Professor: Ronald W. SpahrName:_______________________

(Total points- 100)

(40 pts)1.As an intern with the Bank of Milan, Tennessee, you have observed that this bank makes two types of loans, agriculture loans and consumer loans, and offers two types of deposits, demand deposits and time deposits. You have determined that your bank is not an asset management bank but is a liability management bank, where core deposits plus capital are less than demand for loans. Thus your bank needs to acquire money market funds in the Eurodollar market at a cost of 3.15 percent. If your bank were an asset management bank, you would invest your excess fund in treasury securities that yield an annual rate of 3.00 percent. Your bank has $2,000 in capital. Use the Economics of Banking Handout for this class. The first part of this problem, using the Demand/supply functions, proves that your bank is a liability management bank.

Demand function for agriculture loans (L_A)

r_A = 13.00% - .0005L_A

L_A=$10,000_r_A= _8.0%__

Demand for function for consumer loans (L_C)

r_C = 9.00% - .0002L_C

L_C=$15,000_r_C= _6.00%_

Supply function for demand deposits (D_D)

r_D = -4.00% + .0004375D_D

D_D= $8,000r_D=-0.50%

Supply function for time deposits (D_T)

r_T = 0.00 + .00015D_T

D_T= $10,000r_T=1.50%

Using the economics of banking theory covered in class, we show how the balance sheet for the Bank of Milan, Tennessee would appear assuming an asset management bank, where you have a problem that demand for assets are greater than supply of deposits plus capital.

Bank of Milan, Tennessee

Statement of Financial Conditions (pro forma)

October 1, 2019

Assuming an Asset Management Bank

U.S. Treasury Securities$0 Demand Deposits $8,000.00_

Agriculture Loans$10.000.00Time Deposits$10,000.00_

Consumer Loans$15,000.00Capital2,000.00

Total Assets$25,000.00Total Liab & NW $20,000.00_

Bank of Milan, Tennessee

Statement of Financial Conditions (pro forma)

October 1, 2019

Assuming an Liability Management Bank

U.S. Treasury Securities$_______ Demand Deposits $_________

Agriculture Loans$__________Time Deposits$_________

EuroDollars$__________

Consumer Loans$________Capital2,000.00

Total Assets$________Total Liab & NW $__________

Bank of Milan, Tennessee

Income Statement (pro forma)

October 1, 2019 - September 30, 2020

Assume all rates and balances remain constant for the next year (2020 Fiscal Year)

Revenues

Interest on Treasury Securities_ $_____________________________

Interest on Agriculture Loans__ $_____________________________

Interest on Consumer Loans_$_____________________________

Total Interest Revenue___$_____________________________

Interest Expense

Interest on Demand Deposits___$________________________________

Interest on Time Deposits__ ___$________________________________

Interest on EuroDollars $________________________________

Total Interest Expense____$________________________________

Net Interest Revenue______$_________________________________

$_________Demand Deposits

Bank RR = .10 ($___________)- 84,000 = _$______________

(45 pts)3.Assume today's U.S. Treasury Yield Curve is given below.You can use this to estimate the average rate of inflation for the next thirty years as the difference between the nominal rate on a 30-Year Treasury bond and the Inflation Indexed Treasury bond- (often called Treasury Inflation Protected bonds or TIPs-Real Rate).The shape of the Yield Curve also tells us something about future interest rates.

U.S. Treasury Yield Curve (Nominal Rates)

Date

1 mo

2 mo

3 mo

6 mo

1 yr

2 yr

3 yr

5 yr

7 yr

10 yr

20 yr

30 yr

09/19/19

2.01

1.99

1.93

1.92

1.88

1.74

1.68

1.66

1.73

1.79

2.04

2.22

U.S Treasury Yield Curve (Real Rates-TIPS)

DATE

5 YR

7 YR

10 YR

20 YR

30 YR

09/19/19

0.25

0.21

0.18

0.38

0.57

Your 25 year old client wants to retire when he is 70 years old, and have a retirement income equivalent to $8,000 per month in today's (inflation adjusted) dollars. To estimate the market expectations for average annual inflation for the next 45 years, use the difference between the nominal rate and real rate on TIPs for the 30-year Treasury rates given above. Because of inflation, he will need substantially higher retirement monthly income to maintain the same purchasing power. He plans to purchase a guaranteed lifetime annuity from a AAA rated insurance company[1] one month before he retires (539 months from now). The retirement annuity will begin in exactly 45 years (540 months).At the time the retirement annuity is purchased, the insurance company will add a 5.00 percent premium to the pure premium cost of the purchase price of the annuity. The pure premium is the actuarial cost of his anticipated lifetime annuity.He has savings of $60,000 today that will be invested at an annual return of 6.00%. Given a rate of return of 6.00% for the foreseeable future, how much does he need to save each month (total of 539 payments) until the month before he retires? He will make the first payment next month and the last payment one month before he retires. For life expectancy after retirement, use the Cohort Life Tables for Social Security Area by Sex table below:

