If required reserves are 8%, what does the bank’s balance sheet look like?Ignore any loan loss reserves.. What does the balance sheet look like?... What does the balance sheet look like?
Trang 1H c Vi n Ngân Hàng ọ ệ
Khoa Qu c T ố ế
FINANCIAL ORGANIZATIONAL
INDIVIDUAL ASSIGNMENT
Teacher: Ngô Th H ngị ằ Student: Nguy n Cao Minhễ ID: CA6-068
Class: CityU 6C
Trang 2Extra exercises
I Central Bank
1 Consider a bank policy to maintain 12% of deposits as reserves The bank currently has
$10m in deposits and $200,000 in excess reserves What is the required reserve on a new deposit of $80,000?
Reserves ratio: 12% (total reserves)
Deposits: $10,000,000
Excess reserves: $200,000
Excess reserves ratio: $200,000/$10,000,000*100% = 2%
Required reserves ratio: 12% - 2% = 10%
The required reserve on new deposits of $80,000 is: $80,000 * 10% = $8000
2 If the required reserve ratio is 10%, how much a new $10,000 deposit can a bank lend? What is the potential impact on the money supply? How would your answer change if the Central Bank decided to decrease the required reserve ratio to 8%? Was it a tightened or loosened monetary policy?
Required reserves: $10,000*10% = $1000
Lendable amount: $10,000 - $1000= $9000
The change in money supply is: $9000*1/10% = $90,000 (increase)
If Central bank decided to decrease the required reserve ratio to 8%, we have: Required reserve ratio: 8%
Required reserve: $10,000 * 8% =$800
Lendable amount: $10,000 - $800 = $9200
The change in money supply is: $9200 * 1/8% = $115,000 (increase)
It is an expansionary money policy
II Commercial Bank
3 The balance sheet of TriBank starts with an allowance for loan losses of $1.33m During the year, TriBank charges off worthless loans of $0.84m, recovers $0.22m on loans previously charged off, and charges current income for a $1.48m provision for loan losses Calculate the end-of-year allowance for loan losses.
$1.33m − $0.84m + $0.22m + $1.48m = $2.19m
4 Wiggley S&L issues a standard 30-year fixed rate mortgage at 7.8% for $150,000 Thirty-six months later mortgage rates jump to 13% If the S&L sells the mortgage at this
Trang 3PV = $150,000, I = 7.8/12, N = 360, FV = 0
Compute PMT:
PMT = $1,079.81
After 36 months, the mortgage balance is:
PMT = $1,079.81, I = 7.8/12, N = 324, FV = 0
Compute PV:
PV = $145,764.43
However, at current rates, the remaining cash flows are worth:
PMT = $1,079.81, I = 13/12, N = 324, FV = 0
Compute PV:
PV = $96,637.64
Wiggley S&L expects to take a loss of $49,126 if it sells the mortgage
5 For the upcoming week, Nobel National Bank plans to issue $25m in mortgages and purchase $100m in T-bills New deposits of $35m are expected and other sources will generate $15m in cash What is Nobel’s estimate of funds needed?
$25m + $100m − $35m − $15m = $75m
6 NewBank started its first day of operations with $6m in capital $100m in checkable deposits is received The bank issues a $25m commercial loan and another $25m in mortgages, with the following terms.
Mortgages: 100 standard 30-year fixed-rate mortgages with a nominal annual rate of 5.25% each for $250,000.
Commercial loan: 3-year loan, simple interest paid monthly at 0.75% per month.
a If required reserves are 8%, what does the bank’s balance sheet look like?Ignore any loan loss reserves.
Required Reserves $ 8 million Checkable Deposits $100 million Excess Reserves $48 million Bank Capital $ 6 million Loans $50 million
b NewBank decides to invest $45m in 30-day T-bills The T-bills are currently trading at$4986.70 (including commissions) for a $5,000 face value instrument How many do they purchase? What does the balance sheet look like?
Trang 4cost is $44,999,980.80.
After the transaction, the balance sheet is:
Required Reserves $ 8 million Checkable Deposits $100 million Excess Reserves $ 3 million Bank Capital $ 6 million T-bills $45 million
Loans $50 million
c On the third day of operations, deposits fall by $5m What does the balance sheet look like? Are there any problems?
The cash leaving the bank comes from reserves, first excess and then required Following the outflow, the balance sheet is:
Required Reserves $ 6 million Checkable Deposits $95 million T-bills $45 million Bank Capital $ 6 million Loans $50 million
With $95 million in deposits, the 0.08 $95 M is required in reserves, or $7.6 million. The bank is short $1.6 million in reserves
d To meet any shortfall in the previous question, NewBank will borrow the cash in the federal funds market Management decides to borrow the needed funds for the remainder of the month (now 29 days) The required yield on a discount basis is 2.9% What does the balance sheet look like after this transaction?
