23. 4.00 points value: An insurance company must make payments to a customer of

Question

23. 4.00 points value: An insurance company must make payments to a customer of $8 million in 1 year and $3 million in 4 years. The yield curve is flat at 9%. a. If it wants to fully fund and immunize its obligation to this customer with a single issue of a zero-coupon bond, what maturity bond must it purchase? (Do not round intermediate calculations. Round your answer to 4 decimal places.) Maturity of zero coupon bond years b. What must be the face value and market value of that zero-coupon bond? (Do not round intermediate calculations. Enter your answers in millions rounded to 2 decimal places. Omit the "$" sign in your response.) Face value Market value

Explanation / Answer

Solution:

a)

PV of first payment (P1)= 8/ 1.09

= 7.339

P2 = 3/ (1.09^4) = 2.125

Total PV = 7.339 + 2.125 = 9.465

W1 = 7.339 / 9.465 = 0.7755

W2 = 2.125 / 9.465 = 0.2245

Duration = T1*W1 + T2*W2

= 1*0.7755 + 4*0.2245

= 1.6736 years

b)

Face value of bond = 8 + 3

= 11 million

Market value =11 / (1.09^1.6736)

= 9.52 Million

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