Question: An insurance company issued a $90 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 $10 million in equity to fund a $100 million face value, two-year commercial loan at 10 percent annual interest. Immediately after these transactions were (simultaneously) undertaken, all interest rates went up 1.5 percent.
a. What is the market value of the insurance company's loan investment after the changes in interest rates?
b. What is the duration of the loan investment when it was first issued?
c. Using duration, what is the expected change in the value of the loan if interest rates are predicted to increase to 11.5 percent from the initial 10 percent?
d. What is the market value of the insurance company's $90 million liability when interest rates rise by 1.5 percent?
e. What is the duration of the insurance company's liability when it is first issued?