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 $1.7 million per year to beneficiaries. The yield to maturity on all bonds is 18.0%. a. If the duration of 5-year maturity bonds with coupon rates of 8.0% (paid annually) is 4 years and the duration of 20-year maturity bonds with coupon rates of 3% (paid annually) is 11 years, how much of each of these coupon bonds (in market value) will you want to hold to both fully fund and immunize your obligation? (Do not round intermediate calculations. Enter your answers in millions rounded to 1 decimal place. Omit the "$" sign in your response.) 5 year bond 20 year bond S 6.0 million 3.4 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 ntilli:

Explanation / Answer

PV of obligation = 1.7/0.18 = $9.44 million

Duration of perpetual pension fund = (1+y)/y = 1.18/0.18 = 6.56

To immunize portfolio

6.56 = 4*(1 - w) + 11*w = 4 - 4w + 11w

2.56 = 7w, w = 2.56/7

Current value of 20-year bond = 9.44*(2.56/7) = 3.45 million

You already did till above point.

Now, find par value of 20-year bond; given YTM for all bond is 18%

PV = 3.45, N = 20, y = 18%, PMT = 0.03FV

PV = 3.45 = (0.03FV/0.18)*(1 - 1/1.18^20) + FV/1.18^20

3.45 = 0.197088 FV

FV = 17.504869

Par value = $17.50 million

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