Required Reserves $7.6 million Checkable Deposits $ 95 million T-bills $ 45 million Fed Funds Borrowed $1.6 million Loans $ 50 million Bank Capital $ 6 million
e The end of the month finally arrives for NewBank, and it receives all of the required payments from its mortgages, commercial loans and T-bills How much cash is received? How are these transactions recorded?
The required monthly mortgage payments are:
Trang 5Compute PMT PMT = $138,050.93
The loan payment is: $25 M 0.0075 = $187,500.
These are recorded as:
Cash $325,551 Interest Income $296,875
Loans $ 28,676 The T-bills paid: 9,024 $5,000 = $45,120,000 This is recorded as:
Cash $45,120,000 T-bills $4$ $44,999,980.80
Interest Income $ $120,019.20
f NewBank also pays off its federal funds borrowed How much cash is owed? How is this recorded?
Recall that the formula for discount interest is
PV =FV ×(1−rdays
360)
which means that
(1−rdays
360)
or
FV= 1,600,000
(1−2.9%29
360)
so FV=$1,603,746.53
Fed Funds $1,600,000 Cash $1,603,746.53 Interest Expense $ 3,746.53
Trang 6before any income tax consideration.
Required Reserves $ 7.6 million Checkable Deposits $ 95 million Excess Reserves $43.84 million Bank Capital $6.41 million Loans $49.97 million
h Calculate NewBank’s ROA and NIM for its first month Assume that net interest equals EBT, and that NewBank is in the 34% tax bracket.
Interest income $416,894
Interest expense $ 3,747
ROA = 272,677/101.41 M = 0.2689% (monthly)
i Calculate NewBank’s ROE and final balance sheet including its tax liabilities.
Assets Liabilities
Required Reserves $ 7.6 million Checkable Deposits $95 million
Excess Reserves $43.84 million Taxes Payable $140,470
Loans $49.97 million Bank Capital $6.27 million ROE = 272,677/6,269,530 = 4.35% (monthly)
j If NewBank’s target ROE is 4.5%, how much net fee income must it generate to meet this target?
Trang 7The required net income: 0.045 $6 M = $270,000.
Working backwards, we get:
Taxable income $409,091
Income tax $139,091
Net Income $270,000
Since the taxable income was previously $350,647, this means that $58,444 in net fee income (fees generated less expenses) is needed to meet the target
k After making payments for three years, one of the mortgage borrowers defaults
on the mortgage NewBank immediately takes possession of the house and sells it
at auction for $175,000 Legal fees amount to $25,000 If no loan loss reserve was established for the mortgage loans, how is this event recorded.
The required monthly mortgage payments are:
PV = 250,000, I = 5.25/12, = 360, N FV = 0
Compute PMT PMT = $1,380.51
The remaining balance on the mortgage after 36 payments is:
PMT = $1,380.51, I = 5.25/12, = 360 – 36, N FV = 0
Compute PV PV = $238,845.64
The transaction is recorded as:
Loan Loss Expense $88,845.64
III Mutual Fund
7 A mutual fund charges a 5% upfront load plus reports an expense ratio of 1.34% If an investor plans on holding a fund for 30 years, what is the average annual fee, as a percent, paid by the investor?
5%/30 0.1667%
The expense ratio is an annual charge, so it remains 1.34%
The total fees paid are 1.34% 0.1667% 1.5067%.
8 A mutual fund offers “A” shares which have a 5% upfront load and an expense ratio of 0.76% The fund also offers “B” shares which have a 3% backend load and an expense ratio of 0.87% Which shares make more sense for an investor looking over an 18 year
Trang 8For the “A” shares, the average annual fee is 5%/18 0.76% 1.0378%
For the “B” shares, the average annual fee is 3%/18 0.87% 1.0367%
So, the investor is better off with the “B” shares
IV Insurance company & Pension Fund
9 Research indicates that the 1,000,000 cars in your city experience unrecoverable losses of
$250,000,000 per year from theft, collisions, etc If 30% of premiums are used to cover expenses, what premium must be charged to car owners?
The average loss per car = $250,000,000/1,000,000 cars = $250/car
So, 70% of the premium must equal the payout of $250
Or, 0.70 Premium = $250
Premium = $250/0.70
Premium = $357.14
10 Michael Yass’s car slid off the icy road, causing $2,500 in damage to his car He was also treated for minor injuries, costing $1,300 His car insurance has a $500 deductible, after which the full loss is paid His health insurance has a $100 deductible and covers 75% of medical cost (total) What were Paul’s out-of-pocket costs from the incident?
$500 is deductible
$100 is deductible
Cover 75% of medical
=> Paul paid $100 + (1300 -100)x(100-75%) = $400
=> Paul’s were out of pocket costs from the incident:
$500 + $400 = $900
11 A client needs assistance with retirement planning.
Here are the facts:
• The client, Dave, is 21 years old He wants to retire at 65.
