Question

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)

Answer 1

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