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MBA1 - FINANCE

MBA1 - FINANCE. CRAIG DUNBAR http://www.ivey.uwo.ca/faculty/CDunbar/CDpersonal.htm COURSE PAGE http://www.ivey.uwo.ca/faculty/CDunbar/Finance1_2004.htm. Administrative issues. Materials Textbooks/readings are complementary to cases/classes Supplements

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MBA1 - FINANCE

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  1. MBA1 - FINANCE CRAIG DUNBAR http://www.ivey.uwo.ca/faculty/CDunbar/CDpersonal.htm COURSE PAGE http://www.ivey.uwo.ca/faculty/CDunbar/Finance1_2004.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 (cont’d) • 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 (cont’d) • 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/(1+r)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 don’t 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) type=0 default if payments at end of period; =1 if at start • =PV(Rate, Nper, Pmt, Fv, Type)  present value (single or annuity) note type=0 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 investment’s 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 (1+r)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 1+0.02

  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/(1+r) $98.352 = $100/(1+r) (1+r) = $100/$98.352 (1+r) = 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/h15/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/(1+r) + C2/(1+r)2 + C3/(1+r)3 + C4/(1+r)4 + PRINC/(1+r)4 100 = $5/(1+r) + $5/(1+r)2 + $5/(1+r)3 +$5/(1+r)4 + $100/(1+r)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 Gov’t 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 Rates:Comparing Yields at Different Maturities Yield x x Gov’t of Canada Bonds x 1 Year 20 Years 5 Years Maturity . . . Problems 5 and 6

  45. Term Structure of Interest Rates:Relationship with the Business Cycle Typical Shapes Yield Peak Normal Expansion Trough Maturity

  46. Term Structure of Interest Rates:Interest 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)(1+r) (1+r) = (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 Rates:Interest Rate Forecasting • Assuming “unbiased expectations” (i.e., the market doesn’t systematically overestimate or underestimate future rates), we can determine anymarket 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 t=0 t=1 t=2 t=3

  49. Preferred Share Valuation (cont’d) PV = C1/(1+r) + C2/(1+r)2 + C3/(1+r)3 + C4/(1+r)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%

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