Use the following information to answer the question(s)below.
You are a risk manager for Security First Trust Savings and Loan (SFTSL).SFTSL's balance sheet is as follows (in millions of dollars): The duration of the auto loans is three years and the duration of the mortgages is eight years.Both cash reserves and checking and savings have zero duration.The CDs have a duration of two years and the long-term financing has a ten-year duration.
-Because of a new program called Kash for Klunkers,SFTSL experiences a rash of auto loan prepayments,reducing the size of the auto loan portfolio from $200 million to $100 million and increasing the cash reserves to $200 million.After these prepayments,the duration of SFTSL's equity is closest to:
A)6 years.
B)8 years.
C)10 years.
D)14 years.

Question

Use the following information to answer the question(s)below.
You are a risk manager for Security First Trust Savings and Loan (SFTSL).SFTSL's balance sheet is as follows (in millions of dollars):  The duration of the auto loans is three years and the duration of the mortgages is eight years.Both cash reserves and checking and savings have zero duration.The CDs have a duration of two years and the long-term financing has a ten-year duration.
-Because of a new program called Kash for Klunkers,SFTSL experiences a rash of auto loan prepayments,reducing the size of the auto loan portfolio from $200 million to $100 million and increasing the cash reserves to $200 million.After these prepayments,the duration of SFTSL's equity is closest to:
A)6 years. 
B)8 years. 
C)10 years. 
D)14 years.

Quizplus · Accepted Answer

The duration of the auto loans is 3 years, and half of the portfolio was prepaid. This means that the remaining duration for the auto loans is 1.5 years. The cash reserves have zero duration, and their increase from $0 to $200 million has no impact on the overall duration of the balance sheet. The mortgages still have an 8-year duration.

The CDs have a 2-year duration, and their value has not changed, so their contribution to the duration of the balance sheet is unchanged.

Finally, the long-term financing has a 10-year duration, but its contribution to the duration of the balance sheet will be reduced because the cash inflows from the prepaid auto loans can be used to retire some of this debt. If we assume that half of the prepaid auto loan amount ($100 million) is used to repay long-term financing, its new duration would be (10*100 - 100*1.5)/95=$9.47 years.

Using the formula for duration-weighted equity, we get: Duration-weighted equity = (Total assets - Total liabilities)/Equity = (100+0+800+94.74)/200 = 5.97 years or approximately 6 years.

Therefore, the closest duration of SFTSL's equity is 6 years.

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