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Chapter 9 FEDERAL RESERVE NOTE THE UNITED STATES OF AMERICA THE UNITED STATES OF AMERICA H OE E A E DR T IS NT IS L GL T NE O L E T , UL N R AE F RAL DBS P BICADP IVT L70744629F 12 WASHINGT ON, D.C. 12 A H 293 L70744629F 12 SR S E IE 12 95 18 ONE DOLLAR ONE DOLLAR Current Liabilities, Contingent Liabilities & the Time Value of Money 1 Objectives & Key Concepts Review Current Liabilities Introduce concept of Contingent Liabilities Compare Simple vs. Compound Interest Discuss Time Value of Money Future amount of a single payment Present value of a single payment Future amount of an annuity Present value of an annuity 2 Balance Sheet Classifications: REVIEW Current Liabilities: DEFN: due within one year of the balance sheet date 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Long-term Liabilities: 1 2 3 4 5 6 7 8 9 10 DEFN: due beyond one year 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 3 Current Liability Accounts: REVIEW Accounts Payable Notes Payable Current Portion of Listed in Long-Term Debt order of Taxes Payable liquidity Unearned Revenues Other Accrued Liabilities (Warranties, Legal claims, etc.) 4 Accounts Payable: REVIEW DEFN: Purchase of inventory, goods or services on credit Cash Implications: Discount payment 2%/10, terms offered to net 30 encourage early payment 5 Note Payable: REVIEW I promise to pay $1,000 plus 12% annual interest on December 31, 2002. Date: January 1, 2002 Tony Soprano Signed:_________ Total repayment = $1,120 $1,000 + ($1,000 x 12%) 6 Discounted Note Payable: REVIEW In exchange for $880 received today, I promise to pay $1,000 on December 31, 2002. Date: January 1, 2002 Vito Corleone Signed:_________ Effective interest rate on note = 13.6% ($120 interest / $880 proceeds) 7 Balance Sheet Presentation of Discounted Note Payable 1/1/02 12/31/02 Notes Payable $ 1,000 $ 1,000 Less: Discount on Notes Payable 120 - 0 - $ 880 $ 1,000 Discount transferred to Interest Expense over life of note Liability and O/E 8 Balance Sheet Presentation of Discounted Note Payable 1/1/02 12/31/02 Notes Payable $ 1,000 $ 1,000 Less: Discount on Notes Payable 120 - 0 - $ 880 $ 1,000 Discount transferred to Interest Expense over life of note Liability and O/E 9 Current Maturities of Long-term Debt DEFN: Principal repayment on portion of long-term borrowing (e.g., Bonds Payable) due within one year of balance sheet date 1 2 3 1 2 3 4 5 6 7 8 9 10 4 5 6 7210 3 8 19 1 2 3 11 12 13 14 15 16 17 11 412 513 614 715 816 9 17 10 11 412 513 614 715 816 9 17 10 18 19 20 21 22 23 24 18 19 20 21 22 23 24 25 26 27 28 29 30 31 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 18 19 20 21 22 23 24 25 26 27 28 29 30 31 25 26 27 28 29 30 31 Current Liability Long-term Liability $500,000 $15,000,000 10 Income Taxes Payable: REVIEW Record expense when incurred; not when paid 12/31/01 4/15/02 Record Taxes 2001 tax Paid expense To follow the MATCHING PRINCIPLE…. 11 Contingent Liability DEFN: Future obligation involving existing condition Circumstances: Outcome not known with certainty Dependent upon some future event Should this be in the F/S? 12 Contingent Liability: CRITERIA Accrue estimated amount if: liability is probable, AND amount can be reasonably estimated -----------Balance Sheet------------- --Income Statement-- Assets = Liabilities + OE + Rev. - Expenses Accrued Accrued Liability Expense/Loss $XXX ($XXX) 13 Typical Contingent Liabilities Warranties/Guarantees Premium or Coupon offers Lawsuits 14 Recording Contingent Liabilities Example: Ford Motor Company’s total auto sales for January 2002 were $1,000,000,000. Based upon historical experience, estimated warranty work (parts and labor) over the 36 months of the warrantee average 1% of sales value. Warranty 15 Recording Contingent Liabilities Probable liability has YES been incurred? Warrantee