MBA1 - FINANCE

1
MBA1 - FINANCE

• CRAIG DUNBAR
• http//www.ivey.uwo.ca/faculty/CDunbar/CDpersonal.
  htm
• COURSE PAGE
• http//www.ivey.uwo.ca/faculty/CDunbar/Finance1_20
  04.htm

2
Administrative issues

• Materials
• Textbooks/readings are complementary to
  cases/classes
• Supplements
• Excel spreadsheets provided for data intensive
  cases
• See my class web site for additional material
• Office hours
• Open door (email is best)

3
Class participation grading

• Class-by-class record of participation
• 0 negative contribution
• 1 present but no meaningful contribution
• 2 some meaningful contribution
• 3 superior contribution
• No evaluation for lectures (or mini-lectures)
• Aggregation
• Approximate rule 1 meaningful contribution every
  3 classes should lead to a median grade

4
Finance cases and the operation of the class

• Case preparation
• You can spend a lot of time preparing cases
• The assignment questions can guide you but . . .
• Make a decision!
• Spreadsheet skills are important
• Group work is key (rely on each other)
• In-class
• Some discussion of current (finance) events
• Case discussion
• Sum up / roadmap

5
Security Valuation
6
Security Valuation Overview

• Time value of money overview
• Basic concepts PV, FV, annuities,
• Excel function overview
• Security applications
• Bonds
• price and yield relationships
• term structure of interest rates
• Preferred shares

7
The Time Value of Money

• Companies invest in real assets by raising
  capital to finance their purchase with the hope
  that they generate cash flows that can repay
  capital and retain profits
• These cash flows and capital outlays take place
  at different dates and we need mechanisms to
  trade off value of dollars today against dollars
  tomorrow
• 1.00 today is worth more than 1.00 tomorrow
• 1.00 today can be invested (e.g., buy a T-bill)
  to yield 1.00 next period in principal plus
  interest earned, i or r

"I'll gladly pay you on Tuesday for a hamburger
today."
8
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?
• How much money would you want next year in return
  for making this loan?
• Key issues
• price of beer next week?
• no beer for you today!
• risk of me not paying?

9
Time Value of Money Concepts (contd)

• Example
• 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 r be the nominal return, R be the
  real return and i be the inflation rate
• (1 r) (1 R) x (1 i)

10
Time Value of Money Concepts (contd)

• Expanding this relation
• 1 r 1 R i R x i
• In most cases, R x i is small (be careful in
  certain economies!), so this relation simplifies
  to the following Fisher equation
• r R i
• Note
• In all cases in MBA1 we will be focusing on
  nominal cash flows and nominal rates of return

11
Future Value 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?

12
Compounding Calculations
Definitions Future value 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
13
Future Value Single Amount

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

14
The Magic of Compounding

15
Compounding Frequency

• Suppose you have 100 to invest and can put in 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

16
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 at 3 today to have
  100,000 in hand in 10 years?
• The calculation of the discount factor

FV PV (1 r ) n
PV FV (1 r ) n
17
Present Value Single Amount

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

18
The Magic of Present Value
19
Present Value of Multiple Cash Flows

• Investment A pays 100 each year for the next 2
  years
• 100 100
• ----------------------
• 0 1 2
• If the required return on investment is 10, how
  much would you pay today?
• Investment alternatives
• Buy investment B that pays 100 one year from now
• PV 100 (1 0.1) -1 90.91
• Buy investment C that pays 100 two years from
  now
• PV 100 (1 0.1) -2 82.64

20
Present Value of Multiple Cash Flows

• Total price to purchase investments B and C
  173.55
• Price of investment A must be 173.55 since
  payoff to investment A is the same as what you
  get from buying investments B and C
• What if the price of investment A was not
  173.55?
• You could create an arbitrage trading strategy
• In well functioning markets, arbitrage
  opportunities are so good, we dont expect they
  can exist (at least not for long!)
• General principal present value of multiple cash
  flow is the sum of the present value of
  individual components

21
Annuities

• 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 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?

22
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
23
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

24
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

25
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!

26
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

27
Internal Rate of Return (IRR)

• IRR is the discount rate, r, that equates the
  present value of the cash flows from an
  investment with the investments purchase price
• Example An investment provides an anticipated
  cash flow of 100. The current price of the
  investment is 90.01.
• IRR ?
• 90.91 100/(1 r)
• (1 r) 100/90.91 1.10
• r .10 or 10

28
Excel Functions

• IRR(Values, Guess)
• ? internal rate of return of a stream
• usually use 0.1 as Guess or leave
  blank
• RATE(Nper, Pmt, Pv, Fv, Type)
• ? implied rate (single or annuity)
• sometimes an alternative to IRR function
• From previous example,
• IRR RATE(1, 0, -90.91, 100) 10

29
Bonds

• Bonds are IOUs
• In return for an upfront payment, you receive a
  promise to receive certain fixed payments into
  the future
• 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

30
Zero Coupon Bond Pricing
Price P (1r)n

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

Price 100 98.04 10.02
31
Zero Coupon Bond Yields

• The yield to maturity (YTM) on a bond is simply
  the IRR for the bond
• Example
• The average bid 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?

