A company has liabilities of size 1,050 at each of times t=1, t=2 and t=3. They

Question

A company has liabilities of size 1,050 at each of times t=1, t=2 and t=3. They choose to exactly match liabilities to assets by purchasing a one-year bond with face value F1 paying annual coupons at an annual coupon rate of 3.5%, purchasing a two-year bond with face value F2 coupons at an annual coupon rate of 4.5%, and purchasing a three-year bond with face vale F3 paying annual coupons at an annual coupon rate of 4.5%. Determine the face (par) value F1 for the one-year bond. (Note:You will need to find the face value of all three bonds in order to solve the problem. I am only asking you to enter the face value for the one-year bond). Round your answer to the nearest percent.

Explanation / Answer

Liability Size 1050 Say $ t1 1 Years t2 2 Years t3 3 Years Bond 1 F1 Facevalue Bond 2 F2 Facevalue Bond 3 F3 Facevalue Coupon Rates F1 3.50% F2 4.50% F3 4.50% Present value=Future value/(1+int rate)^duration) Future value of liability = 1050 Present vlue of mathching bond 1 year = 1050/((1+3.5%)^1) Value of Bond = Value of Bond + Value of Coupon Payment Present value = Present price + PV of coupon payment F1 1014.492754 $ Coupon payment for F2 = 4.5% coupon on 1014.493 $ for 2 yrs Coupon for 2 yrs in $ =4.5%*1014.493*2 Coupon for 2 yrs 91.30437 $ F2 = Value of debt - Coupon payment =1050-91.304 $ F2 = Value of debt - Coupon payment 958.696 $ F2 958.696 $ Coupon payment for F3 = 4.5% coupon on 1014.493 $ for 2 yrs + 4.5% of 958.696 for 1yr Coupon for 2 yrs in $ =4.5%*1014.493*2+958.696*4.5% Coupon for 2 yrs 134.44569 $ F2 = Value of debt - Coupon payment =1050-134.44569 F2 = Value of debt - Coupon payment 915.55431 $ F3 915.55431 $ Answer F1 is 1014.492 $

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