商业银行管理课后习题答案Problems5.doc

Problems5.3Depositors and Merchants Bank has an equity-to-asset ratio of 7.5 percent which means its equity multiplier must be:1/(Equity Capital / Assets) = = 1 / 0.075 = 13.33xIn contrast, Newton National Bank has an equity multiplier of:1/(Equity Capital / Assets) = = 16.67xWith an ROA of 0.85 percent Newton National would have an ROE of:ROE = 0.85 x 16.67x = 14.17 percent.In this case Newton National Bank is making greater use of financial leverage and is generating a higher return on equity capital.Depositors and Merchants has an ROE of:ROE = 0.85 x 13.33 x = 11.33 percent.5-4.The income and expense statement for Gilcrest Merchants National Bank, when arranged in proper order, would appear as follows:Among the key ratios that can be calculated are the following:1、ROE=Net Income After Taxes=$5=0.0180 or 1.80 percentEquity Capital$802、ROA=Net Income After Taxes=$5=0.005 or .5 percentTotal Assets$10003、Net Interest Margin =Total Interest Income Total Interest Expenses($61 + $12) ($49 + $6)=0.0180 or 1.8 percentTotal Assets$10004、Net Noninterest =$7 - $18=-0.011 or 1.1 percentMargin$10005、Net operating margin = Total Operating Revenues Total Operating Expenses /Total Assets = = 0.0070 or 0.70 percent.6、Earnings =Total Interest Income-Total Interest Expenses=$61 + $12-$49 + $6SpreadTotal Earning AssetsTotal Interest Bearing $830$710Liabilities0.0880 0.0775 or 8.8 percent 7.75 percent or 1.05 percent7、Profit Margin = = = 0.0625 or 6.25 percent.8、Asset Utilization = = = = 0.08 or 8.0 percent9、Equity Multiplier = = 12.5x10、Employee Productivity =Net Operating Income=$80 - $73= $175,000Ratio# of Full Time Employees$40per employee5-5. The rates of return requested for Shadowwood National Bank are as follows:1-2、ROE =$105ROA=$105$15,765 - $15,440$15,7650.3231 or 32.31 percent0.0067 or .67 percent3、Net Interest =$1875 - $1210=$665= 0.0527 or 5.27 percentMargin$12,612$12,612(If total assets are used as the denominator, NIM = 4.22%.)4、Net Noninterest Margin = = 0.0146 or 1.46 percent.(If total assets are used as the denominator, the noninterest margin is 1.17%).5、Net Operating =($1,875+- $501) ($1,210 + $685 + $381)=$100=0.0063 or.63 percentMargin$15,765$15,7656、Earnings per Share = = $724.14 per share.Alternative Scenario 1:Suppose interest income, interest expenses, noninterest income, and noninterest expenses each increase by 5 percent, with all other items remaining unchanged. If we assume that the 5% increase flows through to net income, resulting in a 5% increase in net income, then the ROE, ROA, and EPS will increase by (at least) 5% also. Actually, the scenario which does not have provision for loan losses, securities gains, and taxes increasing would result in a greater than 5% increase in net income. This would, of course, result in the ROE, ROA, and EPS increases being greater than 5%.Alternative Scenario 2:Suppose Shadowoods interest income, interest expenses, noninterest income, and noninterest expenses decline by 5 percent, all other factors held equal. As with scenario 1, if we assume the decrease flows through to net income, then net income will decrease by 5%. This decrease will result in ROE, ROA, and EPS actually being greater than 5% as a result of the other items, such as provision for loan losses, taxes, and securities gains, not changing.BaseProblemAlternativeScenario 1Alternative Scenario 2Interest Income$1875$1968.75$1781.25Interest Expense12101270.501149.50Net Interest Income$ 665$ 698.25$ 631.75Provision for Loan Losses$ 381$ 381$ 381Noninterest Income$ 501$ 526.05$ 475.95Noninterest Expense685719.25650.75Net Noninterest Income($184)($193.20)($174.8)Net Income Before Taxes$ 100$ 124.05$ 75.95Income Taxes$ 16$ 16$ 16Securities Gaines (or Losses)212121Net Income After Taxes$ 105$ 129.05$ 80.95Common Shares Outstanding145,000145,000145,000Base ProblemAlternativeScenario 1AlternativeScenario 