32
Zero Coupon Bond Yields

• C0 C1/(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

33
Zero Coupon Bond Yields

• What is the effective annual rate of return?
• (1.0168)365/91 1 0.069108 or 6.9108
• What rate would be quoted?
• Annualize using simple interest
• 1.68 x (365/91) 6.72

34
Short-Term Interest Rates Examples

• t-bill yield, e.g., 91-day rate ? issued by
  government
• bank rate ? central bank rate lending to banks
• bankers acceptance (BAs), e.g., 3-month ?
  guaranteed by chartered banks
• commercial paper, e.g., 3-month ? corporate
  borrowing (typically unsecured)
• prime rate ? chartered bank lending to best
  customers
• typically move together (but not lockstep)

35
Canadian Treasury Bills 3 Month

• Recent data
• 22 Sep 2004 2.41
• 29 Sep 2004 2.45
• 6 Oct 2004 2.50
• 13 Oct 2004 2.51
• 20 Oct 2004 2.55
• 27 Oct 2004 2.57

Source - http//www.bankofcanada.ca/en/tbill.htm
36
3 Month Corporate Paper

• Recent Data
• 28 Oct 2004  2.6500
• 29 Oct 2004  2.6500
• 1 Nov 2004  2.6600
• 2 Nov 2004  2.6800
• 3 Nov 2004  2.6800

Source - http//www.bankofcanada.ca/en/monmrt.htm
37
Govt. of Canada Benchmark Bond Yields 10 Year

• Latest 5 business days
• 28 Oct 2004  4.49
• 29 Oct 2004  4.47
• 1 Nov 2004  4.50
• 2 Nov 2004  4.48
• 3 Nov 2004  4.47

Source - http//www.bankofcanada.ca/en/bonds.htm
38
US Selected Interest Rates
Source - http//www.federalreserve.gov/releases/h1
5/update/
39
Coupon Bond Pricing
A coupon bond is a combination of an annuity (the
annual or semi-annual coupon payments) and a zero
coupon bond (with par value due at maturity).
Example 15 year bond with 8 coupons (paid
semi-annually) and 1000 par value. The required
return is 5 every six months

Price 40 x 1- (1.05)-30 1000
846.28 0.05
(1.05)30
40
Coupon Bond Price Changes Three Relationships

• Bond prices move inversely to interest rates (or
  yields)
• Long-term bond prices fluctuate more than
  short-term bond prices for a given change in
  overall interest rates
• High coupon bonds have lower percentage price
  changes than low coupon bonds for a given change
  in interest rates
• . . . Problem 2

41
An Example Interest Rate and Maturity Effects
for an 8 Coupon Bond
42
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)?
• C0 C1/(1r) C2/(1r)2 C3/(1r)3
  C4/(1r)4
• PRINC/(1r)4
• 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

43
Bond Chart Example

• Issuer coupon maturity ask price ask yield
• US Govt 6.00 Oct 08 99.0625 3.33
• Problem 3

current price ()
coupon rate is 6 of 100 face 3 paid every 6
months
current YTM () based on semi- ann
compounding also the interest rate
final coupon and 100 face paid then
44
Term Structure of Interest RatesComparing
Yields at Different Maturities
Yield
x
Govt of Canada Bonds
x
x
1 Year
20 Years
5 Years
Maturity
. . . Problems 5 and 6
45
Term Structure of Interest RatesRelationship
with the Business Cycle
Typical Shapes
Yield
Peak
Normal Expansion
Trough
Maturity
46
Term Structure of Interest RatesInterest Rate
Forecasting

• When would an investor be indifferent between
  these two alternatives
• (a) invest for 2 years at 10.5 per year or
• (b) invest for 1 year at 10 for next year at
  r
• (1)(1.105)(1.105) (1)(1.10)(1r)
• (1r) (1 0.11)
• r 0.11 or 11
• If the one-year rate in one year is 11, the
  investor will be just as well-off (indifferent)
  under either alternative

47
Term Structure of Interest RatesInterest Rate
Forecasting

• Assuming unbiased expectations (i.e., the
  market doesnt systematically overestimate or
  underestimate future rates), we can determine any
  market expectation of future rates
• In general, if the yield curve is upward sloping,
  then interest rates are anticipated to increase
• But, if you expected rates to be 11 one year
  from now and you have a two year investment
  horizon, would you take investment alternative
  (a)?

48
Preferred Share Valuation

• a preferred share typically represents a claim on
  a perpetual stream of dividends
• The price of the pref. represents the present
  value, PV, of these dividend payments,
  DIV,discounted at the required return of the
  preferreds, r or rp

PV
DIV
DIV
DIV
r rp
t0
t1
t2
t3
49
Preferred Share Valuation (contd)

• PV C1/(1r) C2/(1r)2 C3/(1r)3
  C4/(1r)4 ...
• DIV/(1 rp) DIV/(1 rp)2 DIV/(1
  rp)3 ...
• Since the cash flows represent a perpetuity, this
  formulation simplifies to
• PV DIV / rp
• What is the price of a perpetual preferred share
  if the (annual) dividend, DIV, is 2.50, and
  required return, rp, is 6?
• PV DIV / rp
• 2.50 / 0.06
• 41.67

50
Preferred Share Example BMO(as of Oct. 16/03)

• Bank of Montreal Class B series 3 prefs
• dividends per share 1.39
• required return 5.26 (what is this related
  to?)
• current price DIV/ rp 1.39/0.0526 26.42
• note 10-year Canadian government bond yield
  4.96