• Dave has disposable income of $2,000 per month.
• The Individual Retirement Account (IRA) Dave has chosen has an average annual return
of 8%
a If Dave contributes half of his disposable income to the account, what will it be worth at 65?
Compute the future value at 1,000 per month:
N = 44 12; PMT = 1,000; I = 8/12; PV = 0
Compute FV FV = 4,858,811
b How much would he need to contribute to have $5,000,000 at 65?
Trang 9FV = 5,000,000; I = 8/12; = 528; N PV = 0
Compute PMT PMT = 1,029
12 An employee contributes $200 a year (at the end of the year) to her pension plan What would be the total contributions and value of the account after five years? Assume that the plan earns 15% per year over the period.
The total contributions are $200 5 = $1,000.
The future value of the plan is:
N = 5; PMT = 200; I = 15; PV = 0
Compute FV FV = 1,348.47
V Investment Bank
13 Amazon.com issued an IPO in May 1997 Prior to its IPO, the following information on shares outstanding was listed in the final prospectus:
In the IPO, the firm issued 3,000,000 new shares The initial price was $18/share with investment bankers retaining $1.26 as fees The final first-day closing price was $23.50 Question:
a What were the total proceeds from this offering? What part was retained by Amazon? What part by the investment bankers? What percent of the offering is this?
Total proceeds = 3,000,000 × $18.00 = $54,000,000
To Amazon = 3,000,000 × $16.74 = $50,220,000
To the IB = 3,000,000 × $1.26 = $3,780,000, or 7% of the offer price
Trang 10shares What was the market value of these shares at the end of the first day of trading?
Market value = 3,401,376 × $23.50 = $79.93 million
c What was the market value of Amazon.com following its first day as a publicly-held company?
Market cap = (20,858,702 + 3,000,000) × $23.50 = $560.68 million
14 Michael Yass decided to buy 500 IBM shares at $40 per share on margin trading The initial margin is 60%, maintenance margin is 30% What does it mean? If the price of IBM then rises to $50, what is his net worth? How much could he withdraw from his brokerage account?
Investment value: 500 x 40 = $ 20,000
Initial margin: 60% x 20,000 = 12,000
Loans: 8000
Current Margin: (50 x 500) – 8000 = $ 17,000
a Net worth: -20,000 + 17,000 = -3,000
b He could withdraw:
Current margin rate = $17,000/$50 x 500 x 100% = 68% > 30%
Michael will not receive a margin call and he could withdraw some of money
Initial margin: 50 x 500 x 60% = $15,000
Total balance = 15000+8000 = $23000
He could withdraw: 50 x 500 = $25,000
He could withdraw from his brokerage account with the amount of $56
15 Dee Trader opens a brokerage account and purchases 300 shares of Internet Dreams at
$40 per share She borrows $4,000 from her broker to help pay for the purchase
a What is the margin in Dee’s account when she first purchases the stock?
The stock is purchased for $40 x 300 shares = $12,000
Given that the amount borrowed from the broker is $4,000, Dee's margin is the initial purchase price net borrowing: $12,000 - $4,000 = $8,000
b If the price falls to $30 per share by the end of the year, what is the remaining margin in her account? If the maintenance margin requirement is 30%, will she receive a margin call? How much would she have to deposit if she receives a margin call?
If the share price falls to $30, then the value of the stock falls to $9,000
By the end of the year, the amount of the loan owed to the broker grows to:
Principal x (1 + Interest rate) = $4,000 x (1 + 0.08) = $4,320
The value of the stock falls to: $30 x 300 shares = $9,000
The remaining margin in the investor's account is:
Trang 11= $9,000 － $4,320/$9,000 = 0.52 = 52%
Therefore, the investor will not receive a margin call
16 Suppose that Intel currently is selling at $40 per share You buy 500 shares, using
$15,000 of your own money and borrowing the remainder of the purchase price from your broker
a What is percentage increase in the net worth of your brokerage account if the price of Intel immediately changes to (i) $44, (ii) $40, (iii) $36? In each case, would you get a margin call?
Equity increases to: ($44 * 500) - $5,000 = $17,000
Percentage gain = $2,000/$15,000 = 0.1333 = 13.33%
(ii) With price unchanged, equity is unchanged
Percentage gain = 0
(iii) Equity falls to ($36 * 500) - $5,000 = $13,000
Percentage gain = (-$2,000/$15,000) = -0.1333 = -13.33%
b If the maintenance margin is 25%, how low can Intel’s price fall before you get a margin call?
The value of the 500 shares is 500P Equity is (500P - $5,000) You will receive a margin call when:
(500P-$5000)/500P
= 0.25 > when P = $13.33 or lower