FIN 701 Study Guide - Weighted Arithmetic Mean, Yield Curve, Interest Rate Risk

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beigefish258

7 Oct 2013

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Book value accounting assets and liabilities of fi recorded at historic values. Market value accounting assets and liabilities of fi revalued according to current level of interest rates. Marking to market valuing securities at current market price. Duration is a more complete measure of asset"s or liability"s interest rate sensitivity than maturity because it takes into account time of arrival (or payment) of all cash flows and maturity. Duration weighted-average time to maturity on an investment: on time value of money basis, measure period of time required to recover initial investment on the loan. After that time, the fi earns a profit, or return, on the loan. When cash flows are limited to one payment at the end of the period with no intervening cash flows, duration equals maturity. Calculate duration (or macaulay"s duration) for any fixed-income security that pays interest annually.

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The following market value (mark-to-market) balance sheet information is available for Duguay State Bank (amounts in $ thousands and duration in years):

Book Value Market Value

Assets Amount Amount Duration

T-bills $ 180 $ 180 0.50

Loans* 5,000 ______ _____

Total Assets 5,180 ______

Liabilities

Deposits 4,184 4,184 1.00

Total Liabilities 4,184 4,184

Equity 996 _______

Total Lia and NW 5,180 _______

*Since this is a simple bank, it has only one type of loan. The loan has a $5,000 book value (current outstanding principal), amortized loan with annual payments, an interest rate of 6 percent, and 20-years to maturity. Similar loans today would have an interest rate of 7 percent which is the market yield.

Using Excel, determine the market value and duration of the loan and fill in the blanks in the balance sheet above. Please include a copy of your Excel Spreadsheet with your completed exam. What is the average duration of all the assets?

Weighted Average Duration Assets:

b. What is the average duration of all the liabilities?

Weighted Average Duration Liabilities:

c. What is the leverage-adjusted duration gap? What is the interest rate risk exposure?

DG = DA - kDL =

d. What is the forecasted impact on the market value of equity caused by a relative upward shift in the entire yield curve of 1.5 percent [i.e., Dr/(1+r) = 0.0150]?

The market value of the equity will change by the following:

MVE = -DG * (A) * r/(1 + r) =

e. What variables are available to the financial institution to immunize the balance sheet? Taking one variable at a time, how much would each variable need to change to get DGAP equal to 0?

To immunize the institution for interest rate risk, the Leverage Adjusted DG needs to be zero:

DG = D_A âkD_L = 0

The choice is to make the duration of assets equal to:

D_A =

or the duration of liabilities equal to:

D_L =

Or some combination thereof.

The following market value (mark-to-market) balance sheet information is available for Delasho State Bank (amounts in $ thousands and duration in years):

Book Value Market Value

Assets Amount Amount Duration

T-bills $ 180 $ 180 0.50

Loans* 5,000 ______ _____

Total Assets 5,180 ______

Liabilities

Deposits 4,184 4,184 1.00

Total Liabilities 4,184 4,184

Equity 996 _______

Total Lia and NW 5,180 _______

*Since this is a simple bank, it has only one type of loan. The loan has a $5,000 book value (current outstanding principal), amortized loan with annual payments, an interest rate of 6 percent, and 20-years to maturity. Similar loans today would have an interest rate of 7 percent which is the market yield.

Weighted Average Duration Assets:

b. What is the average duration of all the liabilities?

Weighted Average Duration Liabilities:

c. What is the leverage-adjusted duration gap? What is the interest rate risk exposure?

DG = DA - kDL =

d. What is the forecasted impact on the market value of equity caused by a relative upward shift in the entire yield curve of 1.5 percent [i.e., Dr/(1+r) = 0.0150]?

The market value of the equity will change by the following:

MVE = -DG * (A) * r/(1 + r) =

e. What variables are available to the financial institution to immunize the balance sheet? Taking one variable at a time, how much would each variable need to change to get DGAP equal to 0?

To immunize the institution for interest rate risk, the Leverage Adjusted DG needs to be zero:

DG = D_A âkD_L = 0

The choice is to make the duration of assets equal to:

D_A =

or the duration of liabilities equal to:

D_L =

Or some combination thereof.

scarletreindeer576

Please can someone help me with this :

Minicase 1

Interest Rates, Bond Yields, and Duration

CONCEPTS IN THIS CASE

simple loans
fixed-payment loans
coupon bonds
present value
yield-to-maturity
current yield
nominal and real interest rates
rate of return
capital gain
interest-rate and reinvestment risk
duration

You have been hired to analyze the debt securities of your organization. The firm has outstanding loans and bonds. A quick review of the balance sheet shows the following:

	Liability Amount ($)	Nominal Interest (coupon) Rate	Years to Maturity
Selected Liabilities of the firm
Simple Loans	800	5%	1
Fixed-Payment Loans	5,000	12%	19
Long-term Bonds #1	500,000	10%	4
Long-term Bonds #2	1,080,000	10%	10
Liabilities Total	1,585,800

Market Price for Bond #1	930.50
Market Price for Bond #2	859.50
Face Value of Each Bond	1,000.00
Selected Current Assets of the firm
Marketable Securities:
Treasury Bills	100,000

Note: Treasury Bills have a $10,000 face value, which matures in one year. Each Treasury Bill has a cost of $9,580.00

How much interest would the firm pay each year on the simple-interest loan?

How much would you write a cheque for to pay off the loan in one year?

What is the monthly payment needed to pay off the fixed-payment loans?

What is the current yield for each bond if the current price is:

$930.50 for Bond #1?

$859.50 for Bond #2?

What is the expected yield to maturity for each bond?

Bond #1 selling for $930.50?

Bond #2 selling for $859.50

What is the rate of capital gain if both bonds sell for $900.00 in one year?

Bond #1 selling for $930.50 today?

Bond #2 selling for $859.50 today?

If the Yield to Maturity expected by investors changes to 11%:

What will be the market price of Bond #1?

What will be the market price for Bond #2?

What will be the dollar change in price for Bond #1?

What will be the dollar change in price for Bond #2?

What will be the percent change in price for Bond #1?

What will be the percent change in price for Bond #2?

Since the change in expected yield to maturity is the same, why is the amount of change different between the bonds?

If investors holding our 4-year bonds (Bond #1) receive interest income annually for four years, plus the face value of the bonds at maturity,

What will be the total interest earned on the bond over the next four years?

What will be the face value received at maturity?

Given the following projected income stream for Bond #1:

			Projected Reinvestment Rates
Year	Coupon Interest ($)	Face Value ($)	10%	5%
1	100
2	100		10.00	5.00
3	100		21.00	10.25
4	100	1000	33.10	15.76
Total Income	400	1000	64.10	31.01

What is the total cash available over the next four years to the bond holder earning

10%

15%

What is the average annual rate of return for the bond holder earning

10%

15%

Why does the reinvestment rate affect the annual rate of return for the same bond?

If the expected rate of return on our bonds is 10%, what is the duration of Bond #1?

What is the yield to maturity on the Treasury Bills (a discount bond)?

What is the real rate of interest if the nominal rate is 10% and the inflation rate is 3%?

amethystcrow453

FIN 701 Study Guide - Weighted Arithmetic Mean, Yield Curve, Interest Rate Risk

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