#### Transcript Chapter 6

Chapter 6 Accounting and the Time Value of Money ACCT-3030 1 1. Basics Study of the relationship between time and money Money in the future is not worth the same as it is today ◦ because if had money today could invest it and earn interest ◦ not because of risk or inflation Based on compound interest ◦ not simple interest ACCT-3030 2 1. Basics Examples of where TVM used in accounting ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ Notes Receivable & Payable Leases Pensions and Other Postretirement Benefits Long-Term Assets Shared-Based Compensation Business Combinations Disclosures Environmental Liabilities ACCT-3030 3 1I. Future Value of Single Sum The amount a sum of money will grow to in the future assuming compound interest Can be compute by ◦ formula: FV = PV ( 1 + i )n FV = PV x FVIF(n,i) ◦ tables: ◦ calculator: TVM keys FV = future value PV = present value FVIF = future value interest factor ACCT-3030 (Table 6-1) n = periods i = interest rate 4 1I. Future Value of Single Sum Example ◦ If you deposit $1,000 today at 5% interest compounded annually, what is the balance after 3 years? ACCT-3030 5 1I. Future Value of Single Sum Calculate by hand Event Amount Deposit 1-1-x1 $ 1,000.00 Year 1 interest (1000 x .05) End of Year 1 Amount 50.00 1,050.00 Year 2 interest (1050 x .05) End of Year 2 Amount 52.50 1102.50 Year 3 interest (1102.50 x .05) End of Year 3 Amount 55.13 1157.63 ACCT-3030 6 1I. Future Value of Single Sum Calculate by formula FV = 1,000 (1 + . 05)3 = 1,000 x 1.15763 = 1,157.63 ACCT-3030 7 1I. Future Value of Single Sum Calculate by table FV = 1,000 x Table factor for FVIF(3, .05) = 1,000 x 1.15763 = 1,157.63 ACCT-3030 8 1I. Future Value of Single Sum Calculate by calculator Clear calculator: 2nd RESET; ENTER; CE|C and/or: 2nd CLR TVM 3N 5 I/Y 1,000 +/- PV CPT FV = 1,157.63 ACCT-3030 9 1I. Future Value of Single Sum Additional example ◦ If you deposit $2,500 at 12% interest compounded quarterly, what is the balance after 5 years? less than annual compounding so adjust n and i n = 20 periods i = 3% 2,500 x 1.80611 = 4,515.28 20N; 3 I/Y; -2500 PV; CPT FV = 4,515.28 ACCT-3030 10 1II. Present Value of Single Sum Value now of a given amount to be paid or received in the future, assuming compound interest Can be compute by ◦ formula: PV = FV · 1/( 1 + i )n ◦ tables: PV = FV x PVIF(n,i) (Table 6-2) ◦ calculator: TVM keys FV = future value PV = present value PVIF = present value interest factor ACCT-3030 n = periods i = interest rate 11 1II. Present Value of Single Sum Example ◦ If you will receive $5,000 in 12 years and the discount rate is 8% compounded annually, what is it worth today? ACCT-3030 12 1II. Present Value of Single Sum Calculate by formula PV = 5,000 · 1/(1 + . 