An insurance company issued a $95 million one-year, zero-coupon note at 8 percent add-on annual interest (paying one coupon at the end of the year) and used the proceeds plus $15 million in equity to fund a $110 million face value, two-year commercial loan at 10 percent annual interest. Immediately after these transactions were (simultaneously) undertaken, all interest rates went up 2 percent.
a. What is the market value of the insurance company’s loan investment after the changes in interest rates? (Do not round intermediate calculations. Enter your answer in millions rounded to 3 decimal places. (e.g., 32.16))
b. What is the duration of the loan investment when it was first issued? (Do not round intermediate calculations. Round your answer to 3 decimal places. (e.g., 32.161))
c. Using duration, what is the new expected value of the loan if interest rates are predicted to increase to 12 percent from the initial 10 percent? (Do not round intermediate calculations. Enter your answer in millions rounded to 3 decimal places. (e.g., 32.16))
d. What is the market value of the insurance company’s $95 million liability when interest rates rise by 2 percent? (Do not round intermediate calculations. Enter your answer in millions rounded to 3 decimal places. (e.g., 32.161))
e. What is the duration of the insurance company’s liability when it is first issued?