A company must make yearly payments starting at $100,000 and increasing by 6% ev

Question

A company must make yearly payments starting at $100,000 and increasing by 6% every year for 10 years. Payments are due at the end of each year. They can invest in a portfolio of coupon-paying bonds that vary in term from 1 to 10 years (a total of 10 unique bonds). Each bond has a coupon rate equal to the term of the bond (i.e. the 10-year bond has a coupon rate of 10%, the 8-year bond has a coupon rate of 8%). They decide to do an absolute matching strategy to back the liability. At a yield rate of 5% how much would the company need to have available to purchase bonds for this absolute matching strategy?

Explanation / Answer

Calculation of total amount required for investment Year 1 2 3 4 5 6 7 8 9 10 Annual Payment 100000 106000 112360 119101.6 126247.7 133822.6 141851.9 150363 159384.8 168947.9 Term of the bond 1 2 3 4 5 6 7 8 9 10 Coupon rate 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% Coupon amount 10 20 30 40 50 60 70 80 90 100 Face Value 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 Discount Rate 5% Present Value factor of coupon 0.952381 1.85941 2.723248 3.545951 4.329477 5.075692 5.786373 6.463213 7.107822 7.721735 Present Value factor of FV 0.952381 0.907029 0.863838 0.822702 0.783526 0.746215 0.710681 0.676839 0.644609 0.613913 Present Value of Coupon 9.52381 37.18821 81.69744 141.838 216.4738 304.5415 405.0461 517.057 639.704 772.1735 Present Value of Face Value 952.381 907.0295 863.8376 822.7025 783.5262 746.2154 710.6813 676.8394 644.6089 613.9133 Current price of the bond 961.9048 944.2177 945.535 964.5405 1000 1050.757 1115.727 1193.896 1284.313 1386.087 Total no of bonds to be purchased 100 106 112 119 126 134 142 150 159 169 Amount to be invested 96190.48 100087.1 106240.3 114878.3 126247.7 140615 158268.1 179517.9 204700 234176.4 Total Amount to be invested 1460921 Annual Payment = $ 100000 increasing 6% for 10 years Discount rate 5% Present Value factor of coupon = ((1-(1/(1+r)^n)/r) Present value factor of FV   = 1/(1+r)^n Present value of coupon   = Coupon payment * present value factor of coupon Present Value of FV    = Face Value * Present Value factor of FV Total number of bonds to be purchased = Annual Payment /Face Value of Bond Total number of bonds to be purchased is rounded off to the nearest full number Amount to be invested    = Total number of bonds * current price of the bond

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.