Kế toán, kiểm toán - Compute interest and future values

Time Value of MoneyKimmel ● Weygandt ● KiesoFinancial Accounting, Eighth EditionGCHAPTER OUTLINECompute interest and future values.1Compute present values.2LEARNING OBJECTIVESUse a financial calculator to solve time value of money problems.3Payment for the use of money. Difference between amount borrowed or invested (principal) and amount repaid or collected.Elements involved in financing transaction:Principal (p): Amount borrowed or invested.Interest Rate (i): An annual percentage. Time (n): Number of years or portion of a year that the principal is borrowed or invested.LO 1LEARNING OBJECTIVECompute interest and future values.1NATURE OF INTERESTInterest computed on the principal only. NATURE OF INTERESTIllustration: Assume you borrow $5,000 for 2 years at a simple interest rate of 12% annually. Calculate the annual interest cost.Interest = p x i x n = $5,000 x .12 x 2= $1,2002 FULL YEARSILLUSTRATION G-1 Interest computationsSimple InterestLO 1Computes interest onthe principal andany interest earned that has not been paid or withdrawn.Most business situations use compound interest.NATURE OF INTERESTCompound InterestLO 1Illustration: Assume that you deposit $1,000 in Bank Two, where it will earn simple interest of 9% per year, and you deposit another $1,000 in Citizens Bank, where it will earn compound interest of 9% per year compounded annually. Also assume that in both cases you will not withdraw any interest until three years from the date of deposit.Nature of Interest - Compound InterestYear 1 $1,000.00 x 9%$ 90.00$ 1,090.00Year 2 $1,090.00 x 9%$ 98.10$ 1,188.10Year 3 $1,188.10 x 9%$106.93$ 1,295.03ILLUSTRATION G-2Simple versus compound interestLO 1Future value of a single amount is the value at a future date of a given amount invested, assuming compound interest.FUTURE VALUE OF A SINGLE AMOUNTFV = future value of a single amount p = principal (or present value; the value today) i = interest rate for one period n = number of periodsILLUSTRATION G-3 Formula for future valueLO 1Illustration: If you want a 9% rate of return, you would compute the future value of a $1,000 investment for three years as follows:LO 1ILLUSTRATION G-4Time diagramFUTURE VALUE OF A SINGLE AMOUNTWhat table do we use?LO 1Illustration: If you want a 9% rate of return, you would compute the future value of a $1,000 investment for three years as follows:ILLUSTRATION G-4Time diagramFUTURE VALUE OF A SINGLE AMOUNTWhat factor do we use?$1,000Present ValueFactorFuture Valuex 1.29503= $1,295.03LO 1FUTURE VALUE OF A SINGLE AMOUNTWhat table do we use?Illustration:ILLUSTRATION G-5Demonstration problem—Using Table 1 for FV of 1LO 1FUTURE VALUE OF A SINGLE AMOUNT$20,000Present ValueFactorFuture Valuex 2.85434= $57,086.80LO 1FUTURE VALUE OF A SINGLE AMOUNTIllustration: Assume that you invest $2,000 at the end of each year for three years at 5% interest compounded annually.ILLUSTRATION G-6Time diagram for a three-year annuityFUTURE VALUE OF AN ANNUITYLO 1Illustration:Invest = $2,000i = 5%n = 3 yearsLO 1ILLUSTRATION G-7Future value of periodic payment computationFUTURE VALUE OF AN ANNUITYWhen the periodic payments (receipts) are the same in each period, the future value can be computed by using a future value of an annuity of 1 table.Illustration:ILLUSTRATION G-8Demonstration problem—Using Table 2 for FV of anannuity of 1LO 1FUTURE VALUE OF AN ANNUITYWhat factor do we use?$2,500PaymentFactorFuture Valuex 4.37462= $10,936.55LO 1FUTURE VALUE OF AN ANNUITYThe present value is the value now of a given amount to be paid or received in the future, assuming compound interest. Present value variables: Dollar amount to be received (future amount).Length of time until amount is received (number of periods).Interest rate (the discount rate).PRESENT VALUE VARIABLESLO 2LEARNING OBJECTIVECompute present values.2Present Value (PV) = Future Value ÷ (1 + i )nILLUSTRATION G-9Formula for present value p = principal (or present value) i = interest rate for one period n = number of periodsPRESENT VALUE OF A SINGLE AMOUNTLO 2Illustration: If you want a 10% rate of return, you would compute the present value of $1,000 for one year as follows:PRESENT VALUE OF A SINGLE AMOUNTILLUSTRATION G-10Finding present value ifdiscounted for one periodLO 2What table do we use?Illustration: If you want a 10% rate of return, you can also compute the present value of $1,000 for one year by using a present value table.LO 2ILLUSTRATION G-10Finding present value ifdiscounted for one periodPRESENT VALUE OF A SINGLE AMOUNT$1,000x .90909= $909.09What factor do we use?Future ValueFactorPresent ValueLO 2PRESENT VALUE OF A SINGLE AMOUNTILLUSTRATION G-11Finding present value ifdiscounted for two periodWhat table do we use?Illustration: If the single amount of $1,000 is to be received in two years and discounted at 10% [PV = $1,000 ÷ (1 + .102], its present value is $826.45 [($1,000 ÷ 1.21).LO 2PRESENT VALUE OF A SINGLE AMOUNT$1,000x .82645= $826.45Future ValueFactorPresent ValueWhat factor do we use?LO 2PRESENT VALUE OF A SINGLE AMOUNT$10,000x .79383= $7,938.30Illustration: Suppose you have a winning lottery ticket and the state gives you the option of taking $10,000 three years from