# EXERCISE 6-4 (15 20 minutes)

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1 EXERCISE 6-4 (15 20 minutes) (a) (b) (c) (d) Future value of an ordinary annuity of \$4,000 a period for 20 periods at 8% \$183, (\$4,000 X ) Factor (1 +.08) X 1.08 Future value of an annuity due of \$4,000 a period at 8% \$197, Present value of an ordinary annuity of \$2,500 for 30 periods at 10% \$23, (\$2,500 X ) Factor (1 +.10) X 1.10 Present value of annuity due of \$2,500 for 30 periods at 10% \$25, (Or see Table 6-5 which gives \$25,924.03) Future value of an ordinary annuity of \$2,000 a period for 15 periods at 10% \$63, (\$2,000 X ) Factor (1 + 10) X 1.10 Future value of an annuity due of \$2,000 a period for 15 periods at 10% \$69, Present value of an ordinary annuity of \$1,000 for 6 periods at 9% \$4, (\$1,000 X ) Factor (1 +.09) X 1.09 Present value of an annuity date of \$1,000 for 6 periods at 9% \$4, (Or see Table 6-5) EXERCISE 6-5 (10 15 minutes) (a) \$30,000 X = \$149, (b) \$30,000 X = \$249, (c) (\$30,000 X X = \$46, or ( ) X \$30,000 = \$46, (difference of \$.08 due to rounding). 6-19

2 EXERCISE 6-6 (15 20 minutes) (a) Future value of 10% for 10 years (\$12,000 X ) = \$31, (b) Future value of an ordinary annuity of \$600,000 at 10% for 15 years (\$600,000 X ) \$19,063, Deficiency (\$20,000,000 \$19,063,488) \$936, (c) \$70,000 discounted at 8% for 10 years: \$70,000 X = \$32, Accept the bonus of \$40,000 now. (Also, consider whether the 8% is an appropriate discount rate since the president can probably earn compound interest at a higher rate without too much additional risk.) EXERCISE 6-7 (12 17 minutes) (a) \$50,000 X = \$15, \$5,000 X = 42, \$58, (b) \$50,000 X = \$11, \$5,000 X = 38, \$49, The answer should be \$50,000; the above computation is off by 10 due to rounding. (c) \$50,000 X = \$ 9, \$5,000 X = 34,054,30 \$43,

3 EXERCISE 6-8 (10 15 minutes) (a) Present value of an ordinary annuity of 1 for 4 8% Annual withdrawal X \$20,000 Required fund balance on June 30, 2013 \$66, (b) Fund balance at June 30, 2013 \$66, Future value of an ordinary annuity at 8% for 4 years = \$14, Amount of each of four contributions is \$14, EXERCISE 6-9 (10 minutes) The rate of interest is determined by dividing the future value by the present value and then finding the factor in the FVF table with n = 2 that approximates that number: \$123,210 = \$100,000 (FVF 2, i% ) \$123,210 \$100,000 = (FVF 2, i% ) = (FVF 2, i% ) reading across the n = 2 row reveals that i = 11%. EXERCISE 6-10 (10 15 minutes) (a) (b) The number of interest periods is calculated by first dividing the future value of \$1,000,000 by \$92,296, which is the value \$1.00 would accumulate to at 10% for the unknown number of interest periods. The factor or its approximate is then located in the Future Value of 1 Table by reading down the 10% column to the 25-period line; thus, 25 is the unknown number of years Mike must wait to become a millionaire. The unknown interest rate is calculated by first dividing the future value of \$1,000,000 by the present investment of \$182,696, which is the amount \$1.00 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 15-period line to the 12% column; thus, 12% is the interest rate Venus must earn on her investment to become a millionaire. 6-21

4 EXERCISE 6-11 (10 15 minutes) (a) (b) Total interest = Total payments Amount owed today \$162, (10 X \$16,274.53) \$100,000 = \$62, Sosa should borrow from the bank, since the 9% rate is lower than the manufacturer s 10% rate determined below. PV OA 10, i% = \$100,000 \$16, = Inspection of the 10 period row reveals a rate of 10%. EXERCISE 6-12 (10 15 minutes) Building A PV = \$600,000. Building B Rent X (PV of annuity due of 25 periods at 12%) = PV \$69,000 X = PV \$606, = PV Building C Rent X (PV of ordinary annuity of 25 periods at 12%) = PV \$7,000 X = PV \$54, = PV Cash purchase price \$650, PV of rental income 54, Net present value \$595, Answer: Lease Building C since the present value of its net cost is the smallest. 6-22

