ou have been hired as a risk manager for Acorn Savings and Loan.Currently, Acorn's balance sheet is as follows(in millions ofdollars):

Assets

Liabilities

Cash reserves

50.2

50.2

Checking and savings

77.8

77.8

Auto loans

99.5

99.5

Certificates of deposit

97.8

97.8

Mortgages

147.4

147.4

Long-term financing

102.8

102.8

Total Assets

297.1

297.1

Total liabilities

278.4

278.4

Owner's equity

18.7

18.7

Total liabilities and equity

297.1

297.1

When you analyze the duration ofloans, you find that the duration of the auto loans is 1.9

1.9 years, while the mortgages have a duration of 6.9

6.9 years. Both the cash reserves and the checking and savings accounts have a zero duration. The CDs have a duration of 1.9

1.9 years, and thelong-term financing has a 9.4

9.4-year duration.

a. What is the duration ofAcorn's equity?

b. Suppose Acorn experiences a rash of mortgageprepayments, reducing the size of the mortgage portfolio from $ 147.4

$147.4 million to $ 98.3

$98.3 million, and increasing cash reserves to $ 99.3

$99.3 million. What is the duration ofAcorn's equitynow? If interest rates are currently 4 %

4% and were to fall to 3 %

3%, estimate the approximate change in the value ofAcorn's equity.(Assume interest rates are APRs based on monthlycompounding.)

c. Suppose that after the prepayments in part (b), but before a change in interestrates, Acorn considers managing its risk by selling mortgagesand/or buying 10

10-year Treasury STRIPS(zero couponbonds). How many should the firm buy or sell to eliminate its current interest raterisk?