CHAPTER 6 SOLUTIONS TO B EXERCISES E61B (5–10 minutes) Rate of Interest Number of Periods a b c 8% 4% 5% 8 40 20 a b c 8% 6% 4% 25 30 28 E62B (5–10 minutes) (a) Simple interest of $800 per year X 10 Principal Total withdrawn (b) Interest compounded annually—Future value of 1 @ 8% for 10 periods Total withdrawn (c) Interest compounded semiannually—Future value of 1 @ 4% for 20 periods Total withdrawn $ 8,000 10,000 $18,000 2.15892 X $10,000 $21,589.20 2.19112 X $10,000 $21,911.20 Copyright © 2014 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e, Exercise B Solutions (For Instructor Use Only) 61 E63B (10–15 minutes) (a) $14,000 X 1.33823 = $18,735.22 (b) $14,000 X .46651 = $6,531.14 (c) $14,000 X 27.15211 = $380,129.54 (d) $14,000 X 7.46944 = $104,572.16 E64B (15–20 minutes) (a) (b) (c) (d) Future value of an ordinary annuity of $12,000 a period for 20 periods at 6% Factor (1 + .06) Future value of an annuity due of $12,000 a period at 6% Present value of an ordinary annuity of $7,500 for 30 periods at 8% Factor (1 + .08) Present value of annuity due of $7,500 for 30 periods at 8% Future value of an ordinary annuity of $6,000 a period for 15 periods at 8% Factor (1 + .08) Future value of an annuity due of $6,000 a period for 15 periods at 8% Present value of an ordinary annuity of $3,000 for 6 periods at 10% Factor (1 + .10) Present value of an annuity date of $3,000 for 6 periods $441,427.08 ($12,000 X 36.78559) X 1.06 $467,912.70 $84,433.35 ($7,500 X 11.25778) X 1.08 $91,188.02 (Or see Table 65 which gives $91,188.08) $162,912.66 ($6,000 X 27.15211) X 1.08 $175,945.66 $13,065.78 ($3,000 X 4.35526) X 1.10 62 Copyright © 2014 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e, Exercise B Solutions (For Instructor Use Only) at 10% E65B (10–15 minutes) $14,372.36 (Or see Table 65) (a) $50,000 X 5.33493 = $266,746.50 (b) $50,000 X 8.85137 = $442,568.50 (c) ($50,000 X 3.16986 X .56447 = $89,464.54 or (6.14457 – 4.35526) X $50,000 = $89,465.50 (difference of $0.96 due to rounding) E66B (15–20 minutes) (a) Future value of $20,000 @ 5% for 20 years ($20,000 X 2.65330) = $ 53,066.00 (b) Future value of an ordinary annuity of $2,000,000 at 6% for 10 years ($2,000,000 X 13.18079) Deficiency ($30,000,000 – $26,361,580) $26,361,580.00 $ 3,638,420.00 (c) $80,000 discounted at 6% for 10 years: $80,000 X 0.55839 = Accept the cash bonus of $50,000 $ 44,671.20 Copyright © 2014 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e, Exercise B Solutions (For Instructor Use Only) 63 E67B (12–17 minutes) (a) $500,000 X .21455 = $107,275.00 + $50,000 X 9.81815 = 490,907.50 $598,182.50 (b) $500,000 X .14864 = $ 74,320.00 + $50,000 X 8.51356 = 425,678.00 $499,998.00 The answer should be $500,000; the above computation is off by $2 due to rounding (c) $500,000 X .10367 = $ 51,835.00 + $50,000 X 7.46944 = 373,472.00 $425,307.00 E68B (10–15 minutes) (a) Present value of an ordinary annuity of 1 for 4 periods @ 10% Annual withdrawal Required fund balance on June 30, 2017 (b) Fund balance at June 30, 2017 $190,191.60 = $40,980.74 Future amount of ordinary annuity at 10% 4.64100 for 4 years 3.16986 X $60,000 $190,191.60 Amount of each of four contributions is $40,980.74 64 Copyright © 2014 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e, Exercise B Solutions (For Instructor Use Only) E69B (10 minutes) The rate of interest is determined by dividing the future value by the present value and then find the factor in the FVF table with n = 2 that approximate that number: $246,420 = $200,000 (FVF2, i%) $246,420 ÷ $200,000 = (FVF2, i%) 1.2321 = (FVF2, i%)—reading across the n = 2 row reveals that i = 11% E610B (10–15 minutes) (a) The number of interest periods is calculated by first dividing the future value of $2,000,000 by $184,592, which is 10.83471—the value $1 would accumulate to at 10% for the unknown number of interest periods. The factor 10.83471 or its approximate is then located in the “Future value of 1” table by reading down the 10% column to the 25period line; thus, 25 is the unknown number of years Jafri must wait to for his two million (b) The unknown interest rate is calculated by first dividing the future value