University of Provence

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University of Provence

• Earle Traynham
• Professor and Dean
• College of Business Administration
• University of North Florida
• Jacksonville, Florida USA
• February 2002

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University of Provence

• First Principles of Valuation
• Future Value of Compounding
• Present Value and Discounting
• PV and FV of Multiple Cash Flows
• Valuing Level Cash Flows Annuities and
  Perpetuities

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University of Provence

• II. Valuing Stocks and Bonds
• Bonds and Bond Valuation
• Common Stock Valuation
• Net Present Value and Other Investment Criteria
• Opportunity Cost

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University of Provence

• III. Capital Budgeting Cash The Majestic Mulch
  and Compost Company
• IV. Acquisitions and Divestitures

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• Future Value of Compounding
• Investing in a single period
• FV P(1r) 1 Where P Principal invested, and r
  the interest rate on the investment
• What is value of 500 invested for 1 year at 10
• FV 500(1.10)1 500(1.1)1 500(1.10) 550

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• Future Value and Compounding
• Investing for More Than One Period
• FV P(1r)t Where t the number of periods in
  the future
• What is the FV of 500 invested for 2 years at
  10
• FV 500(1.10)2 500(1.21) 605

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• Present Value and Discounting
• PV FV/(1r)t, Where r is the discount rate for
  t periods in the future
• PV for Single Period of Time
• PV 70,000/(10.12)1 62,500
• PV for Multiple Periods of Time
• PV 100,000/(1.075)8 100,000/1.7835)
  56,070

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• The Rule of 72
• Approximate time (in years) required to double
  an investment
• FV/PV 2.0, take 72/r
• Example
• How long will it take a 10,000 investment to
  reach 20,000 at 8?
• 72/8 9 years (actual 9.006 years)

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The Present and Future Value of Multiple Cash
Flows

• Future Value compound the accumulated value
  period by period, or calculate FV of each cash
  flow and sum them
• Example assume you deposit 2000 today, 1000 in
  one year, and 3000 in 2 years all _at_ 8.
  Calculate FV

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The Future Value of Multiple Cash Flows

• Calculate FV of each cash flow and sum
• FV (2000)(1.08)3 (1000)(1.08)2
  (3000)(1.08)1 2519.42 1166.40 3240
  6925.82

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FV - compound the accumulated value period by
period

• Time period 0 2000
• Time period 1 (2000)(1.08) 1000 3160
• Time period 2 (3160)(1.08) 3000 6412.80
• Time period 3 6925.82

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The Present Value of Multiple Cash Flows

• Discount each amount to time period 0, and sum
  them
• Discount back one period at a time, summing as
  you go
• Example What is present value of 1000 per year
  (at end of year) for 5 years, at 6?

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PV Discount each amount to time period 0, and
sum

• PV (1000)/(1.06)1 (1000)/(1.06)2
  (1000)(1.06)3 (1000)(1.06)4 (1000)(1.06)5
  943.40 890 839.62 792.09 747.26
  4212.37

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PV Discount back one period at at time, summing
as you go

• End of year 5 1000
• End of year 4 (1000)/(1.06) (1000)
  1943.40
• End of year 3 (1943.40)/(1.06) (1000)
  2833.40
• End of year 2 (2833.40)/(1.06) (1000)
  3673.01
• End of year 1 (3673.01)/(1.06) (1000)
  4465.11
• Year 0 (4465.01)(1.06) 4212.36

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Example you need 1200 one year from now, 1500
after two years, and 2000 after 3 years. How
much will you have to deposit today _at_ 8

• PV (1200)/(1.08)1 (1500)/(1.08)2
  (2000)/(1.08)3 1111.11 1286.01 1587.66
  3984.78

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Annuities a series of constant cash flows that
occur at regular intervals for a fixed number of
periods

• Present Value of an annuity
• 1
• 1 -
  (1r)t
• APV C x
• r

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Future Value of an annuity

• (1 r)t - 1
• AFV C x
• r

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Present Value of a Perpetuity

• PV C/r
• APV, as t goes to infinity
• C x (1-0) C/r
• r

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Bonds and Bond Valuation

• Bond features
• Terms refers to the number of years to maturity
• Face value the principle payment at maturity
  date
• Coupon interest specified rate of interest
  based on face value.

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Bond Values and Yield

• Market Value of Bond PV of all coupon payments
  plus principle repayment discounted at
  opportunity cost for similar bonds
• Example - 1000 bond, with 9 coupon rate, with
  interest payable each October 1 and April 1, to
  be issued 4/1/2002 and a maturity date of 4/1/2022

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Bond Valuation

• If market rate of interest 9, then bond market
  value 1000
• If market rate of interest 12, then
• PV 45 45 45 45 1000
• (1.06) (1.06)2 (1.06)3 (1.06)40
  (1.06)40
• This may be solved using the short-cut equation
  for the present value of an annuity

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Bond Discounted Yield to Maturity

• The discounted rate of return (yield) is that
  rate that equates the PV of the expected bond
  cash flows to the current market price (P0)
• In this case, you know the bonds features and
  you know its current market price. You want to
  know its effective yield

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Bond Yield to Maturity

• Example A 9, 10 year bond with face value of
  1000 currently sells for 920. What is the
  effective yield?
• P0 920 90 90 90 1000
• (1r) (1r)2 (1r)10 (1r)10
• Solve for r, using the present value of an
  annuity equation

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Bond Prices

• Bonds will sell at Face Value when the market
  rate of interest for similar bonds is equal to
  the coupon rate of interest on the bond
• Bonds will sell at a Discount when similar bonds
  have higher yields
• Bonds will sell at a Premium when similar bonds
  have lower yields

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The Interest Rate Risk of Bonds

• Bond prices vary inversely with market interest
  rates. Bond price falls as market interest rates
  rise, and vice-versa.
• Example 12-year bond with 10 coupon rate,
  purchased at face value of 1000. Two years
  later, the market rate for 10 year bonds is 14.
  What is market price of bond?

