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Texas Instrument BA II Plus

Texas Instrument BA II Plus. Guide to TVM, Bond Valuation, and Stock Valuation. Calculator Guide for Time Value of Money The First Step: Resetting to Factory default and. T=0 T=1 T=2 T=3 . . . T=N-1 T=N. PMT. PMT. PMT. PMT. PMT. PV.

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Texas Instrument BA II Plus

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  1. Texas Instrument BA II Plus Guide to TVM, Bond Valuation, and Stock Valuation

  2. Calculator Guide for Time Value of Money The First Step: Resetting to Factory default and ...

  3. T=0 T=1 T=2 T=3 . . . T=N-1 T=N . . . PMT PMT PMT PMT PMT PV Periodic Interest Rate: I/Y FV Five Keys: N, I/Y, PV, PMT, FV • All TVM calculations deal with Five variables: • N: Maturity (years) • I/Y: Interest per Year (%) • PV: Present Value • PMT: Annuity, Periodic Payment • FV: Future Value • Translate all TVM problems in terms of the five variables Always Remember To CLEAR MEMORIES: 2nd + QUIT + 2nd + CLR TVM

  4. FV, Yield, N • If you deposit $1,000 today and earn 10% per year, what will be the amount in five years? N I/Y PV PMT FV 5 10 -1000 0 ? = 1610.51 • If you deposit $1,000 today and your deposit is expected to grow to $1,611.51 in five years, what is the yield? N I/Y PV PMT FV 5 ? =10 -1000 0 1610.51 • If you deposit $1,000 today and your deposit is expected to grow to $1,611.51 at 10% per year, how many years do you have to keep the money at the bank? N I/Y PV PMT FV ? =5 10 -1000 0 1610.51

  5. PV, and PV of An Annuity • The bank is offering 15% return on your deposit. If you want to have $1,000 in 20 years, how much do you have to deposit today? N I/Y PV PMT FV 20 15 ? 0 1000 = - 61.10 • If you receive $1,000 at the end of each year for the next five years, what is the PV of this annuity? Assume a discount rate of 10%. N I/Y PV PMT FV 5 10 ? 1000 0 = - 3,790.79

  6. An Annuity: FV, Yield • If you deposit $1,000 at the end of each year for the next five years, and if you earn 10% per year, how much will you have accumulated in five years? N I/Y PV PMT FV 5 10 0 -1000 ? = 6,105.10 • If you deposit $1,000 at the end of each year for the next five years, and if you will have accumulated $6,105.10, what is the interest rate? N I/Y PV PMT FV 5 ? 0 -1000 6,105.10 = 10

  7. An Annuity: PMT, N • If you borrow $3,790.79 and promise to pay an equal amount annually for the next five years, what will be the annual payment if the interest rate is 10% N I/Y PV PMT FV 5 10 3,790.79 ? 0 = -1,000 • If you borrow $3,790.79 at 10% per year interest rate and promise to pay $1,000 per year, how many years do you have to pay for? N I/Y PV PMT FV ? 10 3,790.79 -1000 0 = 5

  8. Ordinary Annuity: PMT at the END of each period 1 2 3 . . . N-1 N PMT PMT PMT . . . PMT PMT PV FV Annuity Due: PMT at the BEGINNING of each period 1 2 3 . . . N -1 N PMT PMT PMT PMT . . . PMT FV PV Ordinary Annuity vs Annuity Due

  9. Annuity Due: Payment at the beginning of each period • If you leased your building at $150,000 per year for 10 years, what is the PV of the lease if the discount rate is 15%? First set the payment at the BEGINNING by using the following key combination: 2nd QUIT 2nd BGN 2nd SET 2nd QUIT (the display should showBGN) N I/Y PV PMT FV 10 15 ? 150,000 0 = -865,737.59 After the calculation, remember to reset the payment at END of each period: 2nd QUIT 2nd BGN 2nd SET 2nd QUIT (the display should show nothing)

  10. The cash flows of the bond issued by ABC co. 0 1 2 . . . . 10 $90 P ? $90 $90 + $1,000 yield = 7% (0.07) Bond Valuation - Annual Payment ABC Company issued a 10-year $1,000 bond. Coupon rate is 9% and paid annually and the $1,000 principal will be paid at the end of the tenth year. If the yield on a comparable bond is 7%, what will be the price of the bond? Calculator: i) Set P/Y = 1 using the key combination: 2nd, P/Y, 1, ENTER , 2nd, QUIT ii) Enter the data: 2nd, CLR TVM N I/Y PV PMT FV 10 7 ? 90 1,000 = -1,140.47