5 EXERCISE 6-13 (15 20 minutes) Lance Armstrong, Inc. PV =? i = 5% PV OA =? Principal \$2,000,000 interest \$110,000 \$110,000 \$110,000 \$110,000 \$110,000 \$110, n = 30 Formula for the interest payments: PV OA = R (PVF OA n, i ) PV OA = \$110,000 (PVF OA 30, 5% ) PV OA = \$110,000 ( ) PV OA = \$1,690,970 Formula for the principal: PV = FV (PVF n, i ) PV = \$2,000,000 (PVF 30, 5% ) PV = \$2,000,000 ( ) PV = \$462,760 The selling price of the bonds = \$1,690,970 + \$462,760 = \$2,153,

6 SOLUTIONS TO PROBLEMS PROBLEM 6-1 (a) Given no established value for the building, the fair market value of the note would be estimated to value the building. i = 9% PV =? FV = \$275,000 1/1/07 1/1/08 1/1/09 1/1/10 n = 3 Formula: PV = FV (PVF n, i ) PV = \$275,000 (PVF 3, 9% ) PV = \$275,000 (.77218) PV = \$212, Cash equivalent price of building \$212, Less: Book value (\$250,000 \$100,000) 150, Gain on disposal of the building \$ 62,

7 PROBLEM 6-1 (Continued) (b) i = 11% Principal \$200,000 Interest PV OA =? \$18,000 \$18,000 \$18,000 \$18,000 1/1/07 1/1/08 1/1/09 1/1/2016 1/1/2017 n = 10 Present value of the principal FV (PVF 10, 11% ) = \$200,000 (.35218) = \$ 70, Present value of the interest payments R (PVF OA 10, 11% ) = \$18,000 ( ) = 106, Combined present value (purchase price) \$176, (c) i = 8% PV OA =? \$4,000 \$4,000 \$4,000 \$4,000 \$4, n = 10 Formula: PV OA = R (PVF OA n,i ) PV OA = \$4,000 (PVF OA 10, 8% ) PV OA = \$4,000 ( ) PV OA = \$26, (cost of machine) 6-36

8 PROBLEM 6-1 (Continued) (d) i = 12% PV OA =? \$20,000 \$5,000 \$5,000 \$5,000 \$5,000 \$5,000 \$5,000 \$5,000 \$5, n = 8 Formula: PV OA = R (PVF OA n,i ) PV OA = \$5,000 (PVF OA 8, 12% ) PV OA = \$5,000 ( ) PV OA = \$24, Cost of tractor = \$20,000 + \$24, = \$44, (e) i = 11% PV OA =? \$100,000 \$100,000 \$100,000 \$100, n = 9 Formula: PV OA = R (PVF OA n, i ) PV OA = \$100,000 (PVF OA 9, 11% ) PV OA = \$100,000 ( ) PV OA = \$553,

9 PROBLEM 6-6 i = 12% PV OA =? R = (\$36,000) (\$36,000) \$23,000 23,000 \$63,000 \$63,000 \$63,000 \$63,000 \$43,000 \$43,000 \$43, n = 5 n = 5 n = 20 n = 10 (0 \$27,000 \$9,000) (\$60,000 \$27,000 \$10,000) (\$100,000 \$27,000 \$10,000) (\$80,000 \$27,000 \$10,000) Formulas: PV OA = R (PVF OA n, i ) PV OA = R (PVF OA n, i ) PV OA = R (PVF OA n, i ) PV OA =R (PVF OA n, i ) PV OA = (\$36,000)(PVF OA 5, 12% ) PV OA = \$23,000 (PVF OA 10-5, 12% ) PV OA = \$63,000 (PVF OA 30 10, 12% ) PV OA = \$43,000 (PVF OA 40 30, 12% ) PV OA = (\$36,000)( ) PV OA = \$23,000 ( ) PV OA = \$63,000 ( ) PV OA = \$43,000 ( ) PV OA =(\$129,772.08) PV OA = \$23,000 ( ) PV OA = \$63,000 ( ) PV OA = \$43,000 (.18860) PV OA = \$47, PV OA = \$151, PV OA = \$8, Present value of future net cash inflows: \$(129,772.08) 47, , , \$ 76, Nicole Bobek should accept no less than \$76, for her vineyard business.

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