Pension funds pay lifetime annuities to recipients. If a firm will remain in bus

Question

Pension funds pay lifetime annuities to recipients. If a firm will remain in business indefinitely, the pension obligation will resemble a perpetuity. Suppose, therefore, that you are managing a pension fund with obligations to make perpetual payments of $3.5 million per year to beneficiaries. The yield to maturity on all bonds is 17.5%. a. If the duration of 5-year maturity bonds with coupon rates of 14.8% (paid annually) is 4 years and the duration of 20-year maturity bonds with coupon rates of 8% (paid annually) is 11 years, how much of each of these coupon bonds (in market value) will you want to hold to both fully fund and immunize your obligation? (Do not round intermediate calculations. Enter your answers in millions rounded to 1 decimal place. Omit the "$" sign in your response.) 5 year bond 20 year bond $ 12.3million $7.8 million b. What will be the par value of your holdings in the 20-year coupon bond? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places. Omit the "$" sign in your response.) Par value million

Explanation / Answer

The price of the 20 year bond can be found using pv formuale in excel
=pv(rate,nper,pmt,fv,type)
=pv(17.5%,20,(1000*8%),1000,0)
=478.72
Bond sells at 0.47822 of the par vlaue
Market value= Par value*0.47872
7.8mn=par vlaue*0.47872
Par value=7.8/0.47872=162.94

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