APPENDIX C. Time Value of Money SOLUTIONS TO BRIEF EXERCISES. Accumulated amount = $4,000 + $2,000 = $6,000

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1 BRIEF EXERCISE C-1 APPENDIX C Time Value of Money SOLUTIONS TO BRIEF EXERCISES (a) Interest = p X i X n I = $4,000 X.05 X 10 years I = $2,000 Accumulated amount = $4,000 + $2,000 = $6,000 (b) Future value factor for 10 periods at 5% is (from Table 1) Accumulated amount = $4,000 X = $6, BRIEF EXERCISE C-2 1. a. 8% 5 periods 2. a. 5% 10 periods b. 2.5% 6 periods b. 2% 12 periods BRIEF EXERCISE C-3 FV = p X FV of 1 factor = $10,000 X = $14, BRIEF EXERCISE C-4 FV = p X FV of an annuity factor = $75,000 X = $988, Copyright 2010 John Wiley & Sons, Inc. Weygandt, Financial Accounting, 7/e, Solutions Manual (For Instructor Use Only) C-1

2 BRIEF EXERCISE C-5 FV = p X FV of 1 factor + (p X FV of an annuity factor) = ($5,000 X ) + ($1,000 X ) = $12, $28, = $40, BRIEF EXERCISE C-6 FV = p X FV of 1 factor = $20,000 X = $28, BRIEF EXERCISE C % 6 10% 15 4% % 20 10% 5 6% 8 BRIEF EXERCISE C-8 (a) i = 8%? $20, Discount rate from Table 3 is (8 periods at 8%). Present value of $20,000 to be received in 8 years discounted at 8% is therefore $10, ($20,000 X.54027). C-2 Copyright 2010 John Wiley & Sons, Inc. Weygandt, Financial Accounting, 7/e, Solutions Manual (For Instructor Use Only)

3 BRIEF EXERCISE C-8 (Continued) (b) I = 9%? $20,000 $20,000 $20,000 $20,000 $20,000 $20, Discount rate from Table 4 is (6 periods at 9%). Present value of 6 payments of $20,000 each discounted at 9% is therefore $89, ($20,000 X ). BRIEF EXERCISE C-9 i = 10%? $500, PV = p X PV of 1 factor PV = $500,000 X PV = $310,460 Discount rate from Table 3 is (5 periods at 10%). Present value of $500,000 to be received in 5 years discounted at 10% is therefore $310,460 ($500,000 X.62092). Gonzalez Company should therefore invest $310,460 to have $500,000 in five years. Copyright 2010 John Wiley & Sons, Inc. Weygandt, Financial Accounting, 7/e, Solutions Manual (For Instructor Use Only) C-3

4 BRIEF EXERCISE C-10 i = 9%? $875, PV = p X PV of 1 factor PV = $875,000 X PV = $439, Discount rate from Table 3 is (8 periods at 9%). Present value of $875,000 to be received in 8 years discounted at 9% is therefore $439, ($875,000 X.50187). Lasorda Company should invest $439, to have $875,000 in eight years. BRIEF EXERCISE C-11 i = 6%? $30,000 $30,000 $30,000 $30,000 $30,000 $30, PV of annuity = Annuity X PV of annuity factor PV = $30,000 X PV = $291, Discount rate from Table 4 is Present value of 15 payments of $30,000 each discounted at 6% is therefore $291, ($30,000 X ). Bosco Company should pay $291, for this annuity contract. C-4 Copyright 2010 John Wiley & Sons, Inc. Weygandt, Financial Accounting, 7/e, Solutions Manual (For Instructor Use Only)

5 BRIEF EXERCISE C-12 i = 11%? $120,000 $120,000 $120,000 $120, PV of annuity = Annuity X PV of annuity factor PV = $120,000 X PV = $372,294 Discount rate from Table 4 is Present value of 4 payments of $120,000 each discounted at 11% is therefore $372,294 ($120,000 X ). Modine Enterprises invested $372,294 to earn $120,000 per year for four years. Copyright 2010 John Wiley & Sons, Inc. Weygandt, Financial Accounting, 7/e, Solutions Manual (For Instructor Use Only) C-5

6 BRIEF EXERCISE C-13 Diagram for Principal Diagram for Interest i = 4%? $100, i = 4%? $5,000 $5,000 $5,000 $5,000 $5,000 $5, Present value of principal to be received at maturity: $100,000 X (PV of $1 due in 20 periods at 4% from Table 3)... $ 45, Present value of interest to be received periodically over the term of the bonds: $5,000 X (PV of $1 due each period for 20 periods at 4% from Table 4)... 67, Present value of bonds... $113, BRIEF EXERCISE C-14 The bonds will sell at par or $100,000. This may be proven as follows: Present value of principal to be received periodically: $100,000 X (PV of $1 due in 20 periods at 5% from Table 3)... $ 37,689 Present value of interest to be received periodically over the term of the bonds: $5,000 X (PV of $1 due each period for 20 periods at 5% from Table 4)... 62,311* Present value of bonds... $100,000* *Rounded. C-6 Copyright 2010 John Wiley & Sons, Inc. Weygandt, Financial Accounting, 7/e, Solutions Manual (For Instructor Use Only)

