You have been hired as a risk manager for Acorn Savings and Loan. Currently, Aco
ID: 2818903 • Letter: Y
Question
You have been hired as a risk manager for Acorn Savings and Loan. Currently, Acorn's balance sheet is as follows (in millions of dollars):
Assets
Liabilities
Cash reserves
50.0
Checking and savings
80.0
Auto loans
100.0
Certificates of deposit
100.0
Mortgages
150.0
Long-term financing
100.0
Total Assets
300.0
Total liabilities
280.0
Owner's equity
20.0
Total liabilities and equity
300.0
When you analyze the duration of loans, you find that the duration of the auto loans is 2.0
years, while the mortgages have a duration of 7.0 years. Both the cash reserves and the checking and savings accounts have a zero duration. The CDs have a duration of 2.0 years, and the long-term financing has a 10.0-year duration.
What is the duration of Acorn's equity? The duration of the assets is ___ years? (Round 2 decimal places)The duration of liabilities is how many years? (Round 2 decimal places) The duration of the equity is how many years? (Round 2 decimal places)
Suppose Acorn experiences a rash of mortgage prepayments, reducing the size of the mortgage portfolio from $150.0 million to $100.0 million, and increasing cash reserves to $100.0 million. What is the duration of Acorn's equity now? The duration of the assets is ___ years? (Round 2 decimal places). The duration of the equity is ___ years? (Round 2 decimal places)
If interest rates are currently 4% and were to fall to 3%, estimate the approximate change in the value ofAcorn's equity. (Assume interest rates are APRs based on monthly compounding.)
We would expect the value of Acorn’s equity to (rise or drop) by approximately what percent? (Round 2 decimal places)
Suppose that after the prepayments in part (b), but before a change in interest rates, Acorn considers managing its risk by selling mortgages and/or buying 10-year Treasury STRIPS (zero coupon bonds). How many should the firm buy or sell to eliminate its current interest rate risk? They should (buy or sell) how many million worth of 10-year STRIPS? (Round 2 decimal places)
Assets
Liabilities
Cash reserves
50.0
Checking and savings
80.0
Auto loans
100.0
Certificates of deposit
100.0
Mortgages
150.0
Long-term financing
100.0
Total Assets
300.0
Total liabilities
280.0
Owner's equity
20.0
Total liabilities and equity
300.0
Explanation / Answer
Solution: Durations Auto Loan 2 years Mortgages 7 years Cash Reserves 0 Checking and savings 0 CD s 2 years Long Term Financing 10 years Duration of assets : (in Million $) Duration Cash Reserve $50 0 0 (50*0) Auto Loan $100 2 $200 (100*2) Mortgages $150 7 $1050 (150*7) Total $300 $1250 $1250/$300 Duration Of assets = 4.17 Years Duration of Liabilities : (in Million $) Duration Checking and savings $80 0 0 (0*80) CD s $100 2 200 (2*100) Long Term Financing $100 10 1000 (10*100) Total $280 $1200 $1200/$280 Duration of Liabilities= 4.29 Years Duration of Equity : Equity = Assets - Liabilities (Total assets/Equity*Duration of Assets) - (Total Liabilities/Equity* Duration Of Liabilities) ($300/$20*4.17) -($280/$20*4.29) Duration of Equity = 2.49 Years b) (In Million $) New Mortgage $100 New Cash Reserves $100 Duration of Assets Duration of Equity If interest rate fall from 4% to 3% Duration of assets : (in Million $) Duration Cash Reserve $100 0 0 (100*0) Auto Loan $100 2 200 (100*2) Mortgages $100 7 700 (100*7) Total $300 900 900/300 New Duration of assets = 3 Years Duration of Equity : Equity = Assets - Liabilities (Total assets/Equity*Duration of Assets) - (Total Liabilities/Equity* Duration Of Liabilities) ($300/$20*3) -($280/$20*4.29) -15.06 New Equity Duration -15.06 Change In Equity Value: 14.42 % c) Change In Equity Duration -15 Change In Asset Duration 10 Amount to Exchange -30 So the firm should buy 30 in strips New Asset Duration 4 New Equity Duration 0
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