Capital Markets: Basic Instruments and their Valuation

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Capital MarketsBasic Instruments and their
Valuation
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Markets Overview

• Organizing a Business
• Capital Markets
• Stocks
• Bonds
• Bankruptcy
• Securities Valuation
• Time value of money overview
• PV, FV, annuities, NPV, IRR
• Efficiency

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Organizing a Business

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THE CAPITAL MARKETS
Agents who SUPPLY cash and DEMAND claims
Agents who DEMAND cash and SUPPLY claims

Cash
Households
Households
Intermediary
Businesses
Businesses
Government
Government
Claims to future Cash flows
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Bonds

• Bonds are IOUs
• In return for an upfront payment, you receive a
  promise to receive certain fixed payments into
  the future
• Essential components of a bond
• Maturity
• Frequency of payment
• Zero coupon bonds
• One payment made at maturity of the bond
• Coupon bonds
• Payment made at maturity plus bondholder receives
  regular payments called coupons. Most bonds pay
  coupons semi-annually, some (e.g. Eurobonds) pay
  annually
• Face value (par amount)
• Coupon rate

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Bonds contd.

• Consequences of non-payment
• Priority of claimants, in case of bankruptcy
• Seniority of bond claimants
• Preferred Shares
• Common Equity residual claimants

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Stocks

• A share of ownership in a corporation
• Stocks, share and equities are the same thing
• As owners, stockholders are entitled receive a
  share of the profits of the firm
• Shareholders have the right to vote on corporate
  decisions
• What are Preferred Shares?
• Primary (IPOs and SEOs) and Secondary Markets

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Financial Instruments
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Securities Valuation

• Do the cash flows of securities accrue at one
  time?
• Can we value securities as the sum of their cash
  flows?
• Is 1.00 today worth more to you than 1.00
  tomorrow?

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Securities Valuation contd

• Is 1.00 today worth more than 1.00 tomorrow?
• Yes (to most people)
• This is called the Time Value of Money

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Why is Time Value So Important?

• With a bond, I want to value what price I would
  pay today (PV) based on an anticipated stream of
  future payments (coupons and principal)
• With a preferred share, or common share I want to
  value what price I would pay today (PV) based on
  an anticipated stream of future dividends and
  anticipated future selling price
• Thus, all valuation of any asset is based on time
  value concepts!

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Time Value of Money Concepts

• Beer example
• Suppose you have 5 and I have no money
• Only one of us can buy a beer (costs 5)
• If I borrow from you today, how much would you
  want in return next year?

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Time Value (contd)

• Beer example
• Suppose you have 5 and I have no money
• Only one of us can buy a beer (costs 5)
• If I borrow from you today, how much would you
  want in return next year?
• Key issues
• price of beer next year?
• risk of me not paying?
• no beer for you today!

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Time Value (contd)

• Example 1
• Suppose no change in beer prices (i.e., 0
  inflation)
• Suppose no risk of me not paying you back
• Would you require a return? ? why?

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Time Value (contd)

• Example 1
• Suppose no change in beer prices (i.e., 0
  inflation)
• Suppose no risk of me not paying you back
• You may require, say, 5.25, or a 5 return ?
  why?
• your response implies a required rate of return
  ? an opportunity cost for giving up consumption
  today
• 5 today can be invested (e.g., buy a T-bill) to
  yield 5 next period in principal plus interest
  earned, r

"I'll gladly pay you Tuesday for a hamburger
today."
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Time Value (contd)

• Example 2
• Assume
• You want 10 real return as compensation for
  opportunity cost of giving up consumption today
  and risk of me not paying
• And, beer next year will be 5.10 ? 2 inflation
• How much cash will you require from the loan in
  one year?

