The following market value (mark-to-market) balance sheet information is availab
ID: 2764663 • Letter: T
Question
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 = DA –kDL = 0
The choice is to make the duration of assets equal to:
DA =
or the duration of liabilities equal to:
DL =
Or some combination thereof.
Explanation / Answer
Since, there are multiple parts to the question, the first five have been answered.
__________
Part 1)
The market value of the loan can be calculated with the use of Present Value (PV) function/formula of EXCEL/Financial Calculator. The function/formula for PV is PV(Rate,Nper,PMT,FV) where Rate = Market Yield, Nper = Period, PMT = Interest Payment and FV = Book Value.
________
Here, Rate = 7%, Nper = 20, PMT = 5,000*6% = $300 and FV = $5,000
Using these values in the above formula for PV, we get,
Market Value of Loan = PV(7%,20,300,5000) = $4,470.30
________
Part 2)
The duration of the loan is calculated as follows:
Duration of the Loan = 52,272.82/4,470.30 = 11.69
________
Part 3)
The completed balance sheet is as follows:
________
Part 4)
The weighted average duration of the assets is calculated as follows:
Weighted Average Duration of Assets = (180*.50 + 4,470.30*11.69)/(180 + 4,470.30) = 11.26 years
________
Part 4)
The weighted average duration of the liabilities is calculated as follows:
Weighted Average Duration of Liabilities = (4,184*1)/4,184 = 1 Year
________
Part 5)
The leverage-adjusted duration gap is calculated as follows:
Leverage-Adjusted Duration Gap = 11.26 - (4,184/4,650.3)*1 = 10.36 Years
Since, the duration gap is positive, an increase in interest rates would result in a decline in the market value of equity. This is the interest rate exposure faced by the bank.
Year (A) Annual Cash Flow Present Value of Cash Flow (B) (A*B) 1 300 280.37 280.37 2 300 262.03 524.06 3 300 244.89 734.67 4 300 228.87 915.47 5 300 213.90 1,069.48 6 300 199.90 1,199.42 7 300 186.82 1,307.77 8 300 174.60 1,396.82 9 300 163.18 1,468.62 10 300 152.50 1,525.05 11 300 142.53 1,567.81 12 300 133.20 1,598.44 13 300 124.49 1,618.36 14 300 116.35 1,628.83 15 300 108.73 1,631.01 16 300 101.62 1,625.93 17 300 94.97 1,614.53 18 300 88.76 1,597.67 19 300 82.95 1,576.10 20 5300 1,369.62 27,392.41 Total 4,470.30 52,272.82Related Questions
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