Chapter 3Problems

1) a) Method 1 0 1PV $ 12,000 Interest 9% 12000 13080n 7

Method 2 $ 21,936.47

Method 3 $21,936.47

b) Method 1 0 1 n = 7 $ 12,000 $ 12,270 m = 4

Method 2 $ 22,374.54

Method 3 $22,374.54

c) Reminder Equivalent Annual Yield "EAY" = (FV-PV)/PV

Method 1 Method 2a) 9.00% 9.00%

Better---> b) 9.31% 9.31%9.00%

Alternative 12) PV $ 25,000 m 12

n 1 i 7%

Better ---> Alternative 2m 1i 8%

Method 13) PMT 5000 Periods 0

n 12m 2 Scenario 1i 8.50% FV $ 201,806 0

Scenario 2 $ 210,382 13576.74095868Note: he does not make a deposit at the end of the last period!!

Method 2$201,805.67

$210,382.41

7) PMT 2150 Method 1 0

n 10IRR 18% CF 0

PV = $ 9,662 0

CF 2150PV $ 11,401 2150

Method 2

PVA PMT 2150N 10i 18%PV 9662.285534087

PVA PMT 2150N 9i 18%PV 9251.496930223

$11,401.50 Method 3

PV = $9,662.29

PV = $11,401.50

8) FV $ 45,000 Method 1n 6m 4 PV= $ 15,647 i 18%

Method 2

PV = $15,647

10) Method 1 0 1

-7000 07.92%

No, John should not pay for the lot at $7,000 because it will result in a yield of less than the 10% he thinks he should earn.

Method 2

a) PV 5783.15 Since this is the present value discounted at 10% it is worth less than the asking price, john should not pay the $7,000 asked.N 10 NOi 10%FV 15000

b PV 7000.00N 10i 7.92% This is the rate or return John would earn FV 15000 This was found by using goal seek, but one could also just plug in numbers and estimate the rate be seeing the PV change.

Method 3

pv = 7.92% same as above, no John should not pay $7,000 for the lot because it will yeild less that the 10% he thinks it should.

13) 1) Method 1i 13% 0 1

m 1 5500vs. annual $ 24,991 4867.256637168m 12 monthly $ 24,522 $ 4,833

Method 2Price 0 1 $ 24,990 $ (24,990) 5500

IRR --> 13.00%Arrived at by goal seek changing the purchase price until the IRR equals 13%

0 1 2-24522 0 013.80%

EAY or IRR for 13% compounded monthly --> 13.80%

14) Method 1

i 1.50% <- Periodic Rate 0 119.56% 1.5% -100000 1500

wrong 18% 0.0006708755 -100000 1477.832512563

Solve for the Monthly Periodic Rate that makes the discounted cash flow equal to $0, then express it as an annual rate.

Method 2Right 19.56%Wrong!! 1.50% 18%

Goal Seek to bring sum to $0.0018) Method 1 0 1

i 10% -13000 5000 $ 0.00 -13000 4545.454545455

Method 210.00% IRR Function

2 3 4 5 6 7

14257.2 15540.348 16938.98 18463.49 20125.2 21936.47

2 3 4 5 6 7 8 $ 12,546 $ 12,828 $ 13,117 $ 13,412 $ 13,714 $ 14,022 $ 14,338

0 1 2 3 4 5 $ (12,000) 0 0 0 0 0

0 1 2 3 4 5 $ (12,000) 0 0 0 0 0

<--Wrong!

FV $ 26,807 $26,807 0.072286

Method 1 Method 2FV $ 27,000 $27,000

1 2 3 4 5 6 7

13023.25272 12492.3287464 11983.05 11494.53 11025.93 10576.43 10145.26

13023.25272 12492.3287464 11983.05 11494.53 11025.93 10576.43 10145.26Note: he does not make a deposit at the end of the last period!!

Method 3 FVA Formula FVA = PMT * ((1+(i/m))^(n*m) – 1)/ (i / m) $ 201,805.67

$ 210,382.41 Note: The fomula needs to be adjusted for 1 more period of comounding without a last $5000 deposit.