2a. ROE32.31%39.71%24.91%b. ROA0.670.82%0.51%c. NIM (1)5.27%5.54%5.01% NIM (2)4.22%4.43%4.01%d. EPS$724.14$890.00$558.28e. NNIM (1)-1.46%-1.53%-1.39% NNIM (2)-1.17%-1.23%-1.11%f. NOM0.63%0.79%0.48%g. Net Returns Before Special Transactions0.53%0.69%0.38%Notes: All figures except Common Shares in millions.Equity Capital = Total Assets - Total Liabilities = $ 15,765 - $15,440= $ 325 (millions)Total Assets =$15,765 millionsEarning Assets = $12,612 millionsNIM(1) uses Earning Assets in the denominator; NIM(2) uses Total AssetsNNIM(1) uses Earning Assets in the denominator; NNIM(2) uses Total Assets5-6. Selected balance sheet and income statement data for Farmers and Merchants National Bank are given as follows:Given:ROA = 0.0076 (i.e., 0.76%)Total Assets = $1.69 billion ($1,690 million)Equity Capital = $139 millionSolution:ROE = ROA * = 0.0076 * = 0.0924 or 9.24%Alternative Scenario 1:R0A increases by 50%, with no change in assets or equity capital. Therefore, the new ROA = 0.0076 * 1.5 = 0.0114 or 1.14%.New ROE = 1.14% * 12.16 = 13.86%This represents a 50% increase in ROE. With no changes in assets or equity, the investors funds are more effectively utilized, generating additional income and making the bank more profitable.Alternative Scenario 2:ROA decreases by 50%, with no change in equity or assets.Therefore, the new ROA = 0.0076 * 0.5 = 0.0038 or 0.38%.New ROE = 0.38% * 12.16 = 4.62%This represents a 50% decrease in ROE. The banks management has been less efficient, in this case, in managing their lending and/or investing functions or their operating costs.Alternative Scenario 3:ROA = 0.0076 or 0.76% (as in the original problem)Total assets double in size to $3.38 billion and equity capital doubles in size to $278 million.Therefore, the equity multiplier (i.e. total assets/equity capital) remains the same (E.M. =$3,380/$278 = 12.16). As a result, there is no change in ROE from the original situation (i.e.,0.76% * 12.16 = 9.24%).Alternative Scenario 4:This, of course, is just the reverse of scenario 3. Since the changes in both assets and equity capital are the same, the ratio of the two (i.e., the equity multiplier) remains constant. As a result, there is again no change in ROE.E.M. = Total Assets/Equity Capital = $845/$69.5 = 12.16. Therefore, ROE = 0.76% * 12.16 = 9.24%.5-7.Granite Dells State Bank reports the following information:Given:Total Operating Revenues = $135 millionTotal Operating Expenses = $121 millionTax Liability = $2 millionTotal Assets = $1.17 billionTotal Liabilities = $989 millionSolution:Net Income after Taxes = $135 million -$121 million -$2 million = $12 millionEquity Capital = $1.17 billion - $989 million = $181 millionROE = = $12 million / $181 million = 0.0663 or 6.63%. Alternative Scenario 1:Given: Total operating revenues, total operating expenses, and taxes each grow by 10%, but assets and liabilities remain fixed.Solution:Total revenues = $135 million * 1.10 = $148.5 millionTotal expenses = $121 million * 1.10 = $133.1 millionTax liability = $2 million * 1.10 = $2.2 millionNet Income after Taxes = $148.5 - $133.1 - $2.2 = $13.2 million ROE = $13.2 million/$181 million = 0.0729 or 7.29%Change in ROE = = 10% (ROE increases by 10%)Alternative Scenario 2:Given:Total assets increase by 10% (Total assets = $ 1.17 * 1.10 = $1.287 billion) Total liabilities increase by 10% (Total liabilities = $989 million * 1.10 =1.0879 Revenues and expenses (including taxes) remain unchanged.Solution: Equity Capital = $1.287 billion - $1.0879 billion = $199.1 million ROE = = 0.063 or 6.03%Therefore change in ROE =6.03% - 6.63%=-0.6%= -9%6.63%6.63%(ROE decreases by 9%)Alternative Scenario 3:Given:Total revenues decline by 10% (Total revenues = $135 million * 0.90 = $121.5 million)Total expenses decline by 10% (Total expenses = $121 million * 0.9 = $108.9 million)Tax liability declines by 10% (Tax liability = $2 * 