In: Finance
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., 32.16)) |
Market value of the loan investment | $ million |
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)) |
Duration of the loan investment | years |
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., 32.16)) |
New expected value | $ million |
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)) |
Market value of the liability | $ million |
e. |
What is the duration of the insurance company’s liability when it is first issued? |
Duration of the liability | year(s) |
Solution:
a. The first year interest rate is 7%. Therefore theprice of bond issued by the insurance company prior to increase ininterest rate comes to $ 180 mn (140 x 9%/7%). However since$110 mn is financed by a loan, we will have to reduce the marketvalue of the $110 mn loan to consider the value of the loaninvestment.
Now the interest rates have gone up by 1.7%. So the newyield on the bond should be 8.7%. Therefore the price of thevalue of commercial paper of $140 mn comes to $144827586.207
The market value of the $110 mn bond issued by the insurancecompany works out to $ 88505747.126 (110 x 7%/8.7%)
Therefore the market value of the loan investment of $30 mnworks out to $144827586.207-$88505747.126 = $56321839.080
b. Duration of the loan investment when it was first issued - 1year
c. If the interest rate is expected to rise to 10.7% from 9%,the value of the loan comes to 140mn x 10.7%/9% = $166444444.444.
d. Market value of the liability of insurance company when theinterest rates increase by 1.7% = $88505747.126 (8.7%/7%) x110 mn.