1 / 41

Principles of Business Finance Fin 510

Principles of Business Finance Fin 510. Dr. Lawrence P. Shao Marshall University Spring 2002. CHAPTER 6 Time Value of Money. Future value Present value Rates of return Amortization. Time line for uneven CFs -$50 at t = 0 and $100, $75, and $50 at the end of Years 1 through 3. 0. 1. 2.

anevay
Download Presentation

Principles of Business Finance Fin 510

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Principles of Business FinanceFin 510 Dr. Lawrence P. Shao Marshall University Spring 2002

  2. CHAPTER 6Time Value of Money • Future value • Present value • Rates of return • Amortization

  3. Time line for uneven CFs -$50 at t = 0 and $100, $75, and $50 at the end of Years 1 through 3. 0 1 2 3 i% -50 100 75 50

  4. What’s the FV of an initial $100 after 3 years if i = 10%? 0 1 2 3 10% 100 FV = ? Finding FVs is compounding.

  5. After 1 year: FV1 = PV + INT1 = PV + PV (i) = PV(1 + i) = $100(1.10) = $110.00. After 2 years: FV2 = PV(1 + i)2 = $100(1.10)2 = $121.00.

  6. After 3 years: FV3 = PV(1 + i)3 = 100(1.10)3 = $133.10. In general, FVn = PV(1 + i)n

  7. Three Ways to Find FVs • Use a financial calculator. • Use future value table. • Use future value formula. FVn = PV(1 + i)n. There are 4 variables. If 3 are known, you can solve for the 4th.

  8. What’s the PV of $100 due in 3 years if i = 10%? Finding PVs is discounting, and it’s the reverse of compounding. 0 1 2 3 10% 100 PV = ?

  9. Solve FVn = PV(1 + i )n for PV: 3 1 ö æ ( ) ÷ PV = $100 = $100 PVIF ç ø è i, n 1.10 ( ) = $100 0.7513 = $75.13.

  10. If sales grow at 20% per year, how long before sales double? Solve for n: FVn = 1(1 + i)n; 2 = 1(1.20)n Use FVIF formula to solve. Solution: 3.8 years

  11. What’s the difference between an ordinaryannuity and an annuitydue? Ordinary Annuity 0 1 2 3 i% PMT PMT PMT Annuity Due 0 1 2 3 i% PMT PMT PMT

  12. What’s the FV of a 3-year ordinary annuity of $100 at 10%? 0 1 2 3 10% 100 100 100 110 121 FV = 331

  13. What’s the PV of this ordinary annuity? 0 1 2 3 10% 100 100 100 90.91 82.64 75.13 248.68 = PV

  14. What is the PV of this uneven cashflow stream? 4 0 1 2 3 10% 100 300 300 -50 90.91 247.93 225.39 -34.15 530.08 = PV

  15. Will the FV of a lump sum be larger or smaller if we compound more often, holding the stated I% constant? Why? LARGER! If compounding is more frequent than once a year--for example, semiannually, quarterly, or daily--interest is earned on interest more often.

  16. 0 1 2 3 10% 100 133.10 Annually: FV3 = 100(1.10)3 = 133.10. 0 1 2 3 4 5 6 0 1 2 3 5% 100 134.01 Semiannually: FV6 = 100(1.05)6 = 134.01.

  17. We will deal with 3 different rates: iNom = nominal, or stated, or quoted, rate per year. iPer = periodic rate. EAR = EFF% = . effective annual rate

  18. iNom is stated in contracts. Periods per year (m) must also be given. • Examples: • 8%; Quarterly • 8%, Daily interest (365 days)

  19. Periodic rate = iPer = iNom/m, where m is number of compounding periods per year. m = 4 for quarterly, 12 for monthly, and 360 or 365 for daily compounding. • Examples: 8% quarterly: iPer = 8%/4 = 2%. 8% daily (365): iPer = 8%/365 = 0.021918%.

  20. Effective Annual Rate (EAR = EFF%): The annual rate which causes PV to grow to the same FV as under multi-period compounding. Example: EFF% for 10%, semiannual: FV = (1 + iNom/m)m = (1.05)2 = 1.1025. EFF%= 10.25% because (1.1025)1 = 1.1025. Any PV would grow to same FV at 10.25% annually or 10% semiannually.