0.9 = $1.8 million) Assets and liabilities remain unchanged (Therefore, equity remains unchanged)Solution:Net Income after Tax = $121.5 million - 108.9 million - $1.8 million = $10.8 ROE =$10.8 million = 0.0597 = 5.97%$181 millionTherefore, change in ROE = 5.97% - 6.63% = -0.66% = -10% (ROE decreases by 10%) 6.63% 6.63%Alternative Scenario 4:Given:Assets and liabilities decrease by 10%; therefore, Equity capital decreases by 10%,Operating revenues, operating expenses, and taxes remain unchanged.Solution:Total assets = $1.17 billion * 0.9 = $1.053 billion Total liabilities = $989 million * 0.9 =$890.1 million Equity capital = $1.053 billion - $890.1 million = $162.9 millionROE = = 0.0737 or 7.37% 5-8.Suppose a bank is projected to achieve a 1.25 percent ROA during the coming year. What must its ratio of total assets to total equity capital be if it is to achieve a 12-percent ROE goal?Given:ROA = 1.25% and target ROE = 12%Solution:ROE = ROA * (Total Assets/Equity Capital)Total Assets=ROE=12%= 9.6 xEquity CapitalROA1.25%If ROA unexpectedly falls to 0.75% and target ROE remains 12%:Solution:12%=.75%*Total AssetsEquity CapitalTotal Assets=12%=16 xEquity Capital.75%Alternative Scenario 1:Given:ROA = 1.5% and target ROE = 12%Solution:Total Assets=12% = 8xEquity Capital1.5%Alternative Scenario 2:Given:Banks ROA unexpectedly declines to 0.75%Solution:Total Assets=12% =16 x (The same as part 2 of original problem)Total Equity .75%5-9.The following information is given for Blythe County National Bank:Net Income after Taxes = $16 millionTotal Operating Revenues = $215 millionTotal Assets = $1,250 millionTotal Equity Capital Accounts = $111 millionSolve for the banks net profit margin, asset utilization ration, equity multiplier, and ROE.Solutions:a.Net Profit Margin=Income After Taxes=$16 mill.= 0.0744 or 7.44%Total Operating Revenue$215 mill.b.Asset Utilization=Total Operating Revenues=$215 mill.= 0.172 or 17.2%Total Assets$1250 mill.c.Equity Multiplier=Total Assets=$1250 mill.= 11.26 timesTotal Equity Capital$111 mill.d.ROE=Net Income After Taxes=$16 mill.= 0.1441 or 14.41%Total Equity Capital$111 mill.Alternative Scenario:Given:Total Liabilities= $1,475 millionEquity Capital= $140 millionTotal Noninterest Income= $88 millionTotal Interest Income= $155 millionAfter-Tax Net Income= $24 millionRecalculate Blythe Countys ROE, net profit margin, asset utilization, and equity multiplier.Solutions:a.Net Profit Margin=After Tax Net IncomeTotal interest Income + Total Noninterest Income=$24 mill.=$24 mill.= 0.0988 or 9.88%$155 mill. + $88 mill.$243 mill.b.Asset Utilization=Total Interest Income + Total Noninterest IncomeTotal Liabilities + Equity Capital=$155 mill. + $88 mill.=$243 mill.= 0.1505 or 15.05%$1,475 mill. + $140 mill.$1,615 mill.c.Equity Multiplier=Total Liabilities + Equity CapitalEquity Capital=$1,475 mill. + $140 mill.=$1,615 mill.= 11.54 x$140 mill.$140 mill.d.ROE=After Tax Net Income=$24 mill.= 0.1714 or 17.14%Equity Capital$140 mill.5-10.Lochiel Commonwealth Bank and Trust Company has experienced the following trends over the past five years (all figures in millions of dollars):Given: (Figures in millions of dollars)YearNet IncomeAfter-TaxTotal OperatingRevenuesTotalAssetsTotal EquityCapital12.726.52931823.530.13822034.139.84742244.847.55082555.755.959928YearProfitMarginAssetUtilizationEquityMultiplierROAROE110.2%0.090416.28x0.92%15.0%211.6%0.078819.10X0.92%17.5%310.3%0.084021.55X0.86%18.6%410.1%0.093520.32X0.94%19.2%510.2%0.093321.39X0.95%20.4%If we look at the entire 5-year period, Lochiels profit margin has remained relatively constant. However, from year 2 through year 5, there has been a significant decline (from 11.6% to 10.2%). This can be viewed as troublesome when we note that net income, total operating revenues, and total assets have more than doubled during the five-year period. Two potential areas that management