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ACCT INTERMEDIATE CHP 6 Exercise 6-1 Future value; single amount [LO2] Determine the future value of the following single amounts (Use Table 1) (Round "FV Factor" to 5 decimal places and final answers to the nearest dollar amount. Omit the "$" sign in your response.): 1. 2. 3. 4. Investe d Amoun Interest No. of t Rate Periods $ 13,000 11,000 29,000 59,000 Future Value 5% 9 8 13 10 16 5 12 $ $ $ $ Explanation: 1. FV = $13,000 (1.55133*) = $20,167 *Future value of $1: n = 9, i = 5% (from Table 1) 2. FV = $11,000 (2.71962*) = $29,916 *Future value of $1: n = 13, i = 8% (from Table 1) 3. FV = $29,000 (4.59497*) = $133,254 *Future value of $1: n = 16, i = 10% (from Table 1) 4. FV = $59,000 (1.79586*) = $105,956 *Future value of $1: n = 12, i = 5% (from Table 1) Exercise 6-3 Present value; single amount [LO3] Determine the present value of the following single amounts (Use Table 2) (Round "PV Factor" to 5 decimal places and final answers to the nearest dollar amount. Omit the "$" sign in your response): 1. Futur No. e Inter of Amo est Perio unt Rate ds $ 20,00 Present Value 7% 10 $ 2. 3. 4. 0 14,00 0 25,00 0 40,00 0 8 12 $ 12 20 $ 10 8 $ Explanation: 1. PV = $20,000 (.50835*) = $10,167 *Present value of $1: n = 10, i = 7% (from Table 2) 2. PV = $14,000 (.39711*) = $5,560 *Present value of $1: n = 12, i = 8% (from Table 2) 3. PV = $25,000 (.10367*) = $2,592 *Present value of $1: n = 20, i = 12% (from Table 2) 4. PV = $40,000 (.46651*) = $18,660 *Present value of $1: n = 8, i = 10% (from Table 2) Exercise 6-10 Future value; solving for annuities and single amount [LO4, 8] John Rider wants to accumulate $100,000 to be used for his daughters college education. He would like to have the amount available on December 31, 2016. Assume that the funds will accumulate in a certificate of deposit paying 8% interest compounded annually. Answer each of the following independent questions. Required: (1 If John were to deposit a single amount, how much would he have to invest on December 31, ) 2011? (Use Table 2) (Round "PV Factor" to 5 decimal places and final answer to the nearest dollar amount. Omit the "$" sign in your response.) PV $ (2 If John were to make five equal deposits on each December 31, beginning on December 31, ) 2012, what is the required deposit? (Use Table 3) (Round "FV Factor" to 4 decimal places and final answer to the nearest dollar amount.Omit the "$" sign in your response.) Annuity amount $ (3 If John were to make five equal deposits on each December 31, beginning on December 31, ) 2011, what is the required deposit? (Use Table 5) (Round "FV Factor" to 4 decimal places and final answer to the nearest dollar amount.Omit the "$" sign in your response.) Annuity amount $ Explanation: (1) PV = $100,000 (.68058*) = $68,058 *Present value of $1: n = 5, i = 8% (from Table 2) (2) Annuity amount = $100,000 5.8666* *Future value of an ordinary annuity of $1: n = 5, i = 8% (from Table 3) Annuity amount = $17,046 (3) Annuity amount = $100,000 6.3359* *Future value of an annuity due of $1: n = 5, i = 8% (from Table 5) Annuity amount = $15,783 Exercise 6-11 Future and present value [LO3, 6, 7] Answer each of the following independent questions. Required: Alex Meir recently won a lottery and has the option of receiving one of the following three prizes: (1) $63,000 cash immediately, (2) $19,688 cash immediately and a six-period annuity of $7,875 beginning one year from today, or (3) a six-period annuity of $12,797 beginning one year from today. (1- Assuming an interest rate of 8%, determine the PV value for the above options. (Use Table a) 4) (Round "PV Factor" to 5 decimal places and final answers to the nearest dollar amount. Omit the "$" sign in your response.) Option (1) (2) (3) Present Value $ $ $ (1Which option should Alex choose? b) Option (1) (2 The Weimer Corporation wants to accumulate a sum of money to repay certain debts due on ) December 31, 2020. Weimer will make annual deposits of $95,000 into a special bank account at the end of each of 10 years beginning December 31, 2011. Assuming that the bank account pays 5% interest compounded annually, what will be the fund balance after the last