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Date Posted: 08:21:33 03/02/01 Fri
Author: Richard Fendler (Course Coordinator)
Subject: Solutions to Chapter 7 and 8 Problems

Some students are apparently having difficulty accessing the solutions to Chapter 7 and 8 problems. Others, however, are able to open the links with no problems. I will check into this.

In the meantime, solutions are below. The format may look strange, but all info is there.

Solutions to Problems in Chapters 10, 11, and 12 will be posted during spring break.

Chapter 7
Answers to End of Chapter Assignments and Problems

Assignment 7.1:
1. FV = PV (1+r). Let FV = 2 and PV =1. Thus, 2 = 1(1+r). When you solve for r, you get r=1. Expressed as a percent, the interest rate is 100%.
2. FV = PV (1+r); 7397 = PV(1+.0439) or PV = 7297/1.0439; Solve PV = 7,085.93.
3. a. FV = PV (1+r); 13000 = PV(1.08) or PV = 13000/1.08; Solve for PV = 12,037.04.
b. Note that you will only need 13000 - 4500 = 8,500 one year from today. Thus, FV = PV (1+r); 8500 = PV(1.08) or PV = 8500/1.08; Solve for PV = 7,870.37.
4. FV = PV (1+r); 14739 = PV(1.12) or PV = 14739/1.12; Solve for PV = 13,159.82.

Assignment 7.2:
1. FVn = PV (1+r)n. Let FV = 2 and PV =1. Thus, 2 = 1(1+r)2 or 2½ = (1+r). When you solve for r, you get r=.4142. Expressed as a percent, the interest rate =s 41.42%.
2. PV = FV1(1/1+r)1 + FV2(1/1+r)2 ; PV = 3200(1/1.06)1 + 7300(1/1.06)2 ; PV = 3018.87 + 6496.97 = 9,515.84.
3. Note that the first deposit will grow for one year - that is, it will grow to become 7448 (1.07) = 7969.36. When you add the extra 2476, you will have a total of 10,445.36 in your account.
4. Continuing from #3, the 10,445.36 will grow again by 7 percent to be 10445.367(1.07) = 11,176.54.

Assignment 7.3:
1. FV2 = Deposit0 (1+r)2 + Deposit1 (1+r)1. (Note that the deposit made today (at t=0) will earn interest for 2 years and the deposit made one year from today will earn interest for 1 year). Thus, 4000 = 8000(1.04)2 + Deposit (1.04)1; 4000 = 8652 + Deposit (1.04). Solve for Deposit and you get Deposit = -4,473.85. The negative sign implies that you will withdraw this amount at the end of year one.
2. The question is what is the present value of the investment. That is, what is the present value of 6500 one year from today + 5000 two years from today. We then compare the value of the investment with the cost. If value > cost, you should buy. If value < cost, you should not buy. PV = FV1(1/1+r)1 + FV2(1/1+r)2 ; PV = 6500(1/1.12)1 + 5000(1/1.12)2 ; PV = 5803.57 + 3958.97 = 9,789.54. Do not make investment.
3. 538 = 500 (1+r)1; 1.0760 = 1+r; r = .0760 = 7.6%
4. (1 + rnominal) = (1 + rreal) x (1 + i); (1 + rnominal) = (1.08) x (1.04) = 1.1232. rnominal = .1232 = 12.32%.
5. (1 + rnominal) = (1 + rreal) x (1 + i); (1.122) = (1 + rreal) x (1.036); (1 + rreal) = 1.083. rreal = .083 = 8.3%.

Problems:
1. E(R) [i.e., Expected Return] on first = 11.5%;E(R) on second = 12.1%
Choose both since Expected Return > Required Return. NOTE: This problem implicitly assumes that these two investments are of equal risk. Unless otherwise explicitly stated, for all problems in this book, we will assume that all comparable investments are of equal risk.

2. E(R) on first = 10.2%; E(R) on second = 7.48%
Choose neither since for both E(R) < Required Return.

3. (d) is correct. For (a), PV must be less than 432 since interest rate is greater than 0.for (b), the FV (t=1) must be greater than the PV (t=0) value since interest rate is greater than 0.for (c), you would never pay more than the simple sum of all future cash flows (i.e., 2,300+2,300 = 4,600 < 6,600)

4. 70,661.16

5. 1,680.00; 1,915.20

6. In the following equation, solve for X (note that ^2 means raised to the second power, or int this case, squared): 10,000 = 7,000 (1/1.13)^1 + X(1/1.13)^2 ==> X = 4,859

7. In the following equation, solve for r: 4,100 = 3,500 (1+r)^2 ==> r = 8.233%

8. Buy the two year subscription because the PV of buying a one year subscription today and another one year subscription one year from today = 48 + 48(1/1.10) = 91.64 which is greater than the two year subscription price of 70. This answer of course assumes that you actually want to read this magazine for two years!

