An insurance company is obligated to pay out $12,000 one year from now and $9000

Question

An insurance company is obligated to pay out $12,000 one year from now and $9000 two yeras from now. In order to immunize, the insurance company purchases a combination of two bonds show below to match the payment stream:

Bond 1: A 1 year 6% annual coupon bond with a 5% yield rate

Bond 2: A 2 year 8% annual coupon bond with a 9% yield rate

Bohth bonds have a 1000 par and redemption value.

Calculate the number of Bond 1 and Bond 2 needed to be purchased to meet the obligation.

Calculate the cost to the insurer of purchasing the necessary amounts of each bond for the cash flow matching.

Explanation / Answer

Answer:

To make this immunization successful we need to match up the cash flows exactly.

As $12000 is required in the first year by the insurance company so Bond-1 cash flows should be exactly equal to this amount.

First we need to know the current market value (MV) of this bond by using this formula:

For Bond-1

YTM = 5%

Annual coupon rate = 6%

FV = $1000

And n = 1

Therefore coupon = 6% x $1000 = $60 after a year

And at redemption $1000 will be received too.

So total cash inflow at the end of year + $60 = $1060

So number of bonds to be purchased = $12000/$1060 = 11.32 or 12 bonds.

For Bond-2

YTM = 9%

Annual coupon rate = 8%

FV = $1000

And n = 2

Therefore coupon = 6% x $1000 = $60 after a year

And $60 at the end of year 2

And at redemption $1000 will be received too.

So total cash inflow at the end of year>

So total cash inflow at the end of year two = $60(1+9%)1 + $1000 + $60

                                                                     = $1125.4

So number of bonds to be purchased = $9000/$1125.4 = 7.99 or 8 bonds.

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