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Time Value of Money Chapter 5

Time Value of Money Chapter 5. Future and Present Values Loan Amortization, Annuities Financial Calculator. Time Value of Money. Four Critical Formulas Future Value: value tomorrow of $1 invested today. Present Value: value today of $1 to be received “tomorrow”.

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Time Value of Money Chapter 5

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  1. Time Value of MoneyChapter 5 Future and Present Values Loan Amortization, Annuities Financial Calculator Chapter 2

  2. Time Value of Money • Four Critical Formulas • Future Value: value tomorrow of $1 invested today. • Present Value: value today of $1 to be received “tomorrow”. • Future Value of an Annuity: value several periods from now of a stream of $1 investments. • Present Value of an Annuity: value today of a stream of $1 payments to be received for a set number of future periods. Chapter 2

  3. Important TVM Concepts A. Future Value 1. What $1 invested today should grow to over time at an interest rate i. 2. FV = future value, P = principal, i = int. rate. a. I = interest (dollar amount), I = P  i 3. Single interest:FV = P + I = P + P(i) = P(1+i) 4. Multiple Interest Periods: FVi,n = P (1+i)n b. (1+i)n = Future Value Interest Factor c. FVi,n = P  FVIFi,n Chapter 2

  4. Important TVM Concepts B. Present Value; 1. The value today of $1 to be received tomorrow. 2. Solving the Future Value Equation for PV; a. PV = FV  (1+i) single period discounting. b. PV = FV  (1+i)n multi-period discounting. c. PV = FV  (1+i)-n common form. d. (1+i)-n = Present Value Interest Factor. e. PVIF = 1 / FVIF (and vice-versa for same i, n) Chapter 2

  5. Important TVM Concepts • Future Value of an Annuity (FVA) e.g. Retirement Funds: IRA, 401(k), Keough 1. A series of equal deposits (contributions) over some length of time. 2. Contributions are invested in financial securities; stocks, bonds, or mutual funds. 3. The future value of accumulation is a function of the number and magnitude of contributions, reinvested interest, dividends, and undistributed capital gains. FVA = PMT * FVIFA Chapter 2

  6. Important TVM Concepts • Present Value of an Annuity (PVA) • Insurance Annuities a. Provide recipient with a regular income (PMT) for a set period of time. • The present value (PV) of the payments to be received is the price of the insurance annuity. • PVA = PMT * PVIFA 2. Types of Annuities: a. Ordinary Annuity: payments received at end-of-period. b. Annuity Due: payments received at beginning-of-period Chapter 2

  7. Important TVM Concepts • Annuitize Investment Accumulations • We have accumulated a sum of money and now desire to begin a series of [N] regular payouts: e.g. monthly checks • We assume accumulated funds will continue to earn some rate of return (I/YR) • The accumulation is treated as the present value (PV). • How much income (PMT) will a certain accumulated amount produce? Chapter 2

  8. Computing FVA • FVA formula: 1. FVA = P  ([(1+i)n - 1]  i) = P  FVIFA [(1+i)n - 1]  i = future value interest factor for an annuity or FVIFAi,n. 1. Assumption; steady return rate over time and equal dollar amount contributions. Chapter 2

  9. Computing PVA • PVA formula: 1. PVA = P  ([1 - (1+i)-n]  i) = P  PVIFA [1 - (1+i)-n ]  i = present value interest factor for an annuity or PVIFAi,n. 1. Assumption; constant return rate over time and equal dollar amount distributions. Chapter 2

  10. Current Law A. Traditional and Roth IRAsContribution limits for Traditional and Roth IRAs will rise from $2000 to $5,000 between 2002 and 2008. After 2008, the limit may be adjusted annually for inflation. Tax Year Limit 2002-2004 $3,000 2005-2006 $4,000 2008 $5,000 2009-2010 Indexed to Inflation Chapter 2

  11. Current Law B. 401(k), 403(b), and 457 PlansThese limits are on pretax contributions to certain employer- sponsored retirement plans. Remember that employers have the option of imposing lower limits than the government maximums, which will rise to $15,000 by 2006. Tax Year Limit 2002 $11,000 2003 $12,000 2004 $13,000 2005 $14,000 2006 $15,000 2007-2010 Indexed to Inflation Chapter 2

  12. Sample IRA Problem • Suppose you want to know how much an IRA (individual retirement account) plan will grow to if you deposit $5,000 per year (the maximum under current law) or $416.67 per monthevery month for the next 20 years or 240 monthly deposits. We’ll assume monthly compounded interest and annual rate of 7 percent (7% per annum). • What is the Future Value of the Accumulation (FVA)? Chapter 2

  13. Future Value of an Accumulation 1. Clear the TVM registers; BAII+: press [2nd], then [FV] (CLR TVM) HP10B: press [YK] [INPUT] (CLEAR ALL) 2. Set the Periods per year register BAII+: Press [2nd] [I/Y] for the P/Y function; enter 12, then press [ENTER] [2nd] [CPT] to QUIT this subroutine. HP10B: enter 12, press [YK] [PMT] (P/YR) Chapter 2

  14. Future Value of an Accumulation 3. Enter 240, press [N]. 4. Enter 7, press [I/Y]; interest rate per annum. 5. Enter 416.67, then [+/-] and then [PMT]. 6. BAII+: Press [CPT] then [FV]; 217,054.51 (display) HP10B: Press [FV]: 217,054.51 display (display) Don't clear the values yet. We're going to use them in the next problem. Chapter 2