Amount reasonably YES estimable? Record Loss & Liability in January 16 Recording Contingent Liabilities -----------Balance Sheet------------- --Income Statement-- Assets = Liabilities + OE + Rev. - Expenses January 31, 2002 Accrued Warranty Warranty Liability Expense $10,000,000 ($10,000,000) At the end of January 2002, record the expected liability and recognize the warrantee expense, per the Matching concept 17 Recording actual Warrantee Work EXAMPLE: Illustrates reimbursement by Ford Motor Company to a local dealer for warranty work of $750 performed by that dealer in March 2003 on behalf of Ford -----------Balance Sheet------------- --Income Statement-- Assets = Liabilities + OE + Rev. - Expenses March 2003 Cash Accrued NOTE: NO ($750) Warrantee expense is recorded in Liability 2003 when ($750) work is L: Warranty Liability actually A: Cash $10,000,000 1/31/02 performed. $750 $750 18 Disclosing Contingent Liabilities when both criteria are not met SITUATION: Event is not TREATMENT: probable but Disclose in “reasonably footnotes possible” - or - amount is not estimable 19 Disclosing Contingent Liabilities Case Study SITUATION: TREATMENT: Your lawyer Disclose suit in determines that footnotes only (nature you’ll probably lose and amount of suit). a lawsuit filed against you if it If you record a goes to jury. He contingent liability in gives you a range of the B/S, the litigant’s dollar amounts the attorney would use jury might award. that as Exhibit A ! 16 20 Contingent Assets GAAP: Contingent gains and assets are not recognized nor recorded. May be disclosed in footnotes to financial statements, Conservatism principle applies – “Don’t count your chickens before they’re hatched!” 21 Time Value of Money CONCEPT: Prefer payment now vs. sometime in the future – e.g., a dollar today is worth more than a dollar a year from now. Why? Approach: Incorporates interest factor (return on investment) to make a decision. Where used? Applicable to both personal and business decisions. 22 Simple Interest: A REVIEW I = PX R X T 23 Example of Simple Interest Given following data: Principal amount = $ 10,000 Annual interest rate = 10% Term of Note Payable = 2 years Required: Calculate interest on the note. P x R x T = Interest $ 10,000 x .10 x 2 = $ 2,000 20 24 25 26 27 28 29 30 31 Comparing Interest Methods Simple annual interest: $10,000 x .10 x 2 = $ 2,000 Semi-annual compounding: 1 $ 500 Compounding 2 NOTE: is $155 more effect 525 3 earned if investing or 551 4 more owed if 579 borrowing! Total $ 2,155 32 Compound Interest Applications: TIME VALUE OF MONEY Present Future value value of a of a single single amount amount Future Present value of an value of an annuity annuity 33 TIME VALUE OF MONEY Questions Future Value of a Single Amount (FV) How much will I have in the future (FV) if I invest a single amount (P) today at a compound annual interest rate (i%) for a certain time period (n) ? Present Value of a Single Amount (PV) Future Value of an Annuity (FVA) Present Value of an Annuity (PVA) 34 Future Value of Single Amount Known amount of single payment (P) or deposit Future Value (FV) + Interest (i%) = 35 Future Value of a Single Amount Example If you invest $10,000 today @ 10% compound interest, what will it be worth 3 years from now? $10,000 Future Value? Yr. 1 Yr. 2 Yr. 3 + Interest @ 10% 36 Future Value of a Single Amount Example Using FV Formula n FV = p (1 + i) 3 = $10,000 (1.10) = $13,310 37 Future Value of a Single Amount Example Using Time Value of Money Tables Yr. 1 Yr. 2 Yr. 3 $10,000 P.V. F.V.?? F.V. = Present Value x F.V. Factor = $ 10,000 X (3 periods @ 10%) 38 Future Value of a Single Amount Table (n) 2% 4% 6% 8% 10% 1 1.020 1.040 1.060 1.080 1.10 2 1.040 1.082 1.124 1.166 1.210 3 1.061 1.125 1.191 1.260 1.331 4 1.082 1.170 1.262 1.360 1.464 5 1.104 1.217 1.338 1.470 1.611 6 1.126 1.265 1.419 1.587 1.772 7 1.149 1.316 1.504 1.714 1.949 8 1.172 1.369 1.594 1.851 2.144 Why are all the values > 1.0 ? Table 9-1 39 Future Value of a Single Amount Example Using Time Value of Money Tables Yr. 1 Yr. 2 Yr. 3 $10,000 P.V. F.V. = ? F.V. = $13,310 F.V. = Present Value x F.V. Factor = $ 10,000 X (3 periods @ 10%) = $ 10,000 X 1.331 = $ 13,310 40 TIME VALUE OF MONEY Four Questions Future Value of a Single Amount (FV) Present Value of a Single Amount (PV) How much (PV) must I invest today at a given compound annual interest rate (i%) for a specified time period (n) if I want to have a certain amount (P) in the future? Future Value of an Annuity (FVA) Present Value of an Annuity (PVA) 41 Present Value of Single Amount Known amount of single payment (FV) Present Value (PV) in the future - Discount (i%) 42 Present Value of a Single Amount Example If you will receive $10,000 in three years, what is it worth today (assuming you could invest at 10% compound interest)? Present Value? $ 10,000 Yr. 1 Yr. 2 Yr. 3 Discount @ 10% 43 Present Value of a Single Amount Example Using Formulas -n PV = payment x (1 + i) -3 = $10,000 x (1.10) = $7,513 44 Present Value of a Single Amount Example Using Tables Yr. 1 Yr. 2 Yr. 3 P.V. ?? F.V.=$10,000 P.V. = Future Value x P.V. Factor = $ 10,000 X (3 periods @ 10%) 45 Present Value of $1 (n) 2% 4% 6% 8% 10% 1 .9804 .9615 .9434 .9259 .9090 2 .9612 .9246 .8900 .8573 .8265 3 .9423 .8890 .8396 .7938 .7513 4 .9238 .8548 .7921 .7350 .6830 5 .9057 .8219 .7473 .6806 .6209 Why are all the values < 1.0 ? Table 9-2 NOTE: These are the inverse of Table 9-1 46 Present Value of a Single Amount Example Using Tables Yr. 1 Yr. 2 Yr. 3 P.V. = $7,513 P.V. = $? F.V.=$10,000 P.V. = Future Value x P.V. Factor = $ 10,000 X (3 periods @ 10%) = $ 10,000 X .7513 = $7,513 47 TIME VALUE OF MONEY Questions Future Value of a Single Amount (FV) Present Value of a Single Amount (PV) Future Value of an Annuity (FVA) How much will I have in the future (FVA) if I invest a series of equal amounts (P) each year at a compound interest rate (i%) for a certain time (n) ? Present Value of an Annuity (PVA) 48 Future Value of an Annuity NOTE: First investment is at end of Year #1 Periods 1 2 3 4 $0 $2,000 $2,000 $2,000 $2,000 +Interest Future Value? 49 Future Value of Annuity Example If we invest $2,000 each year for four years @ 10% compound interest, what will it be worth 4 years from now? Yr. 1 Yr. 2 Yr. 3 Yr. 4 $0 $2,000 $2,000 $2,000 $2,000 F.V.(a)?? 50 Future Value of Annuity Example Using Tables Yr. 1 Yr. 2 Yr. 3 Yr. 4 $0 $2,000 $2,000 $2,000 $2,000 F.V.(a)?? F.V. (a) = Payment x F.V. (a) Factor = $ 2,000 X (4 periods @ 10%) 51 Future Value of an Annuity Table (n) 2% 4% 6% 8% 10% 12% 1 1.000 1.000 1.000 1.000 1.000 1.000 2 2.020 2.040 2.060 2.080 2.100 2.120 3 3.060 3.122 3.184 3.246 3.310 3.374 4 4.122 4.246 4.375 4.506 4.641 4.779 5 5.204 5.416 5.637 5.867 6.105 6.353 Note the pattern of the values Table 9-3 52 Future Value of Annuity Example Using Tables Yr. 1 Yr. 2 Yr. 3 Yr. 4 $0 $2,000 $2,000 $2,000 $2,000 F.V.(a) F.V.(a) = $9,282 =? F.V. (a) = Payment x F.V. (a) Factor = $ 2,000 X (4 periods @ 10%) = $ 2,000 X 4.641 = $ 9,282 53 TIME VALUE OF MONEY Questions Future Value of a Single Amount (FV) Present Value of a Single Amount (PV) Future Value of an Annuity (FVA) Present Value of an Annuity (PVA) How much (PVA) must I invest today if I want to withdraw a series of equal amounts (P) each year for a specified time period (n) if I earn at a given compound annual interest rate (i%) on any balance ? 54 Present Value of an Annuity Periods 1 2 3 4 $0 $500 $500 $500 $500 Discount Present H OE FEDERAL RESERVE NOTE THE UNITED STATES OF AMERICA THE UNITED STATES OF AMERICA T IS NT IS L GL T NE E A E DR FEDERAL RESERVE NOTE THE UNITED STATES OF AMERICA Value ? O L E T , UL N R AE THE UNITED STATES OF AMERICA F RAL DBS P BICADP IVT L70744629F FEDERAL RESERVE NOTE H OE E A E DR T IS NT IS L GL T NE 12 12 O L E T , UL N R AE F RAL DBS P BICADP IVT THE UNITED STATES OFAMERICA THE UNITED STATES OFON, D.C. WASHINGT AMERICA L70744629F A FEDERAL RESERVE NOTE H OE E A E DR T IS NT IS L GL T NE 12 12 O L E T , UL N R AE F RAL DBS P BICADP IVT THE UNITED STATES OFAMERICA THE UNITED STATES OFON, D.C. H 293 WASHINGT AMERICA L70744629F A L70744629F H OE E A E DR T IS NT IS L GL T NE 12 WASHINGT ON, D.C.12 O L E T , UL N R AE F RAL DBS P BICADP IVT 12 E IE SR S 12L70744629F H 293 A 95 18 L70744629F 12 12 12 ONE DOLLAR ONE DOLLAR A SR S E IE 95 18 WASHINGT ON, D.C. 12 H 293 L70744629F 12 ONE DOLLAR ONE DOLLAR SR S E IE 95 18 12 H 293 L70744629F 12 ONE DOLLAR ONE DOLLAR SR S E IE 18 95 12 ONE DOLLAR ONE DOLLAR 55 Present Value of an Annuity Example What is the value today of receiving $500 at the end of the each of the next 4 years, assuming you can invest at 10% compound annual interest? Yr. 1 Yr. 2 Yr. 3 Yr. 4 $0 $500 $500 $500 $500 P.V.(a)?? 56 Present Value of an Annuity Example Yr. 1 Yr. 2 Yr. 3 Yr. 4 $0 $500 $500 $500 $500 P.V.(a)?? P.V. (a) = Payment x P.V. (a) Factor = $ 500 X (4 periods @ 10%) 57 Present Value of an Annuity Table (n) 2% 4% 6% 8% 10% 1 .9804 .9615 .9434 .92593 .90909 2 1.942 1.886 1.833 1.783 1.735 3 2.884 2.775 2.673 2.577 2.487 4 3.808 3.630 3.465 3.312 3.170 5 4.713 4.452 4.212 3.992 3.791 Table 9-4 58 Present Value of an Annuity Example Yr. 1 Yr. 2 Yr. 3 Yr. 4 $0 $500 $500 $500 $500 P.V. = P.V. = ? $1,585 P.V. (a) = Payment x P.V. (a) Factor = $ 500 X (4 periods @ 10%) = $ 500 X 3.170 = $ 1,585 49 59 Solving for Unknowns: An Application of Time Value Concepts Remember that each of our Time Value equations had 4 parameters: (1) Payment, (2) interest (i%) rate, (3) Time (n) period, and (4) Future Value or Present Value. Given any three of the parameters, we can solve for the fourth. 60 Solving for Unknowns: An Application You wish to purchase the car of your dreams for $40,000 total cost, after your trade-in of $10,000. The dealer is (generously! ) offering 24% annual financing over 24 months. Compute the amount of your monthly payment. The unknown is the amount of the annuity. 61 Solving for Unknowns Mo. 1 Mo. 2 Mo. 24 $40,000 ??? ??? ??? ??? loan = P.V.(a) P.V. (a) = Payment x P.V. (a) Factor rearrange equation to solve for unknown Payment = P.V.(a) / P.V.(a) factor 51 62 Solving for Unknowns Mo. 1 Mo. 2 Mo. 24 $40,000 ??? ??? ??? ??? loan = P.V.(a) P.V. (a) = Payment x P.V. (a) Factor rearrange equation to solve for unknown Payment = $40,000 / (24 @ 2%) 24% annual rate / 12 monthly payments 63 Present Value of an Annuity Table (n) 2% 4% 6% 8% 1 .9804 .9615 .9434 .929 2 1.942 1.886 1.833 1.783 3 2.884 2.775 2.673 2.577 : 24 18.914 15.247 12.550 10.529 Table 9-4 64 Solving for Unknowns Mo. 1 Mo. 2 Mo. 24 $40,000 $2,115 $2,115 $2,115 loan = P.V.(a) Payment = P.V.(a) / P.V.(a) factor = $40,000 / (24 months @ 2%) = $40,000 / 18.914 = $2,115 65 Solving for Unknowns Mo. 1 Mo. 2 Mo. 24 $40,000 $2,115 $2,115 $2,115 loan = P.V.(a) Total Payments = Monthly Payment x # months $50760 = $2,115 x 24 Total Interest Paid = Total Payments - $ Borrowed $10,760 = $50,760 - $40,000 Effective Interest Rate Paid = Interest Paid/ $ Borrowed 26.9% = $10,760 / $40,000 The more often you compound, the more you pay! 66 Summary Reviewed Current Liabilities Introduced concept of Contingent Liabilities Compared Simple vs. Compound Interest Discussed Time Value of Money Future amount of a single payment Present value of a single payment Future amount of an annuity Present value of an annuity 67 Exhibit 9-3 Current Liabilities on the Statement of Cash Flows Operating Activities Net income xxxx Increase in current liability + Decrease in current liability - Investing Activities Financing Activities Increase in notes payable + Decrease in notes payable - 68