Finance Homework (Should be done in 3 and a half hours)

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Chapter 20

1. On January 1st, the shares and prices for a mutual fund at 4:00 pm are:

Stock	Shares owned	Price
1	1,000	$ 1.92
2	5,000	$ 41.18
3	3,800	$ 19.08
4	9,200	$ 37.19
5	2,000	$ 2.51
cash	n.a.	$5,353.40
Liabilities		$1,500

Stock 3 announces record earnings, and the price of stock 3 jumps to $32.44 in after-market trading. If the fund (illegally) allows investors to buy at the current NAV, how many shares will $25,000 buy? If the fund waits until the price adjusts, how many shares can be purchased? What is the gain to such illegal trades? Assume 5,000 shares are outstanding.

Based on the new information, NAV is:

2. A $2 million fund is charging a back-end load of 2%, 12b-1 fees of 1%, and an expense ratio of 2.9%. Prior to deducting expenses, what must the fund value be at the end of the year for investors to break even?

Chapter 21

3. Your rich uncle dies, leaving you a life insurance policy worth $160,000. The insurance company also offers you an option to receive $10,500/year for 15 years, with the first payment due today. Which option should you use?

With this information, the answer depends on many factors. Do you “need’ the $160,000 today? Can you personally invest the $160,000 at a higher rate with the same level of risk? Is there any risk that the insurance company will not pay in the future? Etc.

Chapter 23:

4. The following financial statement is for the current year. From the past, you know that 10% of fixed-rate mortgages prepay each year. You also estimate that 10% of checkable deposits and 20% of savings accounts are rate sensitive.

Second National Bank
Assets	Liabilities
Reserves	$ 1,500,000	Checkable Deposits	$ 15,000,000
Securities		Money Market Deposits	$ 5,500,000
 1 Year	$ 6,000,000	Savings Accounts	$ 8,000,000
1 to 2 Years	$ 8,000,000	CDs
 2 years	$ 12,000,000	Variables-rate	$ 15,000,000
Residential Mortgages		 1 Year	$ 22,000,000
Variables-rate	$ 7,000,000	1 to 2 Years	$ 5,000,000
Fixed-rate	$ 13,000,000	 2 years	$ 2,500,000
Commercial Loans		Fed Funds	$ 5,000,000
 1 Year	$ 1,500,000	Borrowings
1 to 2 Years	$ 18,500,000	 1 Year	$ 12,000,000
 2 years	$ 30,000,000	1 to 2 Years	$ 3,000,000
Buildings, etc.	$ 2,500,000	 2 years	$ 2,000,000
		Bank Capital	$ 5,000,000

Total	$100,000,000	Total	$100,000,000

What is the current Income GAP for Second National Bank? What will happen to the bank’s current net interest income if rates fall by 75 basis points?

5. The manager for Tyler Bank and Trust has the following assets to manage:

Asset	Value	Duration (in years)	Liability	Value	Duration (in years)
Bonds	115,000,000	9.00	Demand Deposits	690,000,000	1.00
Consumer Loans	345,000,000	2.00	Saving Accounts	??	0.50
Commercial
Loans	575,000,000	5.00

If the manager wants a duration gap of 3.00, what level of Saving Accounts should the bank raise? Assume that any difference between assets and liabilities is held as cash (duration  0).

6. The following financial statement is for the current year:

Second National Bank
Assets	Duration	Liabilities	Duration
Reserves	5,000,000	0.00	Checkable Deposits	15,000,000	2.00
Securities			Money Market Deposits	5,000,000	0.10
 1 Year	5,000,000	0.40	Savings Accounts	15,000,000	1.00
1 to 2 Years	5,000,000	1.60	CDs
 2 years	10,000,000	7.00	Variables-rate	10,000,000	0.50
Residential Mortgages			 1 Year	15,000,000	0.20
Variables-rate	10,000,000	0.50	1 to 2 Years	5,000,000	1.20
Fixed-rate	10,000,000	6.00	 2 years	5,000,000	2.70
Commercial Loans			Interbank Loans	5,000,000	0.00
 1 Year	15,000,000	0.70	Borrowings
1 to 2 Years	10,000,000	1.40	 1 Year	10,000,000	0.30
 2 years	25,000,000	4.00	1 to 2 Years	5,000,000	1.30
Buildings, etc.	5,000,000	0.00	 2 years	5,000,000	3.10
			Bank Capital	5,000,000

Total	$100,000,000		Total	$100,000,000

Calculate the duration gap for the bank.

