Question

An insurance company issued a $110 million one-year, zero-coupon note at 7 percent add-on annual interest (paying one coupon at the end of the year) and used the proceeds plus $30 million in equity to fund a $140 million face value, two-year commercial loan at 9 percent annual interest. Immediately after these transactions were (simultaneously) undertaken, all interest rates went up 1.7 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., 32.161))
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 10.7 percent from the initial 9 percent? (Do not round intermediate calculations. Enter your answer in millions rounded to 3 decimal places. (e.g., 32.161))
d. What is the market value of the insurance company’s $110 million liability when interest rates rise by 1.7 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? (Round your answer to the nearest dollar amount.)

Answer 1

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