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 51.8 Checking and savings 81.3

Auto Loan 103.7 Certificates of deposit 98.3

Mortgages 147.1 Long term Financing 102.3

Total assests= 302.6 Total Liabilities= 281.9

Owners equity=20.7

Total liabilities and equity 302.6

When you analyze the duration of loans you find that the duration of the auto loans is 2.2 years. While the mortgages have a duration of 7.1 years. Both the cash reserves and the checking and savings accounts have zero duration. The CD's have a duration of 2.2 years, and the long term financing has a 9.5-year duration.

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

B. Suppose Acorn experience a rash of mortgage pre-payments, reducing the size of the mortgage portfolio from $147.1 million to 98.1, million, and increasing cash reserves to 100.8 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 APR's based on monthly compounding).

C. Suppose that after the pre-payments in part (b) but before a change in interest rates. Acorn considers managing its risk by selling mortgages and a 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 51.8

Auto Loans 103.7

Mortgages 147.1

Total Assets 302.6

Liabilities

Checking and savings 81.3

Certificates of Deposit 98.3

Long term financing 102.3

Total Liabilities 281.9

Owners Liabilities 20.7

Total Liabilities and equity 302.6