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Bond Price and Market Interest

• 10
• P0 ?100/(10.14)n 1000/(1.14)10
• n1
• P0 100 x 1 (1/1.14)10 1000
• .14
  (1.14)10
• P0 545.27 236.63 781.90

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Total Bond Value

• Total Bond Value Annuity Present Value of
  Coupons Present Value of Face Value
• TBV C x 1-1/(1YTM)t/YTM
• F x 1/(1YTM)t , where YTM yield to
  maturity on bonds in this risk class

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Common Stock Valuation

• Same principles as Present Value of Bonds, with
  qualifications
• Uncertainty of future cash flows in the forms of
  dividends and share price
• Difficulty in determining appropriate discount
  rate

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Zero Growth Case

• PVperpetuity D/r , where D is constant
  dividend, and r is your opportunity cost or
  discount rate

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Constant Growth Case

• P0 D0(1g) D1
• r-g r-g
• where g is the constant growth rate and r is
  your opportunity cost or discount rate
• This equation works as long as rgtg.

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Non-Constant Growth Case

• Where dividend growth rate changes during the
  period of evaluation
• Each growth period must be calculated separately,
  i.e., becomes a series of Constant Growth Case
  Calculations

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Investment Criteria

• Net Present Value the difference, in present
  value, between amount invested and the sum of the
  future cash flows resulting from the investment
• Net Present Value Rule an investment
  opportunity is worthwhile (economically) if the
  NPV is positive, at the required rate of return

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Investment Criteria - continued

• Payback Period the length of time until the
  accumulated investment cash flows
  (non-discounted) equal the original investment,
  i.e., how long to get your money back
• Payback Period Rule accept an investment if it
  pays back original investment within acceptable
  length of time
• Shortcomings timing of cash flows is ignored
  cash flows after payback ignored no objective
  period for choosing cut-off period

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Investment Criteria - continued

• The Average Accounting Return average net
  income attributed to an investment divided by the
  average book value of the assets
• AAR Rule an investment is acceptable if the AAR
  exceeds a specified target level
• Deficiencies ignores time value of money
  accounting income not necessarily related to cash
  flow accounting return may not be related to
  market rates and is arbitrary

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Opportunity Cost

• Required Rate of Return the rate an investor
  can earn elsewhere in the financial markets on
  investments of similar risk
• The higher the risk the higher the required
  return
• Two types of risk systematic and non-systematic

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Opportunity Cost - continued

• Firms usually rely on both debt and equity
  sources of funds
• RD refers to the cost (interest rate) of debt
• RE refers to the cost of equity the rate of
  return required by investors to let you use their
  money

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Opportunity Cost - continued

• Estimating the Cost of Capital requires
  assessing the cost of equity
• RE Rf ß(Rm Rf) , where Rf risk-free
  rate ß measure of sytematic risk of particular
  investment Rm average market rate of interest

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Opportunity Cost - continued

• Weighted Average Cost of Capital
• WACC REXE RDXD(1-t) , where
• XE and XD are respective proportions of equity
  and debt and t tax rate on corporation

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Capital Budgeting important terms

• Incremental Cash Flows only incremental cash
  flows are relevant. Sunk costs are irrelevant to
  the decision. Opportunity costs are any cash
  flow that is lost or forgone, and represent an
  incremental cash flow. Incremental Net working
  capital represent an incremental cash flow.
• Net Working Capital (NWC) Cash Inventory
  (Accounts Receivable Accounts Payable)
• Financing Costs are separate from the
  investment decision and are not part of the
  projects cash flows

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Majestic Mulch and Compost Company

• Selling Price 120/unit for first 3 years, then
  110/unit thereafter
• Starting NWC 20,000 plus 15 of sales
• Variable Costs 60/unit
• Fixed Costs 25,000/year
• Capital Equipment Costs 800,000 initial
• Depreciation Rate MACRS 7 year property
• Equipment Salvage Value 20 or 160,000 in year
  8
• Do we do it?

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Majestic Mulch and Compost Company

• Net Present Value 65,488
• Internal Rate of Return 17.24
• Payback 4.08 years
• Average Accounting Return 11.0

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Acquisitions and Divestitures

• Far less than half of acquisitions create value
  for the acquirers
• Successful acquisitions require excellence in
  three areas strategic fit, acquisition
  economies, successful strategy for integration

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Premium Recapture Characteristics

• Undermanagement
• Synergy
• Restructuring
• Financing and Tax Considerations
• Undervalued Assets

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Divestitures

• Unprofitable
• Strategic Misfit
• Need the cash