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Time Value (contd)

• Example 2
• Beer next year will be 5.10 ? 2 inflation
• You also want 10 real return as compensation
  for opportunity cost of giving up consumption
  today and risk me not paying
• Total cash required in one year from loan
• 5.10 x (1.1) 5.61
• Nominal return on loan 5.61/5.00 1 12.2
• In general, let nom be the nominal return,
  real be the real return and inf be the
  inflation rate
• (1nom) (1real) x (1inf)

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Time Value (contd)

• Aside If we expand this relation
• 1 nom 1 real inf (real x inf)
• In most cases, real x inf is small (be careful
  in certain economies!), so this relation
  simplifies to the following Fisher equation
• nom real inf
• Note
• In virtually all cases in MBA1 we will be
  focusing on nominal cash flows and nominal rates
  of return

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Simple Compound Interest

• In 2003, you have 100,000 in an account and
  assume banks pay 3 nominal interest per year
• What will your account earn after 1 year?
• What about after 2 years? 5 years?

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Compounding Calculations
Definitions Future value (FV) is the amount to
which an investment will grow after earning
interest Simple interest is the interest earned
on the original investment Compound interest is
the interest earned on the interest
Compounding at 3 Interest Starting
Ending Year Balance Interest Balance
1 100.00 3.00 103.00 2
103.00 3.09 106.09 3 106.09
3.18 109.27 4 109.27 3.28
112.55 5 112.55 3.38 115.93
FV PV (1 r ) n
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Future Value Single Amount

• What is the future value (FV) in 5 years (n) of
  100 invested today (PV) at an annual compound
  rate (r) of 3
• (100) FV?
• --------------------------------------------
  ----------- r 3
• 0 1 2 3 4 5
• FV PV (1 r)n 100 x (1.03)5 115.93

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The Magic of Compounding

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Compounding Frequency

• Suppose you have 100 to invest and can put it in
  two accounts.
• Account A pays 5 interest every 6 months
• Account B pays 10 interest every year
• Which account is more desirable?
• . . . Problem 1

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Present Value

• Money in hand today has time value since 1 is
  worth more today than it is tomorrow
• Turn future value problem around
• How much do we need to invest today (PV) at 3
  (r) to have 100,000 in hand (FV) in 10 years
  (n)?

PV FV (1 r)n
FV PV (1 r ) n
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Present Value Single Amount

• How much money must be invested today (PV) to
  grow to 121 (FV) in 2 years (n) if the return on
  investment is 10 (r)?
• PV? 121
• ---------------------- r 10
• 0 1 2
• PV FV/(1r)n 121/(1.10)2 100

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The Magic of Present Value
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Annuities

• A nice feature of present value is that all cash
  flows in time are expressed in todays dollars,
  so you can add them up.
• An annuity is an investment that pays a fixed sum
  each period for a specified period of time
• Example An individual wishes to invest a certain
  amount of money today in a retirement fund that
  will return 10 annually. The individual wishes
  to be able to withdraw 100 (PMT) at the end of
  each of the next 3 years. How much must be
  invested today?
• 100 100 100
• ------------------------------- r
  10
• 0 1 2 3
• PVA?

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Annuities

• 100 100 100
• --------------------------------- r 10
• 0 1 2 3
• PV 100/(1.1) 100/(1.1)2 100/(1.1)3
  248.69
• In general, the present value of a 1 annuity is
• In previous example,
• PVA 100
  248.69

PVA 1 - 1 r
(1 r)n
1 - 1 0.10 (1.10)3
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Perpetuities

• A perpetuity is an annuity that never ends
• 1 1 1
• --------------------------------- . .
  . . r 10
• 0 1 2 3
• PVP?
• PV 1/(1.1) 1/(1.1)2 1/(1.1)3 . . .
• In general, the PV of a 1 perpetuity 1/r
• In this case, PVP 1/0.1 10

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Growing Perpetuity

• What is present value of cash flow that starts at
  1 and grows at 5 per year?
• 1 1.05 1.1025
• --------------------------------- . .
  . . r 10
• 0 1 2 3
• PVGP?
• PV 1/(1.1) 1.05/(1.1)2 1.1025/(1.1)3 .
  . .
• In general, the PV of a 1 growing perpetuity
  (rate g)
• PVGP 1/(r g)
• In this case, PVGP 1/(0.10 0.05) 20