  15. Future Value of an Accumulation • What effect does an extra 10 years of $416.67 deposited per month have on the FVA? The FVA after 30 years of monthly savings... • BAII+: Enter 360, press [N] Press [CPT] [FV]; $508,325.31 (display) HP10B: enter 360, press [N] Press [FV]: $508,325.31 (display) b. =c. The total deposits are 416.67 * 360 = $150,001.20. The other $358,324.11 is the accumulated interest. Chapter 2

  16. Future Value of an Accumulation • What effect does the rate of return have on the size of the accumulation? Suppose the interest rate was 12%, what is the FVA? a. Enter 12, press [I/Y]. b. BAII+: Press [CPT] [FV]; $1,456,246.71 HP10B: Press [FV]: $ 1,456,246.71 • The FVA if we assume 30 years of monthly deposits of 416.67 accumulating at 12% per annum compounded monthly. Chapter 2

  17. Tax-Deferred Retirement Savings B. Other Types of Retirement Savings Plans; 1. 401(k) plans; company and individual contributions. 2. 403(b) plans; used by non-profit organizations. 3. Simple plans; plans fore the self-employed. 4. Keough Plans; for professionals such as doctors and lawyers. Chapter 2

  18. ANNUITIZING ACCUMULATIONS A. Annuitizing Pension Fund Accumulations; • In the last problem, we accumulated $1,456,246.71 over a 30-year period with monthly contributions to an IRA. We assumed a monthly compounded rate of return of 12% per annum. Current tax law permits the annuitization of IRAs and other similar plans at age 59 years and 6 months. • Annuitization of plans must commence when a person reaches 70 years and 6 months. For RMD; http://www.ira.com/faq/faq-54.htm • Annuitizing an accumulation is the reverse process. Now instead of paying into the retirement plan, the plan will make payments to you. Chapter 2

  19. ANNUITIZING ACCUMULATIONS • Suppose we use the $1,456,246.71 to buy a "single payment" ordinary annuity which will guarantee a 7% rate of return P.A. for 25-years. How much will the monthly payment be? • (We’ll ignore the fee-premium for the annuity for the time being.) Chapter 2

  20. ANNUITIZING ACCUMULATIONS • Calculating Monthly Payout 1. Clear TVM registers: BAII+: [2nd] [FV] (CLR TVM) HP10B; [YK] [INPUT] (CLEAR ALL) 2. Enter 300 and press [N] key. 3. Enter 7 and press [I/Y] key. 4. Enter 1456246.71. Press [+/-], then [PV]. 5. BAII+: Press [CPT] key then [PMT] HP10B: Press [PMT] 10,292.45 (display) 7. Total payout over 25 years = $10,292.45 * 300 = $3,087,734.63. (all this from a $150,000 investment) Chapter 2

  21. ORDINARY ANNUITIES A. Calculating the Price of an Insurance Annuity [Policy] using the BA II Plus • Suppose we desire to collect $5,000 per month for 20 years (240 payments) and the rate of return is 9% compounded monthly. • How much must we pay for an annuity contract that will pay 5,000 per month for 20 years? Chapter 2

  22. ORDINARY ANNUITIES • Calculating the Price an Insurance Annuity [Policy] using Financial Calculator; 1. Clear the TVM registers. 2. Enter 240 and press [N]. 3. Enter 9 and press [I/Y]. 4. Enter 5000 and press [PMT]. 5. Press [CPT] and [PV] or [PV] 6. Display should show; -555,724.77 $555,724.77 is the price of annuity. The negative sign reminds us that this is a price (negative cash flow). Chapter 2

  23. Total Returns Chapter 2

  24. INVESTMENT RETURNS Chapter 2

  25. LOAN REPAYMENTS • How much will the monthly payments for a $23,000 car loan be if the per annum rate is 4.75% for 60 months. (SECU payroll-deduct or 5.25% direct pay)? We'll solve this problem using the BAII+. 1. Clear the TVM registers. 2. Check the values set for P/Y (=12). 3. Enter 60, press [N]. 4. Enter 4.75, press [I/YR]. 5. Enter 23000, press [PV]. 6. BAII+: Press [CPT] [PMT]; PMT = -431.41 (display) $436.68 (if direct pay at 5.25%) Chapter 2

  26. MORTGAGE LOANS • How much will the monthly payments for a $160,000 loan be if the per annum rate is 4.75% and the term is 30 years (360 months)? 1. Clear the TVM registers. 2. Check the values set for P/Y (=12). 3. Enter 360, press [N]. 4. Enter 4.75, press [I/YR]. 5. Enter 160,000, press [PV]; $160,000 mortgage loan. 6. BAII+: Press [CPT] [PMT]; PMT =-834.64 (display) Leave these values in the calculator. We’ll use them to compute the amortization schedule. Chapter 2

  27. MORTAGE AMORTIZATION • All loans are amortized over their life. Each payment includes an interest portion and a principle portion. The BAII+ computes amortization schedules using the AMORT function. • BAII+: [2ND] [PV] Chapter 2

  28. MORTAGE AMORTIZATION • BAII+ (12 month totals) • Press [2nd] [PV]: P1 = 1.00 (display) • Press []: P2 = 1 or 12.00 (display) • If P2 = 1.00 then enter 12, [ENTER]: P2 = 12.00 • Press []: BAL = 157,531.03 • Press []: PRN = -2,468.97 • Press []: INT = -7,546.71 • Press []: then press [CPT]: P1 = 13.00 • Press []: P2 = 24.00 (continue [] for values) Chapter 2

  29. HOMEWORK CHAPTER 5 • Selt-Test: ST-1, parts c, f, i, j • Questions: 5-3, 5-4, 5-6 • Problems: 5-1, 5-2, 5-3, 5-4, 5-5 Chapter 2

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