B40'2302 Class

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B40.2302 Class 2

• BM6 chapters 4, 5, 6
• Based on slides created by Matthew Will
• Modified 9/18/2001 by Jeffrey Wurgler

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Principles of Corporate Finance Brealey and Myers
Sixth Edition

• The Value of Common Stocks

• Slides by
• Matthew Will, Jeffrey Wurgler

Chapter 4

• The McGraw-Hill Companies, Inc., 2000

Irwin/McGraw Hill
3
Topics Covered

• How To Value Common Stock
• Capitalization Rates
• Stock Prices and EPS
• Cash Flows and the Value of a Business

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Stocks Stock Market

• Common Stock - Ownership shares in a publicly
  held corporation.
• Secondary Market - Market in which
  previously-issued securities are traded.
• Dividend - Periodic cash distribution from the
  firm to the shareholders.
• P/E Ratio - Price per share divided by earnings
  per share.

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Stocks Stock Market

• Book Value - Net worth of the firm according to
  the balance sheet.
• Liquidation Value - Net proceeds that would be
  realized by selling (liquidating) all assets and
  paying off all creditors.
• Market Value Balance Sheet Balance sheet that
  uses market value of assets and liabilities
  (instead of the usual accounting value).

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Valuing Common Stocks

• Expected Return - The percentage gain that an
  investor forecasts from a specific investment
  over a set period of time. Sometimes called the
  market capitalization rate.

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Valuing Common Stocks

• Expected return can be broken into two parts
• Dividend Yield Capital Appreciation

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Valuing Common Stocks

• Dividend Discount Model - Model of todays stock
  price which states that share value equals the
  present value of all expected future dividends.
• H - Time horizon for your investment.

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Valuing Common Stocks

• Example
• Current forecasts are for XYZ Company to pay
  annual cash dividends of 3, 3.24, and 3.50 per
  share over the next three years, respectively.
  At the end of three years you expect to sell your
  share at a market price of 94.48. What should be
  the price of a share today with a 12 expected
  return?

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Valuing Common Stocks

• No Growth DDM
• If we forecast no growth, and plan to hold our
  stock indefinitely, then we can value the stock
  as a perpetuity.

Assumes all earnings are paid to shareholders. So
Div EPS each year. No retentions, no growth.
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Valuing Common Stocks

• Constant Growth DDM - A version of the dividend
  growth model in which dividends grow at a
  constant rate g.
• When you use the growing perpetuity formula to
  value a stock, you are using the Gordon Growth
  Model.

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Valuing Common Stocks

• Example
• If a stock is selling for 100 in the stock
  market, what might the market be assuming about
  the growth rate of dividends?

Answer The market is assuming the dividend will
grow at 9 per year, indefinitely.
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Valuing Common Stocks

• Example continued
• Suppose in the same example you knew g was 9
  per year, but didnt know r. What is the markets
  estimate of r?

Answer The market has set r at 12 per year.
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Valuing Common Stocks

• If the board elects to pay a lower dividend, and
  reinvest the remainder, the stock price may
  increase because future dividends may be higher.
• Payout Ratio - Fraction of earnings paid out as
  dividends.
• Plowback Ratio - Fraction of earnings retained or
  plowed back into the firm.
• Payout Ratio Plowback Ratio 1

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Valuing Common Stocks

• An accounting return measurement

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Valuing Common Stocks

• Instead of asking an analyst, growth can be
  derived from applying the return on equity to the
  percentage of earnings plowed back into
  operations.
• g Plowback Ratio x ROE

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Valuing Common Stocks

• Example
• We forecast a 5.00 dividend next year, which
  represents 100 of earnings. This will provide
  investors with a 12 expected return. Instead,
  we decide to plow back 40 of the earnings at the
  firms current accounting return on equity of
  20. What is the value of the stock before and
  after the plowback decision?

No Growth (DivEPS)
With Growth (DivltEPS)
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Valuing Common Stocks

• Example - continued
• With the no growth policy, the stock price is
  41.67. With the plowback / growth policy, the
  price rose to 75.00.
• The difference between these two numbers
  (75.00-41.6733.33) is called the Present Value
  of Growth Opportunities (PVGO).

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Valuing Common Stocks

• Present Value of Growth Opportunities (PVGO) Net
  present value of a firms future investments.
• Sustainable Growth Rate - Steady rate at which a
  firm can grow without new external capital ROE x
  Plowback Ratio.