payment is made on December 31, 2020? (Use Table 3) (Round "FV Factor" to 4 decimal places and final answer to the nearest dollar amount. Omit the "$" sign in your response.) FVA $ Explanation: (1-a) (2 PV = $19,688 + $7,875 (4.62288*) ) *Present value of an ordinary annuity of $1: n = 6, i = 8% (from Table 4) PV = $19,688 + $36,405= $56,093 (3 PV = $12,797 (4.62288*) = $59,159 ) *Present value of an ordinary annuity of $1: n = 6, i = 8% (from Table 4) (1-b) Alex should choose option (1). (2) FVA = $95,000 (12.5779*) = $1,194,901 *Future value of an ordinary annuity of $1: n = 10, i = 5% (from Table 3) Exercise 6-13 Solving for unknown annuity payment [LO8] Don James purchased a new automobile for $20,000. Don made a cash down payment of $5,000 and agreed to pay the remaining balance in 30 monthly installments, beginning one month from the date of purchase. Financing is available at a 24% annual interest rate. Required: Calculate the amount of the required monthly payment. (Use Table 4) (Round "PV Factor" to 5 decimal places and final answer to the nearest dollar amount. Omit the "$" sign in your response.) Monthly payment $ Explanation: Annuity = $20,000 5,000 = $670 = Payment 22.39646* *Present value of an ordinary annuity of $1: n = 30, i = 2% (from Table 4) Problem 6-2 Present and future value [LO6, 7, 9] Johnstone Company is facing several decisions regarding investing and financing activities. Address each decision independently. (1 On June 30, 2011, the Johnstone Company purchased equipment from Genovese Corp. ) Johnstone agreed to pay Genovese $10,000 on the purchase date and the balance in five annual installments of $8,000 on each June 30 beginning June 30, 2012. Assuming that an interest rate of 11% properly reflects the time value of money in this situation, at what amount should Johnstone value the equipment? (Use Table 4) (Round "PV Factor" to 5 decimal places and final answer to the nearest dollar amount. Omit the "$" sign in your response.) Equipment $ (2 Johnstone needs to accumulate sufficient funds to pay a $400,000 debt that comes due on ) December 2016. 31, The company will accumulate the funds by making five equal annual deposits to an account paying 4% interest compounded annually. Determine the required annual deposit if the first deposit is made on December 31, 2011. (Use Table 5) (Round "FV Factor" to 4 decimal places and final answer to the nearest dollar amount. Omit the "$" sign in your response.) Required annual deposit $ (3 On January 1, 2011, Johnstone leased an office building. Terms of the lease require Johnstone ) to make 20 annual lease payments of $140,000 beginning on January 1, 2011. A 10% interest rate is implicit in the lease agreement. At what amount should Johnstone record the lease liability on January 1, 2011, before any lease payments are made? (Use Table 6) (Round "PV Factor" to 5 decimal places and final answer to the nearest dollar amount. Omit the "$" sign in your response.) Lease liability $ Explanation: (1) PV = $10,000 + 8,000 (3.69590*) = $39,567 = Equipment *Present value of an ordinary annuity of $1: n = 5, i = 11% (from Table 4) (2) $400,000 = Annuity amount 5.6330* *Future value of an annuity due of $1: n = 5, i = 4% (from Table 5) $400,000 Annuity amount = 5.6330 Annuity amount = $71,010 = Required annual deposit (3) PVAD = 140,000 (9.36492*) = $1,311,089 = Lease liability *Present value of an annuity due of $1: n = 20, i = 10% (from Table 6) Problem 6-3 Analysis of alternatives [LO3, 7] Harding Company is in the process of purchasing several large pieces of equipment from Danning Machine Corporation. Several financing alternatives have been offered by Danning: 1.Pay $1,100,000 in cash immediately. 2.Pay $420,000 immediately and the remainder in 13 annual installments of $80,000, with the first installment due in one year. 3.Make 13 annual installments of $145,000 with the first payment due immediately. 