An insurance company must make payments to a customer of $10 million in 1 year a

Question

An insurance company must make payments to a customer of $10 million in 1 year and $4 million in 5 years. The yield curve is flat at 10%.

If it wants to fully fund and immunize its obligation to this customer with a single issue of a zero-coupon bond, what maturity bond must it purchase? (Do not round intermediate calculations. Round your answer to 4 decimal places.)

What must be the face value and market value of that zero-coupon bond? (Do not round intermediate calculations. Enter your answers in millions rounded to 2 decimal places. Omit the "$" sign in your response.)

An insurance company must make payments to a customer of $10 million in 1 year and $4 million in 5 years. The yield curve is flat at 10%.

Explanation / Answer

duration = 1.8572 years is the requird maturity of ZCB

The market value must be $ 11.57 million, same as the market value of obligations.

So face value = 11.57million * (1.1)^1.8572 = $ 13.81 million

Time until payment Cash flow PV of cash flow Weight time * weight 1 $ 10 million =10/(1+.1) = $ 9.09 million 0.7857 0.7857 5 $ 4 million =4/(1+.1)^5 = $ 2.48 million .2143 1.0715 column sum = $ 11.57 million 1.000 1.8572

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