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Time Value Applications NPV and IRR

• Suppose an investor is considering a cash outlay
  today of -C0 (i.e., cash outflow at time 0)
• The investor expects a cash inflow next period
  (at time 1) of C1 (e.g., bond matures or sells
  stock) but this expected cash flow is not certain
• The riskiness of such an investment should be
  reflected in the interest rate (or discount
  rate), r
• ? the greater the risk, the higher the rate

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Net Present Value (NPV)

• Given an outlay of -C0 today and an anticipated
  future cash flow of C1 and given a discount of
  r should the investment be undertaken?
• NPV is the net addition to wealth (accounting for
  risk) by investing in this
• Where, the appropriate discount rate, r, depends
  on the riskiness of the project
• NPV -C0 C1/(1r)

simple one-period example
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NPV Example

• What is the NPV of a project (or deal) which
  requires an investment of 80 today and provides
  an anticipated cash flow in one year of 100 if
  the appropriate discount rate is 10?
• NPV -80 100/(1.10) -80
  90.91
• 10.91

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NPV Example (continued)

• NPV rule accept any project that has an NPV
  greater than or equal to zero
• If NPV 0, then the investment is providing just
  enough compensation for the risk (e.g., if C0 in
  above example was 90.91) ? the return is then
  equal to the discount rate

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Internal Rate of Return (IRR)

• IRR is the discount rate, r, that makes the NPV
  just equal to zero
• NPV 0 -C0 C1/(1r)
• IRR is an alternative approach to the NPV method
  but usually provides consistent decisions
  compared to NPV
• IRR is often popular because all projects or
  investments can be compared on a basis (rather
  than basis)

IRR
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IRR Example

• A project (investment) requires an outlay of
  90.91 today and provides an anticipated cash
  flow of 100 in one year
• IRR ?
• 0 -90.91 100/(1r)
• 90.91 100/(1 r)
• (1 r) 100/90.91
• (1 r) 1.10
• r .10 or 10
• Using a spreadsheet use GoalSeek
• RATE(1, 0, -90.91, 100) 10

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IRR contd.

• IRR rule accept any project that has an IRR
  greater than or equal to the specified benchmark
  or hurdle rate or opportunity cost

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• . . . Problem 2
• The cash flows for a particular investment
  proposal are as follows
• Yr. 1 Yr. 1 Yr. 2 Yr. 3 Yr. 4
  Yr. 5
• -1,000 100 200 300 400
  500
• a). Using a discount rate of 10 percent,
  calculate the NET PRESENT VALUE for this project.
• b). Calculate the INTERNAL RATE OF RETURN (or
  effective yield) for the cash flows given in part
  (a).

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Key Learning Points

• Capital Markets
• Stocks and Bonds
• Security Characteristics?
• Bankruptcy
• How do you Value Assets?
• They are claims to Cash flows
• Time Value of Money
• PV, FV, Annuities, Perpetuities, NPV and IRR

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Bonds Nomenclature

• A COUPON BOND is a combination of an annuity (the
  annual or semi-annual coupon payments) and a zero
  coupon bond (with face value due at maturity).
• Example
• 15 year bond with 8 coupons (paid semi-annually)
  and 1000 par value.
• This coupon bond pays to the holder, 40 every
  six months for fifteen years
• At the end of fifteen years, the principal amount
  of 1000 is repaid with the final coupon payment
  of 40.