  21. How do we find EFF% for a nominal rate of 10%, compounded semiannually?

  22. EAR = EFF% of 10% EARAnnual = 10%. EARQ = (1 + 0.10/4)4 - 1 = 10.38%. EARM = (1 + 0.10/12)12 - 1 = 10.47%. EARD(360) = (1 + 0.10/360)360 - 1 = 10.52%.

  23. Can the effective rate ever be equal to the nominal rate? • Yes, but only if annual compounding is used, i.e., if m = 1. • If m > 1, EFF% will always be greater than the nominal rate.

  24. When is each rate used? iNom: Written into contracts, quoted by banks and brokers. Not used in calculations or shown on time lines.

  25. iPer: Used in calculations, shown on time lines. If iNom has annual compounding, then iPer = iNom/1 = iNom.

  26. FV of $100 after 3 years under 10% semiannual compounding? Quarterly? mn i æ ö Nom FV = PV 1 . + ç ÷ è ø n m 2x3 0.10 æ ö FV = $100 1 + ç ÷ è ø 3S 2 = $100(1.05)6 = $134.01. FV3Q = $100(1.025)12 = $134.49.

  27. Amortization Construct an amortization schedule for a $1,000, 10% annual rate loan with 3 equal payments.

  28. Step 1: Find the required payments. 0 1 2 3 10% -1,000 PMT PMT PMT 3 10 -1000 0 INPUTS N I/YR PV FV PMT OUTPUT 402.11

  29. Step 2: Find interest charge for Year 1. INTt = Beg balt (i) INT1 = $1,000(0.10) = $100. Step 3: Find repayment of principal in Year 1. Repmt = PMT - INT = $402.11 - $100 = $302.11.

  30. Step 4: Find ending balance after Year 1. End bal = Beg bal - Repmt = $1,000 - $302.11 = $697.89. Repeat these steps for Years 2 and 3 to complete the amortization table.

  31. BEG PRIN END YR BAL PMT INT PMT BAL 1 $1,000 $402 $100 $302 $698 2 698 402 70 332 366 3 366 402 37 366 0 TOT 1,206.34 206.34 1,000 Interest declines. Tax implications.

  32. $ 402.11 Interest 302.11 Principal Payments 0 1 2 3 Level payments. Interest declines because outstanding balance declines. Lender earns 10% on loan outstanding, which is falling.

  33. Amortization tables are widely used--for home mortgages, auto loans, business loans, retirement plans, etc. They are very important! • Financial calculators (and spreadsheets) are great for setting up amortization tables.

  34. On January 1 you deposit $100 in an account that pays a nominal interest rate of 10%, with daily compounding (365 days). How much will you have on October 1, or after 9 months (273 days)? (Days given.)

  35. iPer = 10.0% / 365 = 0.027397% per day. 0 1 2 273 0.027397% ... FV = ? -100 273 ( ) FV = $100 1.00027397 273 ( ) = $100 1.07765 = $107.77.

  36. Now suppose you leave your money in the bank for 21 months, which is 1.75 years or 273 + 365 = 638 days. How much will be in your account at maturity?

  37. iPer = 0.027397% per day. 0 365 638 days ... ... -100 FV = 119.10 FV = $100(1 + .10/365)638 = $100(1.00027397)638 = $100(1.1910) = $119.10.

  38. You are offered a note which pays $1,000 in 15 months (or 456 days) for $850. You have $850 in a bank which pays a 7.0% nominal rate, with 365 daily compounding, which is a daily rate of 0.019178% and an EAR of 7.25%. You plan to leave the money in the bank if you don’t buy the note. The note is riskless. Should you buy it?

  39. iPer = 0.019178% per day. 0 365 456 days ... ... -850 1,000 Ways to Solve: 1. Greatest future wealth: FV 2. Greatest wealth today: PV

  40. 1. Greatest Future Wealth Find FV of $850 left in bank for 15 months and compare with note’s FV = $1,000. FVBank=$850(1.00019178)456 =$927.67 in bank. Buy the note: $1,000 > $927.67.

  41. 2. Greatest Present Wealth Find PV of note, and compare with its $850 cost: PV = $1,000/(1.00019178)456 = $916.27. PV of note is greater than its $850 cost, so buy the note.

More Related