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EPS, P/E, and share price

• Under a no-growth policy, DivEPS, so
• In general, share price capitalized value of
  average earnings under no-growth policy, plus
  PVGO

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EPS, P/E, and share price

• Rearranging,
• EPS/P ratio underestimates r if PVGO gt 0
• Growth stocks sell at high P/E ratios because
  PVGO is high.

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FCF and PV

• Free Cash Flows (FCF) are the theoretical basis
  for all PV calculations.
• FCF is more relevant than EPS.
• FCFt cash inflowst cash outflowst
• PV(firm) PV(FCF)

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FCF and PV

• Valuing a Business
• The value of a business is often computed as the
  present value of FCF out to a valuation horizon
  (H).
• The value at H is sometimes called the terminal
  value or horizon value

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FCF and PV

• Example
• Given the cash flows for Concatenator
  Manufacturing Division, calculate the PV of near
  term cash flows, PV (horizon value), and the
  total value of the firm. r10 and g 6

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FCF and PV

• Example - continued
• .

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Principles of Corporate Finance Brealey and Myers
Sixth Edition

• Why Net Present Value Leads to Better
  Investment Decisions than Other Criteria

• Slides by
• Matthew Will, Jeffrey Wurgler

Chapter 5

• The McGraw-Hill Companies, Inc., 2000

Irwin/McGraw Hill
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Topics Covered

• NPV and its Competitors
• The Payback Period
• The Book Rate of Return
• Internal Rate of Return
• Capital Rationing what to do?
• Profitability Index
• Linear Programming

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NPV and Cash Transfers

• Evaluating projects requires understanding the
  flows of cash.

Cash
Investment opportunities (real assets)
Investment opportunities (financial assets)
Firm
Shareholder
Invest
or pay dividend
so shareholders invest for themselves
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Payback

• The payback period of a project is the time it
  takes before the cumulative forecasted cash
  inflow equals the initial outflow.
• The payback rule says only accept projects that
  payback within some set time frame.
• This rule is common but very flawed.

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Payback

• Example
• Examine the three projects and note the mistake
  we would make if we insisted on only taking
  projects with a payback period of 2 years or less.

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Book Rate of Return

• Book Rate of Return An accounting measure of
  profitability. Also called accounting rate of
  return.
• Note the components reflect tax and accounting
  figures, not market values or cash flows.

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Internal Rate of Return

• The Internal Rate of Return is the discount rate
  that makes the projects NPV 0.
• IRR rule is to accept a project if the IRRgtcost
  of capital.
• Example
• You can purchase a machine for 4,000. The
  investment will generate 2,000 and 4,000 in
  cash flows in the next two years. What is the
  IRR on this investment?

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Internal Rate of Return
IRR28
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Internal Rate of Return

• Pitfall 1 - Strange cash flow patterns
• With some cash flows the NPV of the project
  increases as the discount rate increases.
• This is contrary to the normal relationship.

NPV
Discount Rate
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Internal Rate of Return

• Pitfall 1 Strange cash flow patterns
• Example where IRR gets it wrong for this reason

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Internal Rate of Return

• Pitfall 2 - Multiple Rates of Return (even
  stranger CF patterns)
• Some cash flow patterns can generate NPV0 at two
  different IRRs!
• The following cash flow generates NPV0 at both
  (-50) and 15.2.

NPV
1000
IRR15.2
500
Discount Rate
0
-500
IRR-50
-1000
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Internal Rate of Return

• Pitfall 2 - Multiple Rates of Return
• Example where IRR gets it wrong for this reason

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Internal Rate of Return

• Pitfall 3 - Mutually Exclusive Projects
• IRR ignores the scale of the project.

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Internal Rate of Return

• Pitfall 4 Flat Term Structure Assumption
• IRR has problems when the term structure isnt
  flat.
• In this case, wed need to compare the project
  IRR with the expected IRR (yield to maturity)
  offered by a traded security that
• Has equivalent risk
• Has same time-pattern of cash flows
• At this point easier to calculate NPV!

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Internal Rate of Return

• Even calculating IRR can be hard. Financial
  calculators can perform this function easily,
  though. In the previous example,

HP-10B EL-733A BAII Plus -350,000 CFj -350,000
CFi CF 16,000 CFj 16,000 CFfi 2nd CLR
Work 16,000 CFj 16,000 CFi -350,000
ENTER 466,000 CFj 466,000 CFi 16,000
ENTER IRR/YR IRR 16,000
ENTER 466,000 ENTER IRR CPT
All produce IRR12.96
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Profitability Index

• When resources are limited (capital is
  constrained or rationed) the profitability
  index (PI) provides a tool for selecting among
  various project combinations and alternatives.
• The highest weighted-average PI can indicate the
  right plan in these circumstances.