of $2,000,000 by the present investment of $365,392, which is 5.47357— the amount $1 would accumulate to in 15 years at an unknown interest rate. The factor or its approximate is then located in the “Future value of 1” table by reading across the 15period line to the 12% column; thus, 12% is the interest rate Jones must earn for her investment to gow to two million Copyright © 2014 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e, Exercise B Solutions (For Instructor Use Only) 65 E611B (10–15 minutes) (a) Total payments – Amount owed today = Total interest $488,235.90 (10 X $48,823.59) – $300,000 = $188,235.90 (b) Loh should borrow from the bank, since the 9% rate is lower than the manufacturer’s 10% rate determined below PV – OA10, i% = $300,000 ÷ $48,823.59 = 6.14557—Inspection of the 10period row reveals a rate of 10% E612B (10–15 minutes) Building A—PV = $1,500,000 Building B— Rent X (PV of annuity due of 25 periods at 8%) = PV $125,000 X 11.52876 = PV $1,441,095.00 = PV Building C— Rent X (PV of ordinary annuity of 25 periods at 8%) = PV $21,000 X 10.67478 = PV $224,170.38 = PV Cash purchase price PV of rental income Net present value $1,750,000.00 – 224,170.38 $1,525,829.62 Answer: Lease Building B since the present value of its net cost is the smallest 66 Copyright © 2014 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e, Exercise B Solutions (For Instructor Use Only) E613B (15–20 minutes) Time diagram: PV = ? PV – OA = ? Loyd Inc i = 4% $275,000 $275,000 $275,000 Principal $5,000,000 Interest $275,000 $275,000 $275,000 0 1 2 3 28 29 30 n = 30 Formula for the interest payments: PV – OA = R (PVF – OAn, i) PV – OA = $275,000 (PVF – OA30, 4%) PV – OA = $275,000 (17.29203) PV – OA = $4,755,308.25 Formula for the principal: PV = FV (PVFn, i) PV = $5,000,000 (PVF30, 4%) PV = $5,000,000 (0.30832) PV = $1,541,600 The selling price of the bonds = $4,755,308.25 + $1,541,600 = $6,296,908.25 Copyright © 2014 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e, Exercise B Solutions (For Instructor Use Only) 67 E614B (15–20 minutes) Time diagram: i = 8% R = $2,800,000 $2,800,000 $2,800,000 PV – OA = ? 0 1 2 15 16 24 25 n = 15 n = 10 Formula: PV – OA = R (PVF – OAn, i ) PV – OA = $2,800,000 (PVF – OA25–15, 8%) PV – OA = $2,800,000 (10.67478 – 8.55948) PV – OA = $2,800,000 (2.11530) PV – OA = $5,922,840 OR Time diagram: PV – OA = ? i = 8% R = $2,800,000 $2,800,000 $2,800,000 0 1 2 15 16 24 25 FV(PVn, i) (PV – OAn, i ) 68 Copyright © 2014 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e, Exercise B Solutions (For Instructor Use Only) E614B (Continued) (i) Present value of the expected annual pension payments at the end of the 15th year: PV – OA = R (PVF – OAn, i) PV – OA = $2,800,000 (PVF – OA10, 8%) PV – OA = $2,800,000 (6.71008) PV – OA = $18,788,224 (ii) Present value of the expected annual pension payments at the beginning of the current year: PV = FV (PVF – OAn, i) PV = $18,788,224 (PVF – OA15,8%) PV = $18,788,224 (0.31524) PV = $5,922,800* *$40 difference due to rounding The company’s pension obligation (liability) is $5,922,800 Copyright © 2014 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e, Exercise B Solutions (For Instructor Use Only) 69 E615B (15–20 minutes) (a) PV = $525,000 i = 4% FV = $1,000,000 0 1 2 n = ? FVF(n, 4%) = $1,000,000 ÷ $525,000 = 1.9048 reading down the 4% column, 1.9048 corresponds to approximately 16 ½ years (b) By setting aside $200,000 now, Lee can gradually build the fund to an amount to establish the foundation PV = $200,000 FV = ? 0 1 2 5 6 FV = $200,000 (FVF6, 4%) = $200,000 (1.26532) = $253,064—Thus, the amount needed from the annuity: $1,000,000 – $253,064 = $746,936 $? $? $? FV = $746,936 01256 Payments =FVữ(FVOA6,4%) =$746,936ữ6.63298 =$112,609.41 6ư10 Copyrightâ2014JohnWiley&Sons,Inc.Kieso,IntermediateAccounting,15/e,ExerciseBSolutions(ForInstructorUseOnly) E6ư16B(1015minutes) AmounttoberepaidonMarch1,2023: Time diagram: i = 5% per 6 months PV = $200,000 FV = ? 