Cohort Life Tables for Social Security by Sex

Male

Female

Probability

# of 100,000

Life

Probability

# of 100,000

Life

Age

Death

Living

Expectancy

Age

Death

Living

Expectancy

40

0.00170

96,759

42.94

40

0.00108

98,088

46.22

41

0.00183

96,595

42.01

41

0.00116

97,982

45.27

42

0.00196

96,418

41.09

42

0.00123

97,869

44.33

43

0.00209

96,229

40.17

43

0.00129

97,749

43.38

44

0.00223

96,028

39.25

44

0.00135

97,622

42.43

45

0.00238

95,814

38.33

45

0.00142

97,490

41.49

46

0.00254

95,586

37.43

46

0.00150

97,352

40.55

47

0.00268

95,343

36.52

47

0.00159

97,205

39.61

48

0.00278

95,088

35.62

48

0.00168

97,051

38.67

49

0.00288

94,823

34.71

49

0.00178

96,888

37.74

50

0.00299

94,550

33.81

50

0.00190

96,715

36.80

51

0.00313

94,268

32.91

51

0.00204

96,532

35.87

52

0.00331

93,973

32.01

52

0.00221

96,335

34.94

53

0.00355

93,662

31.12

53

0.00241

96,123

34.02

54

0.00385

93,329

30.23

54

0.00265

95,891

33.10

55

0.00419

92,970

29.34

55

0.00292

95,637

32.19

56

0.00457

92,581

28.46

56

0.00322

95,358

31.28

57

0.00497

92,158

27.59

57

0.00354

95,051

30.38

58

0.00539

91,700

26.73

58

0.00386

94,714

29.49

59

0.00585

91,205

25.87

59

0.00420

94,348

28.60

60

0.00635

90,672

25.02

60

0.00457

93,952

27.72

61

0.00693

90,096

24.18

61

0.00500

93,522

26.84

62

0.00763

89,472

23.34

62

0.00551

93,054

25.97

63

0.00847

88,790

22.52

63

0.00613

92,541

25.12

64

0.00944

88,038

21.70

64

0.00683

91,974

24.27

65

0.01053

87,206

20.91

65

0.00762

91,346

23.43

66

0.01167

86,288

20.12

66

0.00845

90,650

22.61

67

0.01284

85,281

19.36

67

0.00930

89,884

21.80

68

0.01402

84,186

18.60

68

0.01014

89,048

21.00

69

0.01523

83,006

17.86

69

0.01101

88,145

20.21

70

0.01660

81,742

17.13

70

0.01199

87,175

19.42

71

0.01811

80,385

16.41

71

0.01308

86,130

18.65

72

0.01965

78,929

15.70

72

0.01419

85,003

17.89

73

0.02119

77,378

15.01

73

0.01533

83,797

17.15

74

0.02280

75,739

14.32

74

0.01653

82,513

16.40

75

0.02479

74,012

13.64

75

0.01804

81,148

15.67

76

0.02713

72,177

12.98

76

0.01979

79,685

14.95

77

0.02954

70,219

12.32

77

0.02154

78,107

14.24

78

0.03200

68,144

11.68

78

0.02321

76,425

13.54

79

0.03469

65,964

11.05

79

0.02502

74,651

12.85

Expected Inflation =

Expected Remaining Life in Months at Retirement =

Needed per month retirement income.

FV_{45 years} = $8,000 (1._______)⁴⁵ = $8,000() = $__________

Total amount Needed in retirement account one month (month 539) before retirement.

PVA_{month 539} = $__________= $_________(__________)= $______________

Premium and price to Insurance Company

Price = $___________ (1.050) = $____________

Value of Current Savings in 539 months (assuming monthly compounding.

FV_{539 months} = $60,000 (1._______)⁵³⁹= $60,000 (____________)= $___________

Total New Saving needed by month 539 =$_____________

Saving Each month for next 539 Months.

= $_______________

Then,

A = $____________ /______________ = $__________ per month