Question

As of 12/31/2013, an insurance company has a known obligation to pay $1,000,000 on 12/31/2017. To fund this liability, the company immediately purchases 4-year 5% annual coupon bonds totaling $822,703 of par value. The company anticipates reinvestment interest rates to remain constant at 5% through 12/31/2017. The maturity value of the bond equals the par value. Consider two reinvestment interest rate movement scenarios effective 1/1/2014. Scenario A has interest rates drop by 0.5%. Scenario B has interest rates increase by 0.5%. Determine which of the following best describes the insurance company's profit or (loss) as of 12/31/2017 after the liability is paid.

А. Scenario A - (18,910), Scenario B - 19,190
B. Scenario A - (14,760), Scenario B - 14,420
C. Scenario A -(1,310), Scenario B - 1,320

Answer 1

The insurance company's financial performance in response to changes in reinvestment interest rates (Scenario A and B) cannot be accurately determined without specific calculations for reinvested coupons. A change in reinvestment rates affects the final amount at bond maturity, influencing whether the company will incur a profit or loss relative to its $1,000,000 obligation. Examples given provide insight on bond price changes relative to market interest rates.

Step-by-step explanation:

The insurance company's goal is to match the liability with the proceeds from the investment in the 5% annual coupon bonds. Initially, the company invests $822,703 at par value, receiving 5% of this amount annually in coupons. The main concern here is the effect of a change in reinvestment rates on the ability of the company to meet its $1,000,000 obligation. Let's delve deeper into the scenarios outlined:

• Scenario A: If reinvestment rates drop to 4.5%, the reinvested coupons will earn less than anticipated, which may result in a shortfall when the bonds mature.
• Scenario B: If reinvestment rates increase to 5.5%, the reinvested coupons will earn more than initially anticipated, potentially resulting in excess funds after the obligation is met.

However, without the exact calculations showing the final values reached through reinvestment under each scenario, it's not possible to determine the exact profit or (loss) for either scenario A or B. To find these values, we would need to reinvest each annual coupon at the respective new interest rate and sum them with the final bond par value to see if they meet or exceed the $1,000,000 liability.

Additionally, there are parallel examples provided in the question that demonstrate how bond prices are impacted by changes in the market interest rate. When market rates exceed a bond's coupon rate, the bond's price typically falls below its face value to offer a competitive yield to investors.