08)12 = 5,000 x .39711 = 1,985.57 ACCT-3030 13 1II. Present Value of Single Sum Calculate by table PV = 5,000 x Table factor for PVIF(12, .08) = 5,000 x .39711 = 1,985.57 ACCT-3030 14 1II. Present Value of Single Sum Calculate by calculator Clear calculator 12 N 8 I/Y 5,000 FV CPT PV = 1,985.57 ACCT-3030 15 1II. Present Value of Single Sum Additional example ◦ If you receive $1,157.63 in 3 years and the discount rate is 5%, what is it worth today? n = 3 periods i = 5% 1,157.63 x .863838 = 1,000.00 3 N; 5 I/Y; 1157.63 FV; CPT PV = -1,000.00 ACCT-3030 16 1V. Unknown n or i Example 1 ◦ If you believe receiving $2,000 today or $2,676 in 5 years are equal, what is the interest rate with annual compounding? PV = FV x PVIF(n, i) 2,000 = 2,676 x PVIF(5, i) PVIF(5, i) = 2,000/2,676 = .747384 find above factor in Table 2: i ≈ 6% 5 N; -2,000 PV; 2,676 FV; CPT 1/Y ACCT-3030 = 6.00% 17 1V. Unknown n or i Example 2 ◦ Same as last problem but assume 10% interest with annual compounding is the appropriate rate and calculate n. PV = FV x PVIF(n, i) 2,000 = 2,676 x PVIF(n, 10%) PVIF(n, 10%) = 2,000/2,676 = .747384 find above factor in Table 2: n ≈ 3 years 10 I/Y; -2,000 PV; 2,676 FV; CPT N ACCT-3030 = 3.06 years 18 V. Annuities Basics ◦ annuity a series of equal payments that occur at equal intervals ◦ ordinary annuity payments occur at the end of the period ◦ annuity due payments occur at the beginning of the period ACCT-3030 19 V. Annuities Ordinary annuity – payments at end Present Value Year 5 Year 4 Year 3 Year 1 Year 2 |_____|_____|_____|_____|_____| Pmt 1 Pmt 2 Pmt 3 Pmt 4 Evaluate PV ACCT-3030 20 V. Annuities Annuity due – payments at beginning Present value Year 5 Year 2 Year 4 Year 1 Year 3 |_____|_____|_____|_____|_____| Pmt 1 Pmt 2 Pmt 3 Pmt 4 Evaluate PV ACCT-3030 21 V. Annuities For Future Value of an annuity ◦ more difficult Determine whether the annuity is ordinary or due based on the last period ◦ if evaluate right after last pmt – ordinary ◦ if evaluate one period after last pmt – due An important part of annuity problems is determining the type of annuity ACCT-3030 22 V. Annuities Ordinary annuity – payments at end Future Value Year 5 Year 4 Year 3 Year 1 Year 2 |_____|_____|_____|_____|_____| Pmt 1 Pmt 2 Pmt 3 Pmt 4 Evaluate FV ACCT-3030 23 V. Annuities Annuity due – payments at beginning Future Value (evaluate 1 period after last payment) Year 5 Year 2 Year 4 Year 1 Year 3 |_____|_____|_____|_____|_____| Pmt 1 Pmt 2 Pmt 3 Pmt 4 Evaluate FV ACCT-3030 24 V. Annuities Tables available in book for ◦ Future Value of Ordinary Annuity (Table 6-3) ◦ Present Value of Ordinary Annuity (Table 6-4) ◦ Present Value of Annuity Due (Table 6-5) So no table for FV of annuity due ACCT-3030 25 V. Annuities Annuity table factors conversion ◦ to calculate FV of annuity due look up factor for FV of ordinary annuity for 1 more period and subtract 1.0000 ◦ to calculate PV of annuity due (can use table) look up factor for PV of ordinary annuity for 1 less period and add 1.0000 Use calculator ◦ ◦ ◦ ◦ change calculator to annuity due mode 2nd BEG; 2nd SET; 2nd QUIT to change back to ordinary annuity mode 2nd BEG; 2nd CLR WORK; 2nd QUIT (or 2nd RESET) ACCT-3030 26 V1. Future Value of Annuity Can be calculated by ◦ formula: ◦ table: (1 + i)n - 1 FVA(ord) = Pmt ----------------i FVA(ord or due) = Pmt x FVIFA(ord or due) (n, i) ◦ calculator: TVM keys FV = future value PV = present value FVIF = future value interest factor ACCT-3030 n = periods i = interest rate 27 V1. Future Value of Annuity Can be calculated by ◦ formula: (1 + i)n - 1 FVA(due) = Pmt --------------- x (1 + i) i FV = future value PV = present