When you analyze the duration of loans, you find that the duration of the auto loans is 2.1 years, while the mortgages have a duration of 7.1 years. Both the cash reserves and the checking and savings accounts have a zero duration. The CDs have a duration of 2.1 years, and the long-term financing has a 9.9-year duration.

a. What is the duration of Acorn's equity?

b. Suppose Acorn experiences a rash of mortgage prepayments, reducing the size of the mortgage portfolio from $148.1 million to $98.7 million, and increasing cash reserves to $100.5 million. What is the duration of Acorn's equity now? If interest rates are currently 4% and were to fall to 3%, estimate the approximate change in the value of Acorn's equity. (Assume interest rates are APRs based on monthly compounding.)

c. 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?

Assets Cash reserves Auto loans Mortgages Total Assets 51.1 105.5 148.1 304.7 Liabilities Checking and savings Certificates of deposit Long-term financing Total liabilities Owner's equity Total liabilities and equity 82.7 100.4 100.1 283.2 21.5 304.7