7 BRIEF EXERCISE C-15 Diagram for Principal i = 9%? $50, Diagram for Interest i = 9%? $4,000 $4,000 $4,000 $4,000 $4,000 $4, Present value of principal to be received at maturity: $50,000 X (PV of $1 due in 6 periods at 9% from Table 3)... $29, Present value of interest to be received annually: over the term of the note: $4,000 X (PV of $1 due each period for 6 periods at 9% from Table 4)... 17, Present value of note received... $47, Copyright 2010 John Wiley & Sons, Inc. Weygandt, Financial Accounting, 7/e, Solutions Manual (For Instructor Use Only) C-7

8 BRIEF EXERCISE C-16 Diagram for Principal i = 5%? $2,000, Diagram for Interest i = 5%? $80,000 $80,000 $80,000 $80,000 $80,000 $80,000 $80, Present value of principal to be received at maturity: $2,000,000 X (PV of $1 due in 16 periods at 5% from Table 3)... $ 916, Present value of interest to be received periodically over the term of the bonds: $80,000 X (PV of $1 due each period for 16 periods at 5% from Table 4) , Present value of bonds and cash proceeds... $1,783, BRIEF EXERCISE C-17 i = 11%? $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3, PV of annuity = Annuity X PV of annuity factor PV = $3,000 X PV = $15, C-8 Copyright 2010 John Wiley & Sons, Inc. Weygandt, Financial Accounting, 7/e, Solutions Manual (For Instructor Use Only)

9 BRIEF EXERCISE C-17 (Continued) Discount rate from Table 4 is Present value of 8 payments of $3,000 each discounted at 11% is therefore $15, ($3,000 X ). Vinny Carpino should not purchase the tire retreading machine because the present value of the future cash flows is less than the purchase price of the retreading machine. BRIEF EXERCISE C-18 i = 5%? $56,413 $56,413 $56,413 $56,413 $56,413 $56, PV of annuity = Annuity X PV of annuity factor PV = $56,413 X PV = $500, Discount rate from Table 4 is Present value of 12 payments of $56,413 each discounted at 5% is therefore $500, ($56,413 X ). Rodriguez Company should receive $500, from the issuance of the note. BRIEF EXERCISE C-19 i = 12%? $30,000 $40,000 $50, To determine the present value of the future cash flows, discount the future cash flows at 12%, using Table 3. Copyright 2010 John Wiley & Sons, Inc. Weygandt, Financial Accounting, 7/e, Solutions Manual (For Instructor Use Only) C-9

10 BRIEF EXERCISE C-19 (Continued) Year 1 ($30,000 X.89286) = $26, Year 2 ($40,000 X.79719) = 31, Year 3 ($50,000 X.71178) = 35, Present value of future cash flows $94, To achieve a minimum rate of return of 12%, Goltra Company should pay no more than $94, If Goltra pays less than $94,262.40, its rate of return will be greater than 12%. BRIEF EXERCISE C-20 i =?% $3,152 $10, Present value = Future value X Present value of 1 Factor $3,152 = $10,000 X.3152 The for 15 periods is found in the 8% column. Maria Sanchez will receive an 8% return. BRIEF EXERCISE C-21 i = 10% $42,410 $100,000 n =? Present value = Future value X Present value of 1 Factor $42,410 = $100,000 X The at 10% is found in the 9 years row. Lori Burke therefore must wait 9 years to receive $100,000. C-10 Copyright 2010 John Wiley & Sons, Inc. Weygandt, Financial Accounting, 7/e, Solutions Manual (For Instructor Use Only)

11 BRIEF EXERCISE C-22 i =?? $1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $1, $12, n = 20 Present value = Future value X Present value of an annuity factor $12, = $1,000 X The for 20 periods is found in the 5% column. Nancy Burns will therefore earn a rate of return of 5%. BRIEF EXERCISE C-23 i = 8% $1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $7, n =? Present value = Future value X Present value of an annuity factor $7, = $1,000 X The at an interest rate of 8% is shown in the 12-year row. Betty Estes therefore will receive 12 payments. Copyright 2010 John Wiley & Sons, Inc. Weygandt, Financial Accounting, 7/e, Solutions Manual (For Instructor Use Only) C-11

12 BRIEF EXERCISE C-24 10? 19, ,000 N I/YR. PV PMT FV 9.94% BRIEF EXERCISE C-25 10? 42,000 6,500 0 N I/YR. PV PMT FV 8.85% BRIEF EXERCISE C-26 40? 178,000 14,000 0 N I/YR. PV PMT FV 7.42% (semiannual) C-12 Copyright 2010 John Wiley & Sons, Inc. Weygandt, Financial Accounting, 7/e, Solutions Manual (For Instructor Use Only)

13 BRIEF EXERCISE C-27 (a) Inputs: ? 16,000 0 N I PV PMT FV Answer: 85, (b) Inputs: ? 16,000* 200,000 N I PV PMT FV Answer: 168, *200 X $1,000 X.08 Copyright 2010 John Wiley & Sons, Inc. Weygandt, Financial Accounting, 7/e, Solutions Manual (For Instructor Use Only) C-13

14 BRIEF EXERCISE C-28 (a) Note set payments at 12 per year. Inputs: ,000? 0 N I PV PMT FV Answer: (b) Note set payments to 1 per year. Inputs: ,000? 0 N I PV PMT FV Answer: 2, C-14 Copyright 2010 John Wiley & Sons, Inc. Weygandt, Financial Accounting, 7/e, Solutions Manual (For Instructor Use Only)