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Zero Coupons Bond

• A ZERO COUPON BOND, only pays the holder the
  principal or face value at maturity
• No interim payments (or coupons) are due prior to
  maturity,
• At maturity the entire face value is repaid
• The holder will typically have purchased this
  zero coupon bond for less than the face value
• Quite simply, a zero coupon bond is a
• ZERO COUPON BOND

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Zero Coupon Bonds Pricing
Price P (1r)T

• Where P is the bonds principle (or par value) due
  upon maturity, r is the required return and T is
  the time to maturity
• Example 91-day T-bill with 100 par value. The
  required return is 2 over this (one) 91-day
  period

Price 100 98.04 (10.02)
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Zero Coupon Bond Yields

• The yield to maturity (YTM) on a bond is simply
  the IRR for the bond
• Example
• The average bid price on 91-day T-bills is
  98.352 (i.e., this is the price today for the
  bills that will provide a cash flow of 100 in 91
  days)
• what is the YTM or IRR or T-bill rate?

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Zero Coupon Bond Yields contd.

• NPV 0 -C0 C1/(1r)
• 0 -98.352 100/(1r)
• 98.352 100/(1r)
• (1r) 100/98.352
• (1r) 1.0168
• r 1.0168 1
• r .0168 or 1.68 which is a 91-day rate
• Using a spreadsheet
• RATE(1, 0, -98.352, 100) 0.0168

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Zero Coupon Bond Yields contd.

• What is the effective annual rate of return?
• (1.0168)365/91 1 0.0691 or 6.91
• What rate would be quoted?
• By convention, annualize (using simple interest)
• 1.68 x (365/91) 6.72

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Coupon Bond Pricing
Example 15 year bond with 8 coupons (paid
semi-annually) and 1000 par value. Suppose, the
required return is 5 every six months

Price 40 x 1- (1.05)-30 1000
846.28 0.05
(1.05)30
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Coupon Bond Yields

• What is the YTM of a 2-year bond which has a
  price today of 100 and pays semi-annual coupons
  of 5 (i.e., has a coupon rate of 10)?
• NPV 0 -C0 C1/(1r) C2/(1r)2
  C3/(1r)3 C4/(1r)4 PRINC/(1r)4
• 0 -100 5/(1r) 5/(1r)2 5/(1r)3
  5/(1r)4 100/(1r)4
• r 0.05 or 5
• Spreadsheet method
• Yield rate (4, 5, -100, 100) 0.05
• Effective annual rate 1.052 -1 .1025 or
  10.25
• Quoted Bond yield (annualized) 10

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Bond Chart Example

• Issuer coupon maturity ask
  price ask yield
• US Govt 6.00 Oct 08 99.0625 3.33

current price ()
coupon rate is 6 of 100 face 3 paid every 6
months
current YTM ()
final coupon and 100 face paid then
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Appendix B Market Efficiency

• How does this INTRINSIC value relate to the
  market price?
• i.e. how efficient are markets?

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Excel Functions

• FV(Rate, Nper, Pmt, Pv, Type)
• ? future value (single or annuity)
• type0 default if payments at end of period 1
  if at start
• PV(Rate, Nper, Pmt, Fv, Type)
• ? present value (single or annuity)
• note type0 default if payments at end of
  period 1 if at start
• NPV(Rate, Value1)
• ? present value of a stream
• while this function is called NPV, it is
  actually doing a PV calculation!

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Excel Functions

• IRR(Values, Guess)
• ? internal rate of return of a stream
• Guess default is 0.1 or 10 and is
  generally not required
• RATE(Nper, Pmt, Pv, Fv, Type)
• ? implied rate (single or annuity)
• sometimes an alternative to IRR function
• Know when to use (and interpret) positive or
  negative numbers!

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From Previous Examples

• What is the future value (in 5 years) of 100
  invested at an annual compound rate of 3?
• Using a spreadsheet
• FV(0.03, 5, 0, -100) 115.93
• How much money must be invested today to grow to
  121 in 2 years if the return on investment is
  10?
• Using a spreadsheet
• PV(0.10, 2, 0, 121) - 100
• An individual wishes to invest a certain amount
  of money today in a retirement fund that will
  return 10 annually. The individual wishes to be
  able to withdraw 100 at the end of each of the
  next 3 years. How much must be invested today?
• Using a spreadsheet
• PV(0.10,3,100,0) -248.69