factor. Equivalently, the NPV of the project may
  be multiplied by the loan repayment factor.

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Equivalent Annual Cost

• EAC PV of operating cost
• PV of investment cost
• PV of annuity

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Example

• A manager must decide on which sprinkler to
  purchase
• Sprinkler AInvestment cost 5,000Expected
  lifetime 10 yearsAnnual maintenance 500
• Sprinkler BInvestment cost 10,000Expected
  lifetime 20 yearsAnnual maintenance 200
• The cost of capital is 10.
• The EAC for sprinkler A is (5,000/A10,10)500T
  he EAC for sprinkler B is (10,000/A20,10)200
• Where A is the loan repayment factor for t years
  and 10 cost of capital.

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Example

• OR
• PV of operating costs of sprinkler A
• 500 X 6.145 3,073
• PV of investment
• 5000
• EAC
• 3,073 5,000/6.145 1,314

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Example

• PV of operating costs of sprinkler B
• 200 X 8.514 1,703
• PV of investment
• 10,000
• EAC
• 1,703 10,000/8.541 1,370
• THUS YOU CHOOSE A