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GLOBAL FINANCIAL MANAGEMENT

GLOBAL FINANCIAL MANAGEMENT. UNIT 4: Time Value of Money. TouchText. Fundamental Value Components of the Discount Rate Discounting and Valuation Valuing Growing Perpetuities, Perpetuities and Annuities. Problems and Exercises. Next. Investments: Time and Risk. Should I or Shouldn’t I ???.

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GLOBAL FINANCIAL MANAGEMENT

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  1. GLOBAL FINANCIAL MANAGEMENT UNIT 4: Time Value of Money TouchText Fundamental Value Components of the Discount Rate Discounting and Valuation Valuing Growing Perpetuities, Perpetuities and Annuities Problems and Exercises Next
  2. Investments: Time and Risk Should I or Shouldn’t I ??? Investing in a business, or a business investing in a project, necessarily involves time and risk. Thus, financial managers have to understand and value these. Dictionary Time: We prefer money NOW! Risk: We don’t like to take chances (Later) Money IN tomorrow ??? If the goal of financial managers is to maximize the value of a business, then we have to understand valuation. Money OUT today Back Next
  3. Money Today, Money Tomorrow Money today is worth more than money in the future. Why? Time preference – People naturally prefer to have money now. Inflation – Price increases mean that money in the future will buy less. Risk – The future necessarily involves unwanted risk. Dictionary $100 ten years in the future $100 today Back Next
  4. Investments Require Time By definition, Investments involve paying money out today in exchange for possible money in the future. Valuing any investment (or business) necessarily involves understanding how today’s certain money compares against future risky money. Dictionary Future Today time Investment Future Returns on Investment ??? ??? Money $$$$$ OUT today Back Next
  5. Discount Rate Because money loses value over time, money today cannot simply be added or subtracted from future money to determine value. Money is “translated” from one period of time to another period of time by using a Discount Rate (r). The discount rate can be thought of as a bank interest rate. Dictionary Example: r = 8%. Money deposited for 1 year. $100 today $108 in 1 year Back Next
  6. Components of the Discount Rate To focus on the mathematics of discounting, for now we ignore risk, and use a nominal risk-free discount rate “r” (also denoted “RFDR”). Dictionary Example 12% Risk-Adjusted Discount Rate (RADR) (compensation for risk) 8% Nominal Discount Rate (r) (expected inflation) 3% Real Discount Rate (r – E[i]) (natural time preference) Back Next
  7. The Discount Rate: Simplifying Assumptions Though none of the following is true in practice, we make the following simplifying assumptions about the discount rate “r”: Dictionary “r” borrowing = “r” lending: the discount rate used to value money from today to the future is the same discount rate to value future money in today’s terms. “r” is constant over time. There is no risk, so that “r” is a risk-free discount rate. r same, constant Back Next
  8. Investing/Saving Money $100 invested at r = 8% will become $108 in one year, and $116.64 in two years. Dictionary Year 1: $100 x (1 + r) = $100 x (1.08) = $108. Year 2: $100 x (1+ r) x (1 + r) = $100 x (1 + r)2 = $100 x (1.08)2 = $116.64. The process by which interest is earned on interest already earned is known as “compounding”. Invest/Save $100 Today $108 in 1 year …. Or ….. $116.64 in 2 years Back Next
  9. Mathematically, the Savings/Investment Process Creates an Equivalence Dictionary = = At r = 8%, $100 today = $108 in year 1 = $116.64 in year 2 Back Next
  10. Discounting “Discounting” is the process of calculating the value today of money to be received (or paid) in the future. Mathematically, it is the reverse of the savings/investment process. Dictionary At r = 8% $100 Today =$100/(1.08) $108 in Year 1 = $100 Today =$100/(1.08)2 = $100 Today $116.64 in Year 2 Back Next
  11. Notation: Cash Flows and Time As notation …. “C” is a cash flow (+ for cash in, - for cash out) A subscript for the time periods into the future. Time t = 0 is always today. t = 1 is for one time period into the future; t = 2 is for two time periods into the future, and so on. Dictionary C0 is today’s cash flow C1 is cash flow one time period into the future C2 is cash flow two time periods into the future Etc. Back Next
  12. What Is A Time Period? Normally, we can think of a time period as one year. However, a “time period” is determined by the future cash flows. For example, if we want to value a bond that pays coupon interest payments every six months, then six months (one half year) is the relevant time period. The discount rate must correspond to the relevant time period. Dictionary C0 C1 C2 C3 C4 0r1 1r2 2r3 3r4 Back Next