Chapter 24

7. Suppose that you buy a call option on $100,000 T-bond futures contract with an exercise price 110 for a premium of $1,500. If on expiration the futures contract has a price of 107, what is your profit or loss on the contract?

8. Vicky’s Bank and Trust has $100 million in assets and $83 million in liabilities. The duration of the assets is 5.0 years, and the duration of the liabilities is 1.8 years. How many futures contracts does this bank need to fully hedge itself against interest rate risk? The available Treasury bond futures contracts have a duration of 10 years, a face value of $1,000,000, and are selling for $979,000.

9. A bank issues a $5 million commercial mortgage with a nominal APR of 8%. The loan is fully amortized over 15 years requiring monthly payments. The bank plans on selling the loan after 4 months. If the required nominal APR increases by 55 basis points when the loan is sold, what loss does the bank incur?

10. A bank issues a $100,000 fixed-rate, 30-year mortgage with a nominal annual rate of 5.5%. If the required rate drops to 5.0% immediately after the mortgage is issued, what is the impact on the value of the mortgage? Assume the bank hedged the position with a short position in two 10-year T-bond futures. The original price was 64 12/32 and expired at 67 16/32 on a $100,000 face value contract. What was the gain on the futures? What is the total impact on the bank?

Chapter 20

On January 1st, the shares and prices for a mutual fund at 4:00

are:

Stock

Shares owned

Price

1,000

1.92

5,000

1.18

,800

9.08

9,200

7.19

,000

.51

cash

n.a.

$5,353.40

Liabilities

$1,5

Stock 3 announces record earnings, and the price of stock 3 jumps to $32.44 in after

market

trading. If the fund (illegally) allows investors to buy at the current NAV, how many shares will

$25,000 buy? If the fund waits until the

price adjusts, how many shares can be purchased? What is

the gain to such illegal trades? Assume 5,000 shares are outstanding.

Based on the new information, NAV is:

A $2

million fund

is charging a back

end load of 2

%, 12b

1 fees

of 1%, and an expense

ratio of 2

.9%.

Prior to deducting expenses, what must the fund value be at the end of the year for investors to

break even?

Chapter 21

Your rich uncle dies, leaving you a

life insurance policy worth $16

0,000. The insurance company

also of

fers you an op

tion to receive $10,500/year for 15

years, with the first payment due today.

Which option should you use?

With this information, the answer depends on many factors. Do you “need’ the $1

0,000 today?

an you personally invest the $16

0,000 at a higher rate

with the same level of risk? Is there any risk

that the insurance company will not pay in the future? Etc.

Chapter 20

1. On January 1st, the shares and prices for a mutual fund at 4:00 PM are:

Stock Shares owned Price

1 1,000 $ 1.92

2 5,000 $ 41.18

3 3,800 $ 19.08

4 9,200 $ 37.19

5 2,000 $ 2.51

cash n.a. $5,353.40

Liabilities $1,500

Stock 3 announces record earnings, and the price of stock 3 jumps to $32.44 in after-market

trading. If the fund (illegally) allows investors to buy at the current NAV, how many shares will

$25,000 buy? If the fund waits until the price adjusts, how many shares can be purchased? What is

the gain to such illegal trades? Assume 5,000 shares are outstanding.

Based on the new information, NAV is:

2. A $2 million fund is charging a back-end load of 2%, 12b-1 fees of 1%, and an expense ratio of 2.9%.

Prior to deducting expenses, what must the fund value be at the end of the year for investors to

break even?

Chapter 21

3. Your rich uncle dies, leaving you a life insurance policy worth $160,000. The insurance company

also offers you an option to receive $10,500/year for 15 years, with the first payment due today.

Which option should you use?

With this information, the answer depends on many factors. Do you “need’ the $160,000 today?

Can you personally invest the $160,000 at a higher rate with the same level of risk? Is there any risk

that the insurance company will not pay in the future? Etc.