1 2 3 4 5 6 7

2150 2150 2150 2150 2150 2150 21501822.033898 1544.09652399 1308.556 1108.946 939.7848 796.4278 674.9388

2150 2150 2150 2150 2150 2150 21501822.033898 1544.09652399 1308.556 1108.946 939.7848 796.4278 674.9388

$9,662.29

+ 2150 = 11401.5

2 3 4 5 6 7 8

0 0 0 0 0 0 0

No, John should not pay for the lot at $7,000 because it will result in a yield of less than the 10% he thinks he should earn.

Since this is the present value discounted at 10% it is worth less than the asking price, john should not pay the $7,000 asked.

This was found by using goal seek, but one could also just plug in numbers and estimate the rate be seeing the PV change.

same as above, no John should not pay $7,000 for the lot because it will yeild less that the 10% he thinks it should.

2 3 47500 9500 12500

5873.600125 6583.97654164 7666.484 $ 5,791 $ 6,446 $ 7,452

2 3 47500 9500 12500

Arrived at by goal seek changing the purchase price until the IRR equals 13%

3 4 5 6 7 8 90 0 0 0 0 0 0

2 3 4 5 6 7 81500 1500 1500 1500 1500 1500 1500

1455.992623 1434.47549133 1413.276 1392.39 1371.813 1351.54 1331.567

Solve for the Monthly Periodic Rate that makes the discounted cash flow equal to $0, then express it as an annual rate.

2 3 4 5 61000 0 5000 6000 863.65

826.446281 0 3415.067 3725.528 487.5079

9 10 11 12 13 14 15 16 $ 14,661 $ 14,990 $ 15,328 $ 15,673 $ 16,025 $ 16,386 $ 16,754 $ 17,131

6 70 21936.476 7 8 9 10 11 12 130 0 0 0 0 0 0 0

8 9 10 11 12 13 14 15

9731.662 9334.928 8954.367 8589.321 8239.157 7903.268 7581.072 7272.012

9731.662 9334.928 8954.367 8589.321 8239.157 7903.268 7581.072 7272.012

The fomula needs to be adjusted for 1 more period of comounding without a last $5000 deposit.

8 9 10

2150 2150 2150571.9821 484.7306 410.7886

2150 2150 0571.9821 484.7306 0

9 10

0 15000

10 11 12 13 14 15 16 170 0 5500 0 0 0 0 0

9 10 11 12 13 14 15 161500 1500 1500 1500 1500 1500 1500 1500

1311.888 1292.501 1273.4 1254.581 1236.041 1217.774 1199.777 1182.047

17 18 19 20 21 22 23 24 $ 17,517 $ 17,911 $ 18,314 $ 18,726 $ 19,147 $ 19,578 $ 20,019 $ 20,469