9. Assume that the two payments are due one month from today and 2 months from today. Payoff = 791.09

10. Compare 20,000 - 2,850 = 17,150 to the PV of 20,000 two years from today. 20,000(1/1.08)^2 = 17,146.78. Since 17,150 > 17,146.78, choose (b) because it is "cheaper."



Chapter 8
Answers to End of Chapter Assignments and Problems

Every attempt has been made to minimize errors in this answer guide. Typos, however, do sometimes occur. Please report any errors you find via e-mail to fncrjf@gsu.edu.

Assignment 8.1:
1. PV = -30000, FV = 49000, n = 5, Compute I/Y = 10.31%.
PV = -73000, FV = 128000, n = 7, Compute I/Y = 8.35%.
2. Use cash flow register: CF0 = 0, C01 = 22000, F01 = 1, C02 = 27500, F02 = 1, C03 = 33000, F03 = 1, C04 = 35000, F04 = 1; Compute NPV (with I = 6%) = 100,660.33
3. Use cash flow register to find NPV. Then find FV of this amount. Thus, CF0 = 11000, C01 = 13000, F01 = 1, C02 = 17400, F02 = 1, C03 = 12800, F03 = 1, C04 = 9600, F04 = 1; C05 = 17200, F05 = 1; Compute NPV (with I = 8%) = 66878.10. Now find the future value of this amount 10 years from today. PV = 66878.10, I = 8, n = 10, Compute FV = 144,384.81.

Assignment 8.2:
1. PV = -28000, fv = 30000, I = 6, n = 10, Compute PMT = 1,528.26.
2. First find F of deposits. PMT = 2500, I = 8, n = 20, Compute FV20 = 114404.91. Now find withdrawals. PV = 114404.91, n = 25, I = 8, Compute PMT = 10,717.31
3. First find NPV of all cash flows with the unknown cash flow assumed to be 0. That is, CF0 = 5000, C01 = 0, F01 = 10, C02 = -60000, F02 = 1, C03 = 0, F03 = 2, C04 = 25000, F04 = 1, C05 = 0, F05 = 11, C06 = -1500000, F06 = 25; Compute NPV (with I = 7%) = 335884.60. Now find PMT. PV = 335884.60, I = 7, n = 25, Compute PMT = 28,822.43.
4. First find PV20 of perpetuity = 30000/.12 = 250000 (note this is value in year 20).
CF0 = 0, C01 = 12000, F01 = 3, C02 = 17000, F02 = 4, C03 = 21000, F03 = 8, C04 = 24000, F04 = 4; C05 = 274000, F05 = 1; Compute NPV (with I = 12%) = 154,486.56.

Assignment 8.2:
1. PV = -1, FV = 2, I = 7/2 = 3.5, Compute n = 20.1488 semi-annual periods = 10.07 years.
2. Bank A: 10.00%; Bank B: 10.04%; Bank C: 9.95%; Bank D: 9.93%; Bank E: 9.86%.
3. PMT = 140000, n = 10, I = 9, Compute PV = 898472.08. This is value need at the end of year 20. Since first deposit will be made today, set calculator in BEGIN mode. Now, FV = 898472.08, I = 9, n = 20, Compute PMT = 16,111.89.
4. Annual payment = $8,652.62.

Problems:
1. a
2. e
3. d
4. a
5. e
6. b
7.
8. Stated rate = 7.1010%; Effective rate = 7.2270%
9. 17,740.97
10. 8.654%
11. 18.420
12. 76,175.84
13. 5,996.11
14. 4,520,178.42 today; 2,883,820.96 in five years.
15. 263.80
16. 59,739.98
17. 9.50
18. 482.09
19. Amount of payment that goes to principal = 7757.21; Amount that goes to interest = 1,698.79
20. 925,764
21. 86,303.09
22. 17,954.13
23. 276.21
24. 167,790.24
25. 252.33
26. 61.534.10
27. Disregard this question.
28. 165,918.32
29. 71,474.07

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