Solutions To Problems: Chapter 5

Solutions to Problems: Chapter 5
P5-1. Using a time line LG 1; Basic a, b, and c

d. Financial managers rely more on present value than future value because they typically make decisions before the start of a project, at time zero, as does the present value calculation. P5-2. Future value calculation LG 2; Basic Case A N B N C N D N P5-3. 2, I 3, I 2, I 4, I 12%, PV 6%, PV 9%, PV 3%, PV $1,Solve for FV $1, Solve for FV $1, Solve for FV $1, Solve for FV 1.2544 1.1910 1.1881 1.1259

Time to double LG 1; Basic Case A: Computer Inputs: I 12%, PV $100; FV $200 Solve for N 6.12 years Case B: Computer Inputs: I 6%, PV $100; FV $200  N 11.90 years It takes just short of twice as long to double in value. One reason for it being shorter is that in Case B there are more periods over whichcompounding occurs.

Note: You could use the ―Rule of 72‖ to complete the problem. Simply divide 72 by the interest rate to get the number of years it would take to double an initial balance. Case A: 72 Case B: 72 P5-4. Future values LG 2; Intermediate Case A N 20, I 5%, PV $200. Solve for FV $530.66 C N 10; I 9%; PV $10,000. Solve for FV $23,673.64 E P5-5. N 5, I 11, PV $37,000 Solve for FV$62,347.15 Case B N 7, I/Y 8%; PV $4500. Solve for FV $7,712.21 D N 12; I 10%, PV $25,000 Solve for FV $78,460.71 F N 9, I 12, PV $40,000 Solve for FV $110,923.15 12 6 6 years 12 years

Personal finance: Time value LG 2; Intermediate a. FV3 PV $1,837.56 $1,500.00 $337.56 (2) N 6, I 7%, PV $1,500 (2) Interest earned FV6 – FV3 Solve for FV6 $2,251.10 Interest earned $2,251.10 –$1,837.56 $413.54 (3) N9, I 7%, PV $1,500 (3) Interest earned FV9 FV6 Solve for FV9 $2,757.69 Interest earned $2,757.69 –$2,251.10 $506.59 The fact that the longer the investment period is, the larger the total amount of interest collected will be, is not unexpected and is due to the greater length of time that the principal sum of $1,500 is invested. The most significant point is that the incremental interest earned per3-year period increases with each subsequent 3-year period. The total interest for the first 3 years is $337.56; however, for the second 3 years (from year 3 to 6) the additional interest earned is $413.54. For the third 3-year period, the incremental interest is $506.59. This increasing change in interest earned is due to compounding, the earning of interest on previous interest earned. Thegreater the previous interest earned, the greater the impact of compounding. (1) N 3, I 7%, PV $1,500 Solve for FV3 $1,837.56 b. (1) Interest earned Interest earned

c.

P5-6.

Personal finance: Time value LG 2; Challenge a. (1) N 5, I 2%, PV $14,000 (2) N 5, I 4%, PV $14,000 Solve for FV $15,457.13 Solve for FV $17,033.14 b. The car will cost $1,576.01 more with a 4% inflation rate than aninflation rate of 2%. This increase is 10.2% more ($1,576 $15,457) than would be paid with only a 2% rate of inflation. c. Future value at end of first 2 years: N 2, I 2%, PV $14,000 Solve for FV2 $14,565.60 Price rise at end of 5th year: N 3, I 4%, PV $14,565.60 Solve for FV5 $16,384.32 As one would expect, the forecast price is between the values calculated with 2% and 4% interest.

P5-7.Personal finance: Time value LG 2; Challenge Deposit Now: N 40, I 9%, PV $10,000 Solve for FV $314,094.20 Deposit in 10 Years: N 30, I 9%, PV $10,000 Solve for FV $132,676.78

You would be better off by $181,417 ($314,094 $132,677) by investing the $10,000 now instead of waiting for 10 years to make the investment. P5-8. Personal finance: Time value LG 2; Challenge a. c. P5-9. N 5, PV Solve for I N5, PV Solve for I $10,200, FV 15,000 8.02% $7150, FV $15,000 15.97% b. N 5, PV Solve for I $8,150, FV 12.98% $15,000

Personal finance: Single-payment loan repayment LG 2; Intermediate a. c. N 1, I 14%, PV $200 Solve for FV1 $228 N 8, I 14%, PV $200 Solve for FV8 $570.52 b. N 4, I 14%, PV $200 Solve for FV4 $337.79

P5-10. Present value calculation: PVIF LG 2; Basic Case A B C D N N N N 4,...