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Profitability Index

• Example
• We only have 300,000 to invest. Which do we
  select?
• Proj NPV Investment PI
• A 230,000 200,000 1.15
• B 141,250 125,000 1.13
• C 194,250 175,000 1.11

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Linear Programming

• Maximize Cash flows or NPV
• Minimize costs
• Example
• Max NPV 21Xa 16 Xb 12 Xc 13 Xd
• subject to
• 10Xa0 5Xb0 5Xc0 0Xd0 lt 10
• -30Xa1 - 5Xb1 - 5Xc1 40Xd1 lt 12

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Principles of Corporate Finance Brealey and Myers
Sixth Edition

• Making Investment Decisions with the Net
  Present Value Rule

• Slides by
• Matthew Will, Jeffrey Wurgler

Chapter 6

• The McGraw-Hill Companies, Inc., 2000

Irwin/McGraw Hill
45
Topics Covered

• What To Discount
• IMC Project
• Project Interaction
• Timing
• Equivalent Annual Cost
• Replacement
• Cost of Excess Capacity
• Fluctuating Load Factors

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What To Discount

• Only Cash Flow is Relevant

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What To Discount

• Do not confuse average with incremental.
• Treat inflation consistently.
• Include all incidental effects.
• Do not forget working capital requirements.
• Forget sunk costs.
• Include opportunity costs.
• Beware of allocated overhead costs.

Points to watch out for
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IMCs Guano Project

• Revised projections (000s) reflecting inflation

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IMCs Guano Project
Cash flow analysis (1000s)
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IMCs Guano Project

• NPV (using nominal cash flows)

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IMCs Guano Project

• Tax depreciation allowed under the modified
  accelerated cost recovery system (MACRS) -
  (Figures in percent of depreciable investment).

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Optimal timing

• Even projects with positive NPV may be more
  valuable if deferred.
• The relevant NPV is then the current value of
  some future value of the deferred project.

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Optimal timing

• Example
• You may harvest a set of trees at anytime over
  the next 5 years. Given the FV of delaying the
  harvest, which harvest date maximizes current
  NPV?
• ? Harvesting in year 4 is optimal. And relevant
  NPV is 68.3.

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Equivalent Annual Cost

• Equivalent Annual Cost - The cost per period with
  the same present value as the cost of buying and
  operating a machine.

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Equivalent Annual Cost

• Example
• Given the following costs of operating two
  machines and a 6 cost of capital, select the
  lower-cost machine using equivalent annual cost
  method.
• Costs by year
• Machine 0 1 2 3 PV_at_6 EAC
• A 15 5 5 5 28.37 10.61
• B 10 6 6 21.00 11.45

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Machinery Replacement
Annual operating cost of old machine
8 Cost of new machine
Year 0 1 2 3
NPV _at_ 10 15 5 5
5 27.4 Equivalent
annual cost of new machine 27.4/(3-year
annuity factor at, say, 10) 27.4/2.5 11

Do not replace until operating cost of old
machine exceeds 11.
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Cost of Excess Capacity (?)
A project requires warehouse space and this
causes a need for a new one to be built in Year 5
rather than Year 10. A warehouse costs 100
lasts 20 years. Equivalent annual cost _at_ 10
100/8.5 11.7 0 . . . 5 6
. . . 10 11 . . . With project
0 0 11.7 11.7
11.7 Without project 0 0 0
0 11.7 Difference 0
0 11.7 11.7 0 PV
extra cost . . .
27.6
11.7 11.7 11.7
(1.1)6 (1.1)7 (1.1)10
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Fluctuating Load Factors

• You operate in a seasonal business. Your two
  old machines have a capacity of 1,000 units/year.
  Half the year, you operate at 50 capacity. The
  other half, at 100 capacity.
• The operating expenses of your old machines is
  2/unit.
• Discount rate is 10.

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Fluctuating Load Factors

• Could replace with two new machines which have
  1/unit cost

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Fluctuating Load Factors
Third (better) option Replace just one machine.
New machine has low operating cost, so operate it
all year. Keep old machine for peak demands.