value FVIF = future value interest factor ACCT-3030 n = periods i = interest rate 28 V1. Future Value of Annuity Example ◦ Find the FV of a 4 payment, $10,000, ordinary annuity at 10% compounded annually. (You could treat this as 4 FV of single sum problems and would get correct answer but that method is omitted.) ACCT-3030 29 V1. Future Value of Annuity Calculate by formula (1 + .1)4 - 1 FVA-ord = 10,000 ----------.1 = 10,000 x 4.6410 = 46,410 ACCT-3030 30 V1. Future Value of Annuity Calculate by table (Table 6-3) FVA-ord = 10,000 x FVIFA-ord (4, .10) = 10,000 x 4.64100 = 46,410 ACCT-3030 31 V1. Future Value of Annuity Calculate by calculator 4 N; 10 I/Y; -10000 PMT; CPT FV 46,410 ACCT-3030 32 V1. Future Value of Annuity Additional examples ◦ Find the FV of a $3,000, 15 payment ordinary annuity at 15%. FVA-ord = 3,000 x FVIFA-ord (15, .15) = 3,000 x 47.58041 = 142,741 15 N; 15 I/Y; -3000 PMT; CPT FV = 142,741 ACCT-3030 33 V1. Future Value of Annuity Additional examples ◦ Find the FV of a $3,000, 15 payment annuity due at 15%. (table – look up 1 more period -1.0000) FVA-ord = 3,000 x FVIFA-due (15, .15) = 3,000 x 54.71747 = 164,152 2nd BGN; 2nd SET; 2nd QUIT 15 N; 15 I/Y; -3000 PMT; CPT FV = 164,152 ACCT-3030 34 VI1. Present Value of Annuity Can be calculated by ◦ formula: ◦ table: 1 – (1/(1 + i)n) PVA(ord) = Pmt --------------------i PVA(ord or due) = Pmt x PVIFA(ord or due) (n, i) ◦ calculator: TVM keys FV = future value PV = present value PVIF = present value interest factor ACCT-3030 n = periods i = interest rate 35 VI1. Present Value of Annuity Can be calculated by ◦ formula: 1 – (1/(1 + i)n) PVA(due) = Pmt --------------------- x (1 + i) i FV = future value PV = present value PVIF = present value interest factor ACCT-3030 n = periods i = interest rate 36 VI1. Present Value of Annuity Example ◦ What is the PV of a $3,000, 15 year, ordinary annuity discounted at 10% compounded annually? ACCT-3030 37 VI1. Present Value of Annuity Calculate by formula 1 – (1/(1 + .10)15 PVA-ord = 3,000 ---------------.10 = 3,000 x 7.60608 = 22,818 ACCT-3030 38 VI1. Present Value of Annuity Calculate by table (Table 6-4) PVA-ord = 3,000 x PVIFA-ord (15, 10) = 3,000 x 7.60608 = 22,818 ACCT-3030 39 VI1. Present Value of Annuity Calculate by calculator 15 N; 10 I/Y; -3000 PMT; CPT PV 22,818 ACCT-3030 40 VI1. Present Value of Annuity Additional examples ◦ Find the PV of a $3,000, 15 payment annuity due discounted at 15%. PVA-due = 3,000 x PVIFA-due (15, .15) = 3,000 x 6.72488 = 20,175 2nd BGN; 2nd SET; 2nd QUIT 15 N; 15 I/Y; -3000 PMT; CPT PV = 20,173 ACCT-3030 41 VI1. Present Value of Annuity Additional examples ◦ If you were to be paid $1,800 every 6 months (at the end of the period) for 5 years, what is it worth today discounted at 12%? PVA-ord = 1,800 x PVIFA-ord (10, .06) = 1,800 x 7.36009 = 13,248 10 N; 6 I/Y; -1800 PMT; CPT PV = 13,248 ACCT-3030 42 VI1. Present Value of Annuity Additional examples ◦ If you consider receiving $12,300 today or $2,000 at the end of each year for 10 years equal, what is the interest rate? 12,300A-ord = 2,000 x PVIFA-ord (10, i) PVIFA-ord (10, i) = 12,300/2,000 = 6.15000 i ≈ 10% 10 N; -2000 PMT; PV = 12300; CPT I/Y = 9.98% ACCT-3030 43