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 insurance company
Annual interst	=	$118 million * 9%
	=	10.62	million
for 2 years	=	$10.62*2
	=	21.24	million
interest goes up to	=	10.40%
Annual interst	=	$118 million * 10.4%
	=	12.272	million
for 2 years	=	$12.272*2
	=	24.544	million
Realizable value	=	$118	million
Market value	=	$24.544+$118	milllion
		142.544	milllion
		$142.54	million
b)
Duration of loan, when it was first issued
	($ in million)
Period	Cash flow	Period*Cash flow		Pv ofS1@9%	PV of cash flow
1	10.62	10.62		0.917431	9.743119
2	128.62	257.24		0.917431	236
					245.7431
	Duration	=	Present value of cash flows/current loan value
		=	245.7431/118
		=	2.082569	Years
C)
Duration of loan, after increasing interest to 10.4%
	($ in million)
Period	Cash flow	Period*Cash flow		Pv [email protected]%	PV of cash flow
1	12.272	12.272		0.905797	11.11594
2	130.272	260.544		0.820468	213.768
		present value of cash flows		=	224.884
	Duartion	=	Present value of cash flows/current loan value
		=	224.884/118
		=	1.905797	Years
d)
market valeu of insurance company's liability
Value of loan	=	$99	million
interest	=	$99 million* 8.4%
	=	$8.32	million
total value	=	$107.32	million
		(99+8.32)
e)
Duration of liability
	($ in million)
Period	Cash flow	Period*Cash flow		Pv ofS1@17%	PV of cash flow
	99+99*7%
1	105.93	105.93		0.93457	98.999
		present value of cash flow			98.999
	Duration	=	Present value of cash flows/current loan value
		=	98.999/99
		=	0.99	Years