Question

Company ABC has liabilities of 20,000, 50,000, and 70,000 due at the end of years 1, 2, and 3 respectively. The company would like to exactly match these liabilities using the following assets:

A one-year zero coupon bond with a yield of 4%

A two-year zero coupon bond with a yield of 5%

A three-year coupon bond with annual coupons of 6% and a yield of 5.5%

What is the total cost of the asset portfolio that will match the liabilities?

Please answer as soon as possible!!!

Thank you

Answer 1

For Zero coupon bond,  Yield to Maturity = (Face Value / Current Price of Bond) ^ (1 / Years to Maturity) - 1

1) For one year zero coupon bond, assuming face value of $100 and we have Yield of 4% and Years to maturity =1

4% = (100 / current price of bond) ^(1/1) -1

100 / Current price of bond = 1.04

Current price of 1 year zero coupon bond = 100 / 1.04 = $96.15

Numbers of 1 year zero coupon bond requirement = 20,000 / 100 =200

2) For two year zero coupon bond, assuming face value of $100 and we have Yield of 5% and Years to maturity =2

5% = (100 / current price of bond) ^(1/2) -1

(100 / Current price of bond)^(1/2) = 1.05

Current price of bond = 100 / 1.04^2

Current price of 2 year zero coupon bond = $92.46

Numbers of 2 year zero coupon bond requirement = 50,000 / 100 =500

3) Price of 3 year 6% coupon bond , 5.5% yield and assuming $100 face value

Price = C1 / (1+YTM)^1 + C2 / (1+YTM)^2 + (C3+Principal) / (1+YTM)^3

= 6 / 1.05 + 6 / 1.05^2 + 106 / 1.05^3

Price =$102.72

Numbers of 3 year 6% coupon bond requirement = 70,000 / 100 =700

Total cost of Asset portfolio = Number of 1 year zero coupon bonds * price per 1 year zero coupon bonds+ Number of 2 year zero coupon bonds * price per 2 year zero coupon bonds+ Number of 3 year 6% coupon bonds *price per 3 year 6% coupon bonds

= 200 * 96.15 + 500 * 92.46 + 700 * 102.72

Total cost of Asset portfolio = $137,364

This will match with the liabilities of 20,000, 50,000, and 70,000 due at the end of years 1, 2, and 3 respectively.