Banking and Insurance Chapter seven solution (4-10).docx

7-4. Farmville Financial reports a net interest margin of 2.75 percent in its most recent financial report, with total interest revenue of $95 million and total interest costs of $82 million. What volume of earning assets must the bank hold? Suppose the bank’s interest revenues rise by 5 percent and its interest costs and earnings assets increase by 9 percent. What will happen to Farmville’s net interest margin? The relevant formula is: $95 mill.  $82 mill. Total earning assets Net interest margin = 0.0275 = Then, total earning assets must be $473 million. If revenues rise by 5 percent, and interest costs and earnings assets rise by 9 percent, net interest margin is: $95(1.05)  $82(1.09) 473(1.09) Net interest margin =

=

99.75  89.38 515.57

= 0.0201 or 2.01 percent 7-5. If a credit union’s net interest margin, which was 2.50 percent, increases 10 percent and its total assets, which stood originally at $575 million, rise by 20 percent, what change will occur in the bank's net interest income? The correct formula is: Net interest income Net interest margin  Total earning assets Original net interest income = Net interest margin × Total earning assets = 2.5% × $575 million = $14.375 million New net interest income: 0.025 1.10 

Net interest income $575 million×1.20

Net Interest Income = 0.0275 × 690 = $18.975 million Change in net interest income = New net interest income – Original net interest income = $18.975 million - $14.375 million = $4.6 million. 7-6. The cumulative interest rate gap of Poquoson Savings Bank increases 60 percent from an initial figure of $25 million. If market interest rates rise by 25 percent from an initial level of 3 percent, what changes will occur in this thrift’s net interest income? New net interest income = New market interest rate × Increase in assets = 3.75 percent × $40 million = $1.5 million Initial net interest income = Initial market interest rate × Initial assets = 3 percent × $25 million = $0.75 million Percent change in net interest income = ($1.5 million – $0.75 million)/ $0.75 million = 100 percent Thus, the bank's net interest income will increase by 100 percent. 7-7. New Comers State Bank has recorded the following financial data for the past three years (dollars in millions): Interest revenues Interest expenses Loans (excluding nonperforming) Investments Total deposits Money market borrowings

Current Year $82 64 450 200 450 150

Previous Year $80 66 425 195 425 125

Two Years Ago $78 68 400 200 400 100

What has been happening to the bank’s net interest margin? What do you think caused the changes you have observed? Do you have any recommendations for New Comers’ management team? Net interest margin (NIM) = Net interest income/Total earning assets Where, Net interest income = Net interest revenues - Net interest expenses Total earning assets = Loans + Investments NIM (Current) = ($82-64)/ (450 + 200) = 18/650 = 0.028 or 2.77% NIM (Previous) = ($80-66)/ (425 + 195) = 14/620 = 0.0226 or 2.26% NIM (Two years ago) = ($78-68)/ (400 + 200) = 10/600 = 0.0167 or 1.67%

The net interest margin has been increasing over the years. As interest revenues and expenses as well as the bank’s assets have increased consistently over the years, there has been a constant increase in the net interest margin. If the bank can further cut down on its interest expenses and increase its assets in the next years, the net interest margin will increase at a higher rate. 7-8 The First National Bank of Dogsville finds that its asset and liability portfolio contains the following distribution of maturities and repricing opportunities:

Loans Securities Interest-sensitive assets Transaction deposits Time accts. Money market borrowings Interest-sensitive liabilities

Coming Week $200.00 21.00

Next 30 Days $300.00 26.00

Next 31-90 Days $475.00 40.00

More Than 90 Days $525.00 70.00

$320.00 100.00 136.00

$ 0.00 290.00 140.00

$ 0.00 196.00 100.00

$ 0.00 100.00 65.00

When and by how much is the bank exposed to interest rate risk? For each maturity or repricing interval, what changes in interest rates will be beneficial and which will be damaging, given the current portfolio position? Coming Week $200 21 $221

Next 30 Days $300 26 $326

Next 31-90 Days $475 40 $515

More Than 90 Days $525 70 $595

Transaction deposits Time Accts. Money Mkt. Borr. Total IS Liab.

$320

$−

$−

$−

100 136 $556

290 140 $430

196 100 $296

100 65 $165

GAP

−335

−104

+219

+430

Cumulative GAP

−335

−439

−220

+210

Loans Securities Total IS Assets

First National has a negative gap in the nearest period and therefore would benefit if interest rates fall. In the next period it has a slightly negative gap and would therefore benefit of interest rate rise. However, its cumulative gap is still negative. The third period is positive gap and hence the bank would benefit if interest rates rise. In the final period the gap is positive and the bank would benefit if interest rates rise. Its cumulative gap is slightly positive and also shows that rising interest rates would be beneficial to the bank overall.

7-9 Sunset Savings Bank currently has the following interest-sensitive assets and liabilities on its balance sheet with the interest-rate sensitivity weights noted. Interest-Sensitive Assets Federal fund loans Security holdings Loans and leases Interest-Sensitive Liabilities Interest-bearing deposits Money-market borrowings

$ Amount $ 50.00 50.00 350.00 $ Amount $ 250.00 90.00

Rate Sensitivity Index 1.00 1.20 1.45 Rate Sensitivity Index 0.75 0.95

What is the bank’s current interest-sensitive gap? Adjusting for these various interest rate sensitivity weights what is the bank’s weighted interest-sensitive gap? Suppose the federal funds interest rate increases or decreases 50 basis points. How will the bank’s net interest income be affected (a) given its current balance sheet makeup and (b) reflecting its weighted balance sheet adjusted for the foregoing rate-sensitivity indexes? Dollar IS Gap

= ISA - ISL = ($50 + $50 + $350) − ($250 + $90)

= $110

  Weighted IS Gap    1   $50    1.20    50    1.45    350    0.75    $250    0.95    $90

 $50  $60  $507.5  $187.5  $85.5  $617.5  $273  $344.5

a.)

Change in Bank’s Income = IS Gap × Change in interest rates = ($110) (0.005) = $0.55 million

Using the regular IS Gap; net income will change by plus or minus $550,000 b.)

Change in Bank’s Income = Weighted IS Gap × Change in interest rates

= ($344.50) (0.005) = $1.72250 Using the weighted IS Gap; net income will change by plus or minus $1,722,500. 7-10 Sparkle Savings Association has interest-sensitive assets of $400 million, interestsensitive liabilities of $325 million, and total assets of $500 million. What is the bank’s dollar interest-sensitive gap? What is Sparkle’s relative interest-sensitive gap? What is the value of its interest-sensitivity ratio? Is it asset sensitive or liability sensitive? Under what scenario for market interest rates will Sparkle experience a gain in net interest income? A loss in net interest income? Dollar Interest-Sensitive Gap = ISA – ISL = $400 million − $325 million = $75 million

Relative IS Gap Interest-Sensitivity Ratio

= =

ISA ISL

ISA – ISL Bank Size =

$400 $325

=

$75 $500

= 0.15

= 1.23

Here, the interest sensitivity gap is positive and asset sensitive as the interest sensitive assets are greater than interest sensitive liabilities. Sparkle Savings Association, being an asset sensitive financial firm, will have a positive relative IS gap and an interest-sensitivity ratio greater than 1. In case of a positive IS gap, there will be a gain in net interest income if the market interest rates are rising. For a positive IS gap, there will be a loss in net interest income, if the market interest rates are falling.