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- 1. The Time Value of Money Topic 03 GSB711 – Managerial Finance Reading: Chapter: The Time Value of Money (Pages 108 – 152) Questions: 3, 4, 5, 6, 10, 11, 12 and 18 Problems: 22, 25, 27, 34, 35, 36, 40, 44, 46, 48, 50, 55, 59, 63, 68, 76, and 80.
- 2. Topics Covered Future Values and Compound Interest Present Values Multiple Cash Flows Level Cash Flows Perpetuities and Annuities Effective Annual Interest Rates Inflation & Time Value
- 3. Future Values Future Value - Amount to which an investment will grow after earning interest. Compound Interest - Interest earned on interest. Simple Interest - Interest earned only on the original investment.
- 4. Future Values Example - Simple Interest Interest earned at a rate of 6% for five years on a principal balance of $100. Interest Earned Per Year = 100 x .06 = $ 6
- 5. Example - Simple Interest Interest earned at a rate of 6% for five years on a principal balance of $100. Today Future Years 12345 Interest Earned Value 100 Future Values 6 106 6 112 6 118 6 124 6 130 Value at the end of Year 5 = $130
- 6. Example - Compound Interest Interest earned at a rate of 6% for five years on the previous year’s balance. Interest Earned Per Year =Prior Year Balance x .06 Future Values
- 7. Example - Compound Interest Interest earned at a rate of 6% for five years on the previous year’s balance. Today Future Years 12345 Interest Earned Value 100 Future Values 6 106 6.36 112.36 6.74 119.10 7.15 126.25 7.57 133.82 Value at the end of Year 5 = $133.82
- 8. Future Values Future Value of $100 = FV
- 9. Future Values Example - FV What is the future value of $100 if interest is compounded annually at a rate of 6% for five years?
- 10. Future Values with Compounding Interest Rates
- 11. Manhattan Island Sale Peter Minuit bought Manhattan Island for $24 in 1626. Was this a good deal? To answer, determine $24 is worth in the year 2008, compounded at 8%. FYI - The value of Manhattan Island land is well below this figure.
- 12. Present Values Present Value Value today of a future cash flow. Discount Factor Present value of a $1 future payment. Discount Rate Interest rate used to compute present values of future cash flows.
- 13. Present Values
- 14. Present Values Example You just bought a new computer for $3,000. The payment terms are 2 years same as cash. If you can earn 8% on your money, how much money should you set aside today in order to make the payment when due in two years?
- 15. Present Values Discount Factor = DF = PV of $1 Discount Factors can be used to compute the present value of any cash flow.
- 16. The PV formula has many applications. Given any variables in the equation, you can solve for the remaining variable. Time Value of Money(applications)
- 17. Present Values with Compounding Interest Rates
- 18. Value of Free Credit Implied Interest Rates Internal Rate of Return Time necessary to accumulate funds Time Value of Money(applications)
- 19. Example Your auto dealer gives you the choice to pay $15,500 cash now, or make three payments: $8,000 now and $4,000 at the end of the following two years. If your cost of money is 8%, which do you prefer? PV of Multiple Cash Flows
- 20. Present Values $8,000 $4,000 $ 4,000 Present Value Year 0 4000/1.08 4000/1.082 Total = $3,703.70 = $3,429.36 = $15,133.06 Year 0 1 2 $8,000
- 21. Perpetuities & Annuities
- 22. PV of Multiple Cash Flows PVs can be added together to evaluate multiple cash flows.
- 23. Perpetuity A stream of level cash payments that never ends. Annuity Equally spaced level stream of cash flows for a limited period of time. Perpetuities & Annuities
- 24. Perpetuities & Annuities PV of Perpetuity Formula C = cash payment r = interest rate
- 25. Perpetuities & Annuities Example - Perpetuity In order to create an endowment, which pays $100,000 per year, forever, how much money must be set aside today in the rate of interest is 10%?
- 26. Perpetuities & Annuities Example - continued If the first perpetuity payment will not be received until three years from today, how much money needs to be set aside today?
- 27. Perpetuities & Annuities PV of Annuity Formula C = cash payment r = interest rate t = Number of years cash payment is received
- 28. Perpetuities & Annuities PV Annuity Factor (PVAF) - The present value of $1 a year for each of t years.
- 29. Perpetuities & Annuities Example - Annuity You are purchasing a car. You are scheduled to make 3 annual installments of $4,000 per year. Given a rate of interest of 10%, what is the price you are paying for the car (i.e. what is the PV)?
- 30. Perpetuities & Annuities Applications Value of payments Implied interest rate for an annuity Calculation of periodic payments Mortgage payment Annual income from an investment payout Future Value of annual payments
- 31. Perpetuities & Annuities Example - Future Value of annual payments You plan to save $4,000 every year for 20 years and then retire. Given a 10% rate of interest, what will be the FV of your retirement account?
- 32. Effective Interest Rates Effective Annual Interest Rate - Interest rate that is annualized using compound interest. Annual Percentage Rate - Interest rate that is annualized using simple interest.
- 33. Effective Interest Rates example Given a monthly rate of 1%, what is the Effective Annual Rate(EAR)? What is the Annual Percentage Rate (APR)?
- 34. Effective Interest Rates example Given a monthly rate of 1%, what is the Effective Annual Rate(EAR)? What is the Annual Percentage Rate (APR)?
- 35. Inflation - Rate at which prices as a whole are increasing. Nominal Interest Rate - Rate at which money invested grows. Real Interest Rate - Rate at which the purchasing power of an investment increases. Inflation
- 36. Inflation Annual U.S. Inflation Rates from 1900 - 2007 Annual Inflation, %
- 37. Inflation approximation formula
- 38. Example If the interest rate on one year govt. bonds is 6.0% and the inflation rate is 2.0%, what is the real interest rate? Inflation
- 39. Inflation Remember: Current dollar cash flows must be discounted by the nominal interest rate; real cash flows must be discounted by the real interest rate.
- 40. Summary Time has value Future Value – Compounding Present Value – Discounting Multiple Cash Flows Perpetuities Annuities Effective Annual Rate and Annual Percentage Rate Inflation and time value - Consistency

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