14 15 16 17 18 19 20 210 0 0 0 0 0 0 0

16 17 18 19 20 21 22 23

6975.551 6691.176 6418.394 6156.733 5905.739 5664.978 5434.031 5212.5

6975.551 6691.176 6418.394 6156.733 5905.739 5664.978 5434.031 5212.5

18 19 20 21 22 23 24 250 0 0 0 0 0 7500 0

17 18 19 20 21 22 23 241500 1500 1500 1500 1500 1500 1500 1500

1164.578 1147.367 1130.411 1113.706 1097.247 1081.031 1065.056 1049.316

25 26 27 28 $ 20,930 $ 21,401 $ 21,882 $ 22,375

22 23 24 25 26 27 280 0 0 0 0 0 $ 22,374.54

24

5000

0

26 27 28 29 30 31 32 330 0 0 0 0 0 0 0

25 26 27 28 29 30 31 321500 1500 1500 1500 1500 1500 1500 1500

1033.809 1018.531 1003.479 988.6489 974.038 959.644 945.46172399 931.489

34 35 36 37 38 39 40 41 42 430 0 9500 0 0 0 0 0 0 0

33 34 35 36 37 38 39 40 41 421500 1500 1500 1500 1500 1500 1500 1500 1500 1500

917.724 904.161 890.799 877.635 864.665 851.886 839.297 826.893 814.673 802.634

44 45 46 47 480 0 0 0 12500

43 44 45 46 47 48 49 50 51 521500 1500 1500 1500 1500 1500 1500 1500 1500 1500

790.772 779.086 767.572 756.229 745.053 734.043 723.195 712.507 701.977 691.603

53 54 55 56 57 58 59 601500 1500 1500 1500 1500 1500 1500 101500

681.383 671.313 661.392 651.618 641.988 632.5 623.153 41544

Chapter 3 4 3 2years 0 1 2 3

Problem 5 $ 2,500.00 $ - $ 750.00 $ 3,528.95 $ - $ 891.08

Interest Rate 9%

Not Part of the Question, but what are these payments worth today given a 12% discount rate?

$ 3,592 $ 2,232 $ - $ 534

Problem 11Years 0 1 2 3

8.14% -100000 15000 15000 15000

No, this would not be an acceptble investment for Dallas Development

Not part of the question, but what if they viewed their IRR as compounded monthly?

8.14% -100000 0 0 0Err:523

Problem 15 9 8 7Years 0 1 2 3

Interest 10% $ 3,137.27 $ 3,137.27 $ 3,137.27

$ 7,397.52 $ 6,725.02 $ 6,113.65

Payment Formula ($3,137.27) Annual Compounding

($244.09) Monthly Payments($2,929.04) Total Annual Payments ($0.0586)

Not the Question, but what if the payments are made annually, but the interest compounds monthly?

$ 3,067.09 $ 3,067.09 $ 3,067.09 $ 7,515.75 $ 6,803.35 $ 6,158.48

1 04 5

$ 1,300.00 $ 1,417.00 $ 5,837.03

Not Part of the Question, but what are these payments worth today given a 12% discount rate?

$ 826

4 5 6 7 8 9

15000 15000 15000 15000 15000 15000

Not part of the question, but what if they viewed their IRR as compounded monthly?

0 0 0 0 0 0

6 5 4 3 2 14 5 6 7 8 9

$ 3,137.27 $ 3,137.27 $ 3,137.27 $ 3,137.27 $ 3,137.27 $ 3,137.27 $ 5,557.86 $ 5,052.60 $ 4,593.28 $ 4,175.71 $ 3,796.10 $ 3,451.00

Not the Question, but what if the payments are made annually, but the interest compounds monthly?

$ 3,067.09 $ 3,067.09 $ 3,067.09 $ 3,067.09 $ 3,067.09 $ 3,067.09 $ 5,574.73 $ 5,046.31 $ 4,567.99 $ 4,135.00 $ 3,743.05 $ 3,388.26

10 11 12 13 14 15

15000

0 0 15000 0 0 0

010

$ 3,137.27 $ 3,137.27 $ 50,000.00

$ 3,067.09 $ 3,067.09 $ 50,000.00

16 17 18 19 20 21

0 0 0 0 0 0

22 23 24 25 26 27

0 0 15000 0 0 0

28 29 30 31 32 33

0 0 0 0 0 0

34 35 36 37 38 39

0 0 15000 0 0 0

40 41 42 43 44 45

0 0 0 0 0 0

46 47 48 49 50 51

0 0 15000 0 0 0

52 53 54 55 56 57

0 0 0 0 0 0

58 59 60 61 62 63

0 0 15000 0 0 0

64 65 66 67 68 69

0 0 0 0 0 0

70 71 72 73 74 75

0 0 15000 0 0 0

76 77 78 79 80 81

0 0 0 0 0 0

82 83 84 85 86 87

0 0 15000 0 0 0

88 89 90 91 92 93

0 0 0 0 0 0

94 95 96 97 98 99

0 0 15000 0 0 0

100 101 102 103 104 105

0 0 0 0 0 0

106 107 108 109 110 111

0 0 15000 0 0 0

112 113 114 115 116 117

0 0 0 0 0 0

118 119 120

0 0 15000