Please answer question 1. Thank you very much. Show work need it in the next "Hour"

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 Cash reserves Auto loans Mortgages Total Assets Liabilities 51.8 Checking and savings 81.2 93.3 Certificates of deposit 98.7 150.1 Long-term financing 95.4 295.2 Total liabilities 275.3 Owner's equity 19.9 Total liabilities and equity 295.2 When you analyze the duration of loans, you find that the duration of the auto loans is 1.9 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 2.2 years, and the long-term financing has a 9.2 year duration. a. What is the duration of Acorn's equity? (In years?) Round 2 decimals places b. Suppose Acorn experiences a rash of mortgage prepayments, reducing the size of the mortgage portfolio from $150.1 million to $100.1 million, and increasing cash reserves to $101.8 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 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? a) Duration of Acom's equity: The duration of the portfolio is the value-weighted average of the duration of each investment in the portfolio. The duration of the portfolio with market values A and B and durations DA and DB, is calculated as follows: Duration A+B = [A / (A+B)]DA + [A / (A+B)]DB The given balance sheet, in millions of dollars, is as follows: Assets Liabilities Cash reserves 51.8 Checking and savings 81.2 Auto loans 93.3 Certificates of deposit 98.7 Mortgages 150.1 Long-term financing 95.4 Total liabilities 275.3 Total assets 295.2 Owner's equity 19.9 Total liabilities and equity 295.2 The duration of auto loans is 1.9 years, mortgage 7.1 years, cash reserves and the checking and savings accounts 0 years, CDs 2.2 years and long term financing 9.2 years. Substitute: Asset duration = [51.8 / 295.2]*0 + [93.3 / 295.2]*1.9 + [150.1 / 295.2]*7.1 = 0 + 0.60 + 3.61 = 4.21 years Liability duration = [81.2 / 295.2]*0 + [98.7 / 295.2]*2.2 + [95.4 / 295.2]*9.2 = 0 + 0.74 + 2.97 = 3.71 years Equity = assets - liabilities Equity duration DE = DA-L = [A / (A-L)]*DA - [L / (A-L)]*DL = [295.2 / 19.9]*4.21 - [275.3 / 19.9]*3.71 = 62.45 - 51.32 = 11.156 years = 11.13 years. b) Duration of the portfolio: The duration of the portfolio is the value-weighted average of the duration of each investment in the portfolio. The duration of the portfolio with market values A and B and durations DA and DB, is calculated as follows: Duration A+B = [A / (A+B)]*DA + [A / (A+B)]*DB The given balance sheet, in millions of dollars, is as follows: Assets Liabilities Cash reserves 101.8 Checking and savings 81.2 Auto loans 93.3 Certificates of deposit 98.7 Mortgages 100.1 Long-term financing 95.4 Total liabilities 275. 3 Total assets 295.2 Owner's equity 19.9 Total liabilities and equity 295. 2 The duration of auto loans is 1.9 years, mortgage 7.1 years, cash reserves and the checking and savings accounts 0 years, CDs 2.2 years and long term financing 9.2 years. Substitute: Asset duration = [101.8 / 295.2]*0 + [93.3 / 295.2]*1.9 + [100.1 / 295.2]*7.1 = 0 + 0.601 + 2.408 = 3.01 years Liability duration = [81.2 / 295.2]*0 + [98.7 / 295.2]*2.2 + [95.4 / 295.2]*9.2 = 0 + 0.736 + 2.973 = 3.71 years Equity = assets - liabilities To find equity duration: Equity duration DE = DA-L = [A / (A-L)]*DA - [L / (A-L)]*DL = [295.2 / 19.9]*3.01 - [275.3 / 19.9]*3.71 = 44.65 - 51.32 = - 6.67 years If the interest rate falls to 3% from 4%, the change in the value of firm's equity: Percentage change in value - Duration * [ / (1 + r/k)] Where is the small change in interest rate, r is the current interest rate and expressed as an APR with k compounding periods per year. Percentage change in value - (-6.67)* [1 / (1 + 0.04)] Percentage change in value 6.41% c) The firm can decrease the asset duration by selling mortgage in exchange of cash. The amount of exchange can be calculated as follows: Amount to exchange = (change in portfolio duration * portfolio value) / change in asset duration The change in equity duration is 6.67 years with portfolio value of $19.9 million. The duration of treasury STRIPS is 10 years. Amount to exchange = (6.67 * 19.9) / 10 Amount to exchange = $13.27 million. Thus the firm should buy 10-year treasury STRIPS $13.27 million