3/1/13 3/1/14 3/1/15 3/1/21 3/1/21 3/1/23 n = 20 6month periods Formula: FV = PV (FVFn, i) FV = $200,000 (FVF20, 5%) FV = $200,000 (2.65330) FV = $530,660 Amount of annual contribution to retirement fund: Time diagram: i = 8% R R R R R FV – AD = R = ? ? ? ? ? $530,660 3/1/18 3/1/19 3/1/20 3/1/21 3/1/22 3/1/23 Future value of ordinary annuity of 1 for 5 periods at 8% Factor (1 + .08) Future value of an annuity due of 1 for 5 periods at 8% Periodic rent ($530,660 ÷ 6.33593) 5.86660 X 1.08000 6.33593 $83,754.08 Copyright © 2014 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e, Exercise B Solutions (For Instructor Use Only) 611 E617B (10–15 minutes) Time diagram: i = 10% R R R PV – OA = $250,000 ? ? ? 0 1 24 25 n = 25 Formula: PV – OA = R (PV – OAn, i) $250,000 = R (PVF – OA25, 10%) $250,000 = R (9.07704) R = $250,000 ÷ 9.07704 R = $27,542.02 E618B (10–15 minutes) Time diagram: i = 6% PV – OA = ? $200,000 $200,000 $200,000 $200,000 $200,000 0 1 2 8 9 10 n = 10 Formula: PV – OA = R (PVF – OAn, i%) PV – OA = $200,000 (PVF – OA10, 6%) PV – OA = $200,000 (7.36009) R = $1,472,018 612 Copyright © 2014 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e, Exercise B Solutions (For Instructor Use Only) The recommended method of payment would be the 10 annual payments of $200,000, since the present value of those payments ($1,472,018) is less than the alternative immediate cash payment of $1,500,000 Copyright © 2014 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e, Exercise B Solutions (For Instructor Use Only) 613 E619B (10–15 minutes) Time diagram: i = 6% PV – AD = ? R = $200,000 $200,000 $200,000 $200,000 $200,000 0 1 2 8 9 10 n = 10 Formula: Using Table 64 Using Table 65 PV – AD = R (PVF – OAn, i) PV – AD = R (PVF – ADn, i) PV – AD = $200,000 (7.36009 X 1.06) PV – AD = $200,000(PVF – AD10, 6%) PV – AD = $200,000 (7.80169) PV – AD = $200,000 (7.80169) PV – AD = $1,560,338 PV – AD = $1,560,338 The recommended method of payment would be the immediate cash payment of $1,500,000, since that amount is less than the present value of the 10 annual payments of $200,000 ($1,560,338) 614 Copyright © 2014 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e, Exercise B Solutions (For Instructor Use Only) E620B (5–10 minutes) (a) Estimated Cash Probability Expected Outflow X Assessment = Cash Flow $2,800 30% $ 840 6,400 40% 2,560 8,500 30% 2,550 $3,950 (b) Estimated Cash Probability Expected Outflow X Assessment = Cash Flow $3,400 40% $1,360 7,100 50% 3,550 7,400 10% 740 $5,650 (c) Estimated Cash Probability Expected Outflow X Assessment = Cash Flow $(1,000) 20% $ (200) 3,000 70% 2,100 4,000 10% 400 $2,300 Copyright © 2014 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e, Exercise B Solutions (For Instructor Use Only) 615 E621B (10–15 minutes) Estimated Cash Probability Expected Outflow X Assessment = Cash Flow $ 500 10% $ 50 1,200 25% 300 2,000 50% 1,000 2,500 15% 375 X PV Factor, n = 4, i = 4% $ 1,725 X0.85480 Present Value $1,474.53 E622B (15–20 minutes) (a) This exercise determines the present value of an ordinary annuity or expected cash flows as a fair value estimate Cash flow Probability Expected Estimate X Assessment = Cash Flow $1,000,000 30% $ 300,000 1,600,000 50% 800,000 2,100,000 20% 420,000 X PV Factor, n = 6, I = 4% Present Value $ 1,520,000 X 5.24214 $ 7,968,053 The fair value estimate of the trade name is less than the carrying value; thus, an impairment is recorded (b) This fair value is based on unobservable inputs—Houston’s own data on the expected future cash flows associated with the trade name. This fair value estimate is considered Level 3 616 Copyright © 2014 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e, Exercise B Solutions (For Instructor Use Only) ... Copyright © 2014 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e, Exercise B Solutions (For Instructor Use Only) E614B (Continued) (i) Present value of the expected annual pension payments at the end of the 15th year:... Copyright © 2014 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e, Exercise B Solutions (For Instructor Use Only) 63 E67B (12–17 minutes) (a) $500,000 X .21455... 64 Copyright © 2014 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e, Exercise B Solutions (For Instructor Use Only) E69B (10 minutes) The rate of interest is determined by dividing the future value by the present