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Date Posted: 11:48:51 11/01/00 Wed
Author: Roichard Fendler
Subject: FENDLER TVM SOLUTION SET

FI 3300 Time Value of Money Take-Home Problem Set
Answer Key and Solutions
Fall 00

1. B
2. B
3. A
4. B
5. A
6. Effective rate = 10.25%. PMT = 1000, N=3, CPT FV3 = 3318.01. Now, PV = 3318.01, N=2, I=10.25, CPT FV = $4,033.06.
7. CF0 = -250,000, C01=40000, F01=2, C02=30000, F02=2; I=16, CPT NPV = -150,002.26. This is the PV (in year 0) of the missing 12 payments. Since the first missing payment does not start until year 5, we need to find FV4. PV=150002.26, N=4, I=16, CPT FV4 = 271600.00. Now, PV = 271600.00, N=12, I=16, CPT PMT = $52,259.84
8. BANK A: PV=10000, N=30, I=9/2=, CPT FV = 37,453.18
BANK B: PV=10000, N=180, I=8.9/12=, CPT FV = $37813.22
BANK C: PV=10000, N=5475, I=8.8/365=, CPT FV = 37428.26
BANK D: PV=10000, N=15000000, I=8.75/1000000=, CPT FV = 37154.51
9. FV=100000, I=10, N=10, I=10, CPT FV = $38,554.33
10. PV=-46500, N=(10)(365)=3650, FV=100000, CPT I = .02. To find nominal rate, multiply by 365. Thus, rate = 7.66%.
11. Effective annual rate = 12.01%. First find amount needed on 12/31/05. FV=100000, I=12.01, N=5, CPT PV = 56717.36. Now, FV=56717.36, N=6, I=12.01, CPT PMT = $6,987.27
12. Find NPV with unknown deposits as 0; then find equivalent payment. CF0=14000, C01=0, F01=19, C02=-100000, F02=1; I=7; CPT NPV = -11841.90. Now, PV = -11841.90, I=7, N=6, CPT PMT = $2,484.38.
13. Effective rate = 8.30. PV =18325/.083 = $220,783.13
14. CF0=6000, C01=6600, F01=1, C02=7260, F02=1, C03=7986, F03=1, C04=8784.60, F04=1; CPT NPV (at I=12 = 28947.53. Then, PV=28947.53, N=5, I/Y=12, CPT FV = $51,015.45
15. CF0=-100, C01=125, F01=1, C02=2000, F02=1, C03=3000, F03=2, C04=0, F04=1, C05=-2000, F05=1, CPT NPV (at I = 12) = $4,634.63
16. PV=5625000, I/Y=9, N=30, CPT PMT = $547,516.98.
17. PV=-20000, N=60, PMT=444.89, CPT I/Y=1%, so annual rate = 12%. Now, PMT=444.89, I=1, N=(60-16)=44, CPT PV = $15,773.78
18. CF0=-2600, C01=525, C02=600, C03=750, C04=0, C05=750, C06=800 (F0_ = 1 for all numbers), CPT NPV (at I =10) = -146.10 - this is the Present Value of the missing cash flow.
So, PV=146.10, N=4, I/Y=10, CPT FV=$213.91
19. Compute three separate Future Values and sum. PV=15000, N=36, I/Y=12/12=1, CPT FV=21461.53; PV=12000, N=24, I/Y=12/12=1, CPT FV=15236.82; PV=25000, N=12, I/Y=12/12=1, CPT FV=28170.63. Sum of FV's = $64,868.97.
20. CF0=-24307.85, C01=2000, F01=3, C02=0, F02=6, C03=10000, F03=1, CPT NPV (at I=8.3) = -14676.22. Now PV 14676.22, N=3, I=8.3, CPT FV=18642.30. Finally, PV=18642.30, N=6, I=8.3, CPT PMT = $4069.39.
21. First find interest rate. PV=-100000, N=12, PMT=9456, CPT I = 2 (or 24% p.a.). Find payoff after 4th payment (i.e., with 8 payments remaining) = 69269.75. Find payoff after 5th payment (i.e., with 7 payments remaining) = 61199.15. Repayment of principle due to fifth monthly payment is differnece in payoffs = 69269.75-61199.15 = $8,070.60
22. First compute payment = 1494.73. Next compute payoff after 60th payment = 181808.96. Thus, reduction in balance after 60th payment is 190000-181808.96 = 8191.04. Total payments made = (60)(1494.73) = 89683.80. Difference between total and reduction in balance = interest = $81,492.76.
23. PMT=1,500,000, I=8.16, N=8, CPT PV = $8,567,864.42.
24. CF0=30000, C01=0, F01=9, C02=-96215.88, F02=25; Compute NPV (at I=9) = -405144.83. Now, PV = 405144.83, N=10, I=9, CPT PMT = $63,129.70
25. $63,129.70

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