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-...
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
Homework Answers
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.
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