Question

In: Finance

An insurance company issued a $110 million one-year, zero-coupon note at 7 percent add-on annual interest...

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)  

Solutions

Expert Solution

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.


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