  11. The cash flows of the bond issued by ABC co. 0 1 2 . . . . 10 $90 1,140.47 $90 $90 + $1,000 yield ? Bond Yield - Annual Payment ABC Company issued a 10-year $1,000 bond. Coupon rate is 9% and paid annually and the $1,000 principal will be paid at the end of the tenth year. If the price of the bond is $1,140.47, what will be the yield to maturity? Calculator: i) Set P/Y = 1 using the key combination: 2nd, P/Y, 1, ENTER , 2nd, QUIT ii) Enter the data: 2nd, CLR TVM N I/Y PV PMT FV 10 ? -1,140.47 90 1,000 = 7.00

  12. The cash flows of the bond issued by ABC co. 0 1 2 . . . . 20 $45 P ? $45 $45 + $1,000 yield = 7% (0.07), semi-annual yield = 3.5% Bond Valuation - Semi-annual Payment ABC Company issued a 10-year $1,000 bond. Coupon rate is 9% and paid semi-annually and the $1,000 principal will be paid at the end of the tenth year. If the yield on a comparable bond is 7%, what will be the price of the bond? Calculator: i) Set P/Y = 1 using the key combination: 2nd, P/Y, 1, ENTER , 2nd, QUIT ii) Enter the data: 2nd, CLR TVM N I/Y PV PMT FV 20 3.5 ? 45 1,000 = -1,142.12

  13. The cash flows of the bond issued by ABC co. 0 1 2 . . . . 20 $45 1,142.12 $45 $45 + $1,000 yield ? Bond Yield - Semi-annual Payment ABC Company issued a 10-year $1,000 bond. Coupon rate is 9% and paid semi-annually and the $1,000 principal will be paid at the end of the tenth year. If the price of the bond is $1,142.12, what is the yield on the bond? Calculator: i) Set P/Y = 1 using the key combination: 2nd, P/Y, 1, ENTER , 2nd, QUIT ii) Enter the data: 2nd, CLR TVM N I/Y PV PMT FV 20 ?-1,142.12 45 1,000 = 3.50 Semi-annual rate: Thus it is 3.5x2 =7% /year

  14. Stock Valuation: Constant Dividend • Common stocks have no maturity. (The price of a share) = PV (all future dividends) • Special Case 1: Constant dividends DIV1=DIV2=.......=DIV This is just an ordinary perpetuity. Therefore, the price of a share is: Example: If XYZ Co. is expected to pay out dividends at $2 per year, what is the price of the stock assuming the discount rate is 10%. ANS: P0 = $2 / 0.1 = $20

  15. Stock Valuation: Growing Dividend • Special Case 2: Gordon Model Dividends expected to grow at constant rate, g < r: DIVt = DIV0 (1+g) t , t = 1 - 4 This is just a growing perpetuity. Therefore, the price of a share is: Example: Company A expects dividends $2 next year growing at 10% per year in subsequent years and the discount rate is 15%. What is the stock price for A today? Ans:Apply Gordon Model PA = 2/(0.15 - 0.10) = $40

  16. Stock Valuation: Variable Growth Dividend Example: The dividends for ABC stock are: DIV1 = $5, growing at g1=25%/year for three years and at g2 = 4% thereafter. The discount rate is r=12%. What is the price at t=0, P0?

  17. $1,705.48 i = 10% 0 1 2 3 $600 $400 $1,000 Calculator Guide for Uneven CF’sTexas Instruments BAII PLUS Example: UNEVEN CASH FLOWS Find the PV of a stream of cash flows (CFs): $1,000 in year 1, $600 in year 2, and $400 in year 3 assuming a discount rate of 10%.

  18. $19,393.65 i = 10% 0 1 2 3 4 5 6 $5,000 $5,000 $5,000 $5,000 $3,000 $4,000 CF1CF2=5000CF3 repeated 4 times Calculator Guide for TVM, Repeated CF’sTexas Instruments BAII PLUS Example: UNEVEN CASH FLOWS with repeated portion Find the PV of a stream of cash flows (CFs): $3,000 in year 1, $5,000 per year in years 2 to 5, and $4,000 in year 6 assuming a discount rate of 10%.

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