4.Make one lump-sum payment of $1,570,000 nine years from date of purchase. Required: (a Determine the present value, assuming that Harding can borrow funds at an 5% interest rate. ) (Use Table 2, Table 4, and Table 6) (Round "PV Factor" to 5 decimal places and final answers to the nearest dollar amount. Omit the "$" sign in your response.) Alternative 1 2 3 4 PV $ $ $ $ (b Determine the best alternative for Harding. ) Harding should choose alternative 1. Explanation: Alternative 2: PV = $420,000 + 80,000 (9.39357*) = $1,171,486 *Present value of an ordinary annuity of $1: n = 13, i = 5% (from Table 4) Alternative 3: PV = PVAD = $145,000 (9.86325*) = $1,430,171 *Present value of an annuity due of $1: n = 13, i = 5% (from Table 6) Alternative 4: PV = $1,570,000 (.64461*) = $1,012,038 *Present value of $1: n = 9, i = 5% (from Table 2) Problem 6-6 Solving for unknowns [LO8] The following situations should be considered independently. (1 John Jamison wants to accumulate $60,000 for a down payment on a small business. He will ) invest $27,991 today in a bank account paying 10% interest compounded annually. Approximately how long will it take John to reach his goal? (Use Table 2) (Round "PV Factor" to 5 decimal places. Round your final answer to the nearest whole year.) Time taken years (2 The Jasmine Tea Company purchased merchandise from a supplier for $16,751. Payment was ) a noninterest-bearing note requiring Jasmine to make 3 annual payments of $6,500 beginning one year from the date of purchase. What is the interest rate implicit in this agreement? (Use Table 4) (Round your "PV factor" to 5 decimal places and final answer to the closest interest rate. Omit the "%" sign in your response.) Interest rate % (3 Sam Robinson borrowed $9,750 from a friend and promised to pay the loan in 11 equal ) annual installments beginning one year from the date of the loan. Sam's friend would like to be reimbursed for the time value of money at a 9% annual rate. What is the annual payment Sam must make to pay back his friend? (Use Table 4) (Round "PV Factor" to 5 decimal places and final answer to the nearest dollar amount. Omit the "$" sign in your response.) Annual payment $ Explanation: (1) PV of $1 factor = $27,991 = .46651* $60,000 *Present value of $1: n = ?, i = 10% (from Table 2, n = approximately 8 years) (2) PVA Annuity factor = Annuity amount Annuity factor = $16,751 $6,500 = 2.57710* *Present value of an ordinary annuity of $1: n = 3, i = ? (from Table 4, i = approximately 8%) (3) Annuity amount = PVA Annuity factor Annuity amount = $9,750 = $1,433 6.80519* = Payment *Present value of an ordinary annuity of $1: n = 11, i = 9% (from Table 4) Problem 6-13 Lease vs. buy alternatives [LO3, 7, 9] Kiddy Toy Corporation needs to acquire the use of a machine to be used in its manufacturing process. The machine needed is manufactured by Lollie Corp. The machine can be used for 10 years and then sold for $12,000 at the end of its useful life. Lollie has presented Kiddy with the following options: 1. Buy machine. The machine could be purchased for $189,000 in cash. All maintenance and insurance costs, which approximate $5,000 per year, would be paid by Kiddy. 2. Lease machine. The machine could be leased for a 10-year period for an annual lease payment of $24,000 with the first payment due immediately. All maintenance and insurance costs will be paid for by the Lollie Corp. and the machine will revert back to Lollie at the end of the 10year period. Required: (a Assuming that a 12% interest rate properly reflects the time value of money in this ) situation and that all maintenance and insurance costs are paid at the end of each year, find the present value for the following options. Ignore income tax considerations.(Use Table 2, Table 4, and Table 6) (Round "PV Factor" to 5 decimal places and final answers to the nearest dollar amount. Negative amounts should be indicated by a minus sign. Omit the "$" sign in your response.) PV Buy option Lease option $ $ (b Determine which option Kiddy should choose. (expression error) ) Kiddy Toy should lease the machine. Explanation: Buy option: PV = $189,000 5,000 (5.65022*) + 12,000 (0.32197**) *Present value of an ordinary annuity of $1: n = 10, i = 12% (from Table 4) **Present value of $1: n = 10, i = 12% (from Table 2) PV = $189,000 28,251 + 3,864 PV = $213,387 Lease option: PVAD = $24,000 (6.32825*) = $151,878 *Present value of an annuity due of $1: n = 10, i = 12% (from Table 6) ... View Full Document