  13. Cash Flow Streams: Present Value (PV) A “stream” of cash flows is simply a series of cash flows at different times in the future. To value a cash flow stream, simply discount each cash flow to the present, and then add up all the Present Values (PVs) of those cash flows. Dictionary C1 C2 C3 C4 C5 Back Next
  14. Cash Flow Streams: Net Present Value (NPV) Most returns on investment are characterized by future cash flow streams. Subtracting the investment cost from the PV of the future cash flow stream gives us the Net Present Value (NPV). Dictionary -----------future---------- today C1 C2 C3 C4 C5 NPV = - INV0 + PV (future cash flow stream) Back Next
  15. General vs. Special Cash Flow Streams The general formula for valuing future cash flows is alwaysvalid. Dictionary However, sometimes the expected future cash flows follow a regular pattern that allows us to simplify the PV equation. This is particularly important – indeed, essential - when the cash flows are assumed to continue forever. Back Next
  16. Valuing a Growing Perpetuity A Perpetuity is constant cash flow stream that goes on forever. A Growing Perpetuity is a cash flow stream that grows at a constant rate “g” each period, forever. Dictionary The value of a growing perpetuity can be written as … forever The value of a growing perpetuity can be simplified as … *See, but don’t learn, proof (below) Back Next Proof
  17. Proof: Growing Perpetuity Formula Dictionary [same] Take Notes Back Next
  18. Valuing a Regular (Constant) Perpetuity A (regular, constant) Perpetuity has a constant cash flow stream that goes on forever. It can be viewed as a growing perpetuity with a growth rate of zero. Therefore, …. Dictionary Back Next
  19. Valuation: One Period Before First Cash Flow Caution! The (growing) perpetuity formula assumes that the first cash flow comes exactly one period into the future. Put another way, the value that is obtained from using the (growing) perpetuity formula will be the value as of one period before the first cash flow, whenever that cash flow might occur. Dictionary Value = C/r C CCCC ………. Back Next
  20. Example: Growing Perpetuity Find the value: Growing Perpetuity C1 = $120, g = 4%, r = 9% >>> Dictionary Back Next
  21. Example: Growing Perpetuity; First Cash Flow in Year 4 Find the value: Growing Perpetuity C1 = $120, g = 4%, r = 9%. when the first cash flow doesn’t come until year 4. Dictionary (Answer: The valuation formula (with result $2,400) is correct as of one period before the first cash flow (i.e. year 3). So, the $2,400 must be discounted by 3 years to get to today. >>> Back Next
  22. Annuities and Perpetuities An annuity is a constant stream of cash flows, but only for a finite period of time (T). Dictionary One way to think about an annuity is to think of it as (a) a perpetuity starting in time period (year) 1, (b) minus a perpetuity of the same amount that starts at year T + 1. Perpetuity (starting t = 1) This (less) Perpetuity (T + 1) Equals Annuity Back Next
  23. Valuing Annuities For an annuity of constant $”C” per period, for a total of “T” periods, at discount rate “r”… Dictionary First cash flow year 1, so PV0First cash flow year T + 1, so PVT Annuity PV = C x [annuity factor (r,T)] Back Next
  24. Annuity Valuation: Example Example: A person wins the lottery. The lottery winner is said to receive $5 million, but it is actually a series of 20 annual payments starting in 1 year, of $250,000 per year. If the discount rate is 6%, what is the value of this person’s winnings? Dictionary (Answer) Back Next
  25. Combining the Valuation Formulas The various valuation formulas provided above can be combined to suit any particular cash flow stream. Example: A particular government bond pays a coupon interest rate of 6% per year (= $60), at the end of each year, for the next 9 years. At the end of year 9, the bond owner receives his/her last interest payment, plus the $1,000 the par value of the bond. If the discount rate is 7%, then what is the value of the bond? Dictionary (answer) Back Next
  26. End of Unit 4 Questions and Problems The following problems require the calculation of various statistics using MS Excel. The problems are linked to actual Excel spreadsheets, where students should do their work. Dictionary Back Next
  27. End of Unit 4 Questions and Problems Dictionary Back Next
  28. End of Unit 4 Questions and Problems Dictionary Back End
  29. End of Unit 4 Questions and Problems Dictionary Back End
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