Question
In: Finance
An insurance company issued a $99 million one-year, zero-coupon note at 7 percent add-on annual interest...
|
An insurance company issued a $99 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 $19 million in equity to fund a $118 million face value, two-year commercial loan at 9 percent annual interest. Immediately after these transactions were (simultaneously) undertaken, all interest rates went up 1.4 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 10.4 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 $99 million liability when interest rates rise by 1.4 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
a. Market value of the loan investment:
Face Value of loan investment = $118 million
Coupon Rate = 9%
Current Market Rate = 10.4%
Cash Flows :
1st Year = $118 million * 9% = $10.62 million
2nd year = $118 million * 9% + $118 million (Principal) = $128.62 million
Present Value of Cash flows discounted at 10.4%
PV of cash flows = (10.62 million/1.104) + (128.62 million/1.104^2) = $115.1482 million
Market Value of Loan Investment = $115.1482 million
b. Duration at initial Issue:
| Year | Cash flow | Cash flow x Year | PV of Cash flow (9%) |
| 1 | 10.62 | 10.62 | 9.74 |
| 2 | 128.62 | 257.24 | 216.51 |
| Total | 226.26 | ||
| Face value of loan | 118.00 | ||
| Duration (Total / facevalue) |
1.92 |
c.
| Current duration | 1.92 |
| Increase in rates | -0.014 |
| Duration x change in rate | -0.02684404 |
| Change in value of investment (Change in duration x value of investment) | -3.16759633 |
| Current value after change in rates($118million+Change in Value of Investment) | 114.8324037 |
d.
| Period | Interest | Principal | Total | Present value(7%+1.4%) |
| End of Year 1 | 6.93 | 99 | 105.93 | 97.7214022 |
| Market value of loan = 97.7214 | ||||
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