should investigate are (1) the mix of funding sources and (2) non-interest expenses.Since ROE has grown much more rapidly than ROA (ROE grew at an average annual rate of 8% compared to only a 0.8% average annual growth rate in ROA), we should be concerned that Lochiel is increasing its liability sources of funding, thereby increasing its leverage to keep its ROE growing. This can cause serious problems with its income as interest rates rise, driving up its cost of funds.With regard to its noninterest expenses, if these are growing faster than the banks noninterest income, then there is greater pressure on the banks net interest margin to offset the increasing negative spread between noninterest income and noninterest expenses.Since bank regulators place a great deal of emphasis on capital adequacy, these two areas, leverage and noninterest margin, could be moving Lochiel to a precarious capital adequacy positionAlternative Scenario 1:Given:Total Equity Capital increases by 30% between year 1 and year 5.Solution:Equity Capital in year 5 = Equity Capital in year 1 *1.30 = $18 million * 1.30= $23.4 millionThis should make us less content since the equity capital position would be less than originally proposed, compounding the concern we have about increased leverage. Specifically, the equity multiplier would be 25.6 times ($599/$23.4=25.6x) as compared to 21.39 times.Alternative Scenario 2:Given:Asset Utilization Ratio increased by 25% between year 1 and year 5.Solution:ROE = Profit Margin *Asset Utilization Ratio * Equity Multiplier = 10.2% * (0.0904 * 1.25) *21.39 = 10.2% * 0.113 x 21.39 = 24.65%Change in ROE = (24.65% - 20.4%)/20.4% = 0.208 or 20.8%.Alternative Scenario 3:Given:Profit margin increased by 15% between year 1 and year 5.Solution:ROE= Profit Margin * Asset Utilization Ratio * Equity Multiplier = (10.2% * 1.15) * 0.0933 * 21.39 = 23.41%.Change in ROE = (23.41% - 20.4%)/20.4% = 0.148 or 14.8%.5-11.Wilmington Hills State Bank has just submitted its Report of Condition and Report of Income to its principal supervisory agency. Given the following figures solve for the banks ROE and its components.Given: Net Income Before Taxes and Securities Transactions = $27 million.Taxes = $6 millionTotal Operating Revenues = $780 millionTotal Assets = $2,100 millionEquity Capital = $125 millionSolution:a.Tax Management= Net Income After TaxesEfficiency RatioNet Income Before Taxes and Securities Transactions=$27 million - $6 million - $21 million $27 million $27 million=0.778 or 77.8 percent.b.Expense Control = Net Income Before Taxes and Securities Gains Total Operating Revenues= $ 27 million = 0.035 or 3.5 percent. $780 millionc.Asset Management Efficiency Ratio = Total Operating Revenues (Asset Utilization) Total Assets= $ 780 million=0.371 or 37.1 percent.$2,100 milliond.Funds Management =Total Assets=$ 2,100 million = 16.80 x.Efficiency RatioEquity Capital$125 millione.ROE =Net Income after Taxes = $ 21 million= 0.168 or 16.8% Equity Capital $125 millionAlternative Scenario 1:Given: Net Before-Tax Income increases by 20% and everything else remains unchanged.Solution:ROE=ROA*Total Assets=Net Income After Taxes*Total AssetsTotal EquityTotal AssetsTotal Equity=($27 x 1.20) - $6*$2,100=$32.4 - $6*$2,100$2,100$125$2,100$125=0.0126*16.8=0.2117 or 21.17 %This represents a 26% increase in ROE, from 16.8% to 21.17%. Since the equity multiplier did not change, this increase in ROE is due to the increase in ROA, from 1% to 1.26%.Alternative Scenario 2:Given:Total Assets increase by 20%Solutions:Asset Management Efficiency Ratio = = .31This represents a decrease of 16.4%.Funds Management Efficiency Ratio = = 20.16 timesThis represents an increase of 20%.ROE would not change since the decrease in the asset management efficiency ratio is offset by the increase in the funds management efficiency ratio.Alternative Scenario 3:Given:Equity Capital