now or taking the present value of $10,000 now. The state uses an 8% rate in discounting. How much will you receive if you accept your winnings now?Future ValueFactorPresent ValueLO 2PRESENT VALUE OF A SINGLE AMOUNTIllustration: Determine the amount you must deposit today in your SUPER savings account, paying 9% interest, in order to accumulate $5,000 for a down payment 4 years from now on a new car.Future ValueFactorPresent Value$5,000x .70843= $3,542.15LO 2PRESENT VALUE OF A SINGLE AMOUNTThe value now of a series of future receipts or payments, discounted assuming compound interest.Necessary to know the:Discount rate, Number of payments (receipts).Amount of the periodic payments or receipts.PRESENT VALUE OF AN ANNUITYLO 2Illustration: Assume that you will receive $1,000 cash annually for three years at a time when the discount rate is 10%. Calculate the present value in this situation.What table do we use?ILLUSTRATION G-14Time diagram for a three-year annuityLO 2PRESENT VALUE OF AN ANNUITYWhat factor do we use?$1,000 x 2.48685 = $2,486.85Annual ReceiptsFactorPresent ValueLO 2PRESENT VALUE OF AN ANNUITYIllustration: Kildare Company has just signed a capitalizable lease contract for equipment that requires rental payments of $6,000 each, to be paid at the end of each of the next 5 years. The appropriate discount rate is 12%. What is the amount used to capitalize the leased equipment?$6,000 x 3.60478 = $21,628.68LO 2PRESENT VALUE OF AN ANNUITYIllustration: Assume that the investor received $500 semiannually for three years instead of $1,000 annually when the discount rate was 10%. Calculate the present value of this annuity.$500 x 5.07569 = $2,537.85LO 2PRESENT VALUE OF AN ANNUITYTwo Cash Flows:Periodic interest payments (annuity). Principal paid at maturity (single sum).PV OF A LONG-TERM NOTE OR BOND012349105,0005,0005,000$5,000. . . . .5,0005,000100,000LO 2012349105,0005,0005,000$5,000. . . . .5,0005,000100,000Illustration: Assume a bond issue of 10%, five-year bonds with a face value of $100,000 with interest payable semiannually on January 1 and July 1. Calculate the present value of the principal and interest payments.LO 2PV OF A LONG-TERM NOTE OR BONDPV of PrincipalLO 2 $100,000 x .61391 = $61,391PrincipalFactorPresent ValuePV OF A LONG-TERM NOTE OR BOND $5,000 x 7.72173 = $38,609PaymentFactorPresent ValuePV of InterestLO 2PV OF A LONG-TERM NOTE OR BONDIllustration: Assume a bond issue of 10%, five-year bonds with a face value of $100,000 with interest payable semiannually on January 1 and July 1. Present value of Principal $61,391Present value of Interest 38,609 Bond current market value $100,000 LO 2PV OF A LONG-TERM NOTE OR BONDIllustration: Now assume that the investor’s required rate of return is 12%, not 10%. The future amounts are again $100,000 and $5,000, respectively, but now a discount rate of 6% (12% ÷ 2) must be used. Calculate the present value of the principal and interest payments.ILLUSTRATION G-20Present value of principaland interest—discountLO 2PV OF A LONG-TERM NOTE OR BONDIllustration: Now assume that the investor’s required rate of return is 8%. The future amounts are again $100,000 and $5,000, respectively, but now a discount rate of 4% (8% ÷ 2) must be used. Calculate the present value of the principal and interest payments.LO 2ILLUSTRATION G-21Present value of principaland interest—premiumPV OF A LONG-TERM NOTE OR BONDLO 3ILLUSTRATION G-22Financial calculator keysN = number of periodsI = interest rate per periodPV = present valuePMT = paymentFV = future valueLEARNING OBJECTIVEUse a financial calculator to solve time value of money problems.3Using Financial CalculatorsILLUSTRATION G-23Calculator solution forpresent value of a single sumPRESENT VALUE OF A SINGLE SUMAssume that you want to know the present value of $84,253 to be received in five years, discounted at 11% compounded annually.LO 3Using Financial CalculatorsILLUSTRATION G-24Calculator solution forpresent value of an annuityPRESENT VALUE OF AN ANNUITYAssume that you are asked to determine the present value of rental receipts of $6,000 each to be received at the end of each of the next five years, when discounted at 12%.LO 3Using Financial CalculatorsUSEFUL APPLICATIONS – Auto LoanThe loan has a 9.5% nominal annual interest rate, compounded monthly. The price of the car is $6,000, and you want to determine the monthly payments, assuming that the payments start one month after the purchase.LO 3ILLUSTRATION G-25Calculator solution for auto loan payments.791679.5% ÷ 12Using Financial CalculatorsUSEFUL APPLICATIONS – Mortgage LoanYou decide that the maximum mortgage payment you can afford is $700 per month. The annual interest rate is 8.4%. If you get a mortgage that requires you to make monthly payments over a 15-year period, what is the maximum purchase price you can afford?LO 3ILLUSTRATION G-26Calculator solution for mortgage amount.708.4% ÷ 12“Copyright © 2016 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in Section 117 of the 1976 United States Copyright Act without the express written permission